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XU, CHANG-YUE, LI-WEI CHEN, and XI-YUN LU. "NUMERICAL SIMULATION OF SHOCK WAVE AND TURBULENCE INTERACTION OVER A CIRCULAR CYLINDER." Modern Physics Letters B 23, no. 03 (2009): 233–36. http://dx.doi.org/10.1142/s0217984909018084.
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The interaction of shock wave and turbulence for transonic flow over a circular cylinder is investigated using detached-eddy simulation (DES). Several typical cases are calculated for free-stream Mach number M∞ from 0.85 to 0.95, and the physical mechanisms relevant to the shock wave and turbulence interaction are discussed. Results show that there exist two flow states. One is unsteady flow state with moving shock waves interacting with turbulent flow for M∞ < 0.9 approximately, and the other is quasi-steady flow with stationary shocks standing over the wake of the cylinder for M∞ > 0.9, suppressing the vortex shedding from the cylinder. Moreover, local supersonic zones are identified in the wake of the cylinder and generated by two processes, i.e., reverse flow and shock wave distortion induced the supersonic zone. Turbulent shear layer instabilities are revealed and associated with moving shock wave and traveling pressure wave.
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Xu, Y. F., S. C. Hu, Y. Cai, and S. N. Luo. "Origins of plastic shock waves in single-crystal Cu." Journal of Applied Physics 131, no. 11 (2022): 115901. http://dx.doi.org/10.1063/5.0080757.
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We investigate shock wave propagation in single-crystal Cu with large-scale molecular dynamics simulations. Plastic shock waves propagate via dislocation nucleation or growth. With decreasing particle velocity, a remarkable drop in plastic shock wave velocity relative to the linear shock velocity–particle velocity relation is observed in the elastic–plastic two-wave regime for different loading directions. This reduction can be attributed to the changes in the mechanisms of plastic shock wave generation/propagation, from the dislocation nucleation-dominant mode, to the alternating nucleation and growth mode, and to the growth-dominant mode. For weak shocks, the plastic shock advances at the speed of the growth of existing dislocations (below the maximum elastic shock wave speed), considerably slower than the dislocation nucleation front for strong shocks (above the maximum elastic shock wave speed).
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Levihin, A.A., and I.A. Volobuev. "Microturbine Wave Compressor Optimal Regimes." Problemele Energeticii Regionale 2(43) (August 13, 2019): 1–9. https://doi.org/10.5281/zenodo.3367056.
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The work is devoted to the problem of improving the efficiency of air compression in the compressor of the microturbine installation. The wave compressor in which compression occurs as in a supersonic air intake is investigated. The purpose of the study isto find the region of existence of optimal shock-wave structures at which the stagnation pressure loss in a wave compressor will be minimal. Two cases were studied: compression in a system of two shock waves of the same direction; compression in a centered isentropic wave. The research method combines a numerical experiment with an analytical study of shock-wave structures. Calculations showed that the wave compressor is more efficient than traditional blade machines, if the Mach number at the intake to it is more than 2.2. The regions of existence of shock-wave structures with a reflected discontinuity: a rarefaction wave, a shock wave, and a weak discontinuity are analyzed analytically. The weak reflected discontinuity corresponds to the highest compression efficiency. The study obtained the following most important results. A shock-wave compressor with two shock waves of the same direction can operate at the optimum mode in the range of intake Mach numbers from 2.089 to 2.46. A compression ratio of 5.76 can be obtained in this case. A centered compression wave can provide a compression ratio in one stage up to 10-12 with Mach number from 3.2 to 3.48. At higher degrees of compression, irregular shock-wave structures are formed
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Grady, Dennis. "Wave Structuring in the Shock Compression of Geologic Matter at the Planetary and Laboratory Scales." Annual Review of Earth and Planetary Sciences 53, no. 1 (2025): 81–99. https://doi.org/10.1146/annurev-earth-040523-124246.
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The response of geologic matter when subjected to large-scale impact or explosion is dependent on the time history of the encompassing shock wave. The kinetics of localized physical and chemical transitions brought about by the shock wave are responsive to this time history. Solid-state viscosity of the media is responsible for establishing the time history of a shock wave. In 2003, researcher H. Jay Melosh recognized the need for an understanding of solid viscosity spanning the petrologic and lithologic scales, and accordingly, he undertook the assessment and analysis of available nuclear ground shock measurements. This review furthers Melosh's epic efforts. In pursuing both the nuclear ground shock data and supporting laboratory test data, it undertakes methods for determining and calculations of the viscosity of solid materials on the respective scales. Further, applicability of viscoelasticity in modeling the shock response on the scales of concern is demonstrated and applied. The review closes with a discussion of universal features of the shock wave viscous time history in solid materials. Solid viscosity as an adiabatic invariant is presented, and commonalties of the solid shock wave with the nonlinear dynamics of ocean waves are noted. ▪ This article reviews Melosh's analysis of nuclear ground shock measurements with application to shock wave structuring viscosity. ▪ It discusses viscoelastic calculations with application to wave structure of nuclear ground shocks and laboratory shock waves in brittle granular solids, and universal features of the viscous shock wave structure and invariance of the dissipative action are considered. ▪ It also discusses wave action invariance in both the nonlinear dynamics of ocean waves and the steady wave structure of shock waves in solid matter.
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Matsuda, Atsushi, Naoki Aoyama, and Yoshiaki Kondo. "OS21-3 Shock Wave Modulation due to Discharged Plasma using the Shock Tube(Multiphase Shock Wave,OS21 Shock wave and high-speed gasdynamics,FLUID AND THERMODYNAMICS)." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2015.14 (2015): 261. http://dx.doi.org/10.1299/jsmeatem.2015.14.261.
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Леонович, Анатолий, Anatoliy Leonovich, Цюган Цзун, et al. "Alfvén waves in the magnetosphere generated by shock wave / plasmapause interaction." Solar-Terrestrial Physics 5, no. 2 (2019): 9–14. http://dx.doi.org/10.12737/stp-52201902.
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We study Alfvén waves generated in the magnetosphere during the passage of an interplanetary shock wave. After shock wave passage, the oscillations with typical Alfvén wave dispersion have been detected in spacecraft observations inside the magnetosphere. The most frequently observed oscillations are those with toroidal polarization; their spatial structure is described well by the field line resonance (FLR) theory. The oscillations with poloidal polarization are observed after shock wave passage as well. They cannot be generated by FLR and cannot result from instability of high-energy particle fluxes because no such fluxes were detected at that time. We discuss an alternative hypothesis suggesting that resonant Alfvén waves are excited by a secondary source: a highly localized pulse of fast magnetosonic waves, which is generated in the shock wave/plasmapause contact region. The spectrum of such a source contains oscillation harmonics capable of exciting both the toroidal and poloidal resonant Alfvén waves.
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Singh, Manpreet, Federico Fraschetti, and Joe Giacalone. "Electrostatic Plasma Wave Excitations at the Interplanetary Shocks." Astrophysical Journal 943, no. 1 (2023): 16. http://dx.doi.org/10.3847/1538-4357/aca7c6.
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Abstract Over the last few decades, different types of plasma waves (e.g., the ion acoustic waves (IAWs), electrostatic solitary waves, upper/lower hybrid waves, and Langmuir waves) have been observed in the upstream, downstream, and ramp regions of the collisionless interplanetary (IP) shocks. These waves may appear as short-duration (only a few milliseconds at 1 au) electric field signatures in the in-situ measurements, with typical frequencies of ∼1–10 kHz. A number of IAW features at the IP shocks seem to be unexplained by kinetic models and require a new modeling effort. Thus, this paper is dedicated to bridging this gap in understanding. In this paper, we model the linear IAWs inside the shock ramp by devising a novel linearization method for the two-fluid magnetohydrodynamic equations with spatially dependent shock parameters. It is found that, for parallel propagating waves, the linear dispersion relation leads to a finite growth rate, which is dependent on the shock density compression ratio, as Wind data suggest. Further analysis reveals that the wave frequency grows towards the downstream region within the shock ramp, and the wave growth rate is independent of the electron-to-ion temperature ratio, as Magnetospheric Multiscale (MMS) in-situ measurements suggest, and is uniform within the shock ramp. Thus, this study helps in understanding the characteristics of the IAWs at the collisionless IP shocks.
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INOUE, YOSHINORI, and TAKERU YANO. "Propagation of strongly nonlinear plane N-waves." Journal of Fluid Mechanics 341 (June 25, 1997): 59–76. http://dx.doi.org/10.1017/s0022112097005405.
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Formation and evolution of N (-like) waves is studied without the restriction of low amplitude, namely weak nonlinearity. To this end, the classical piston problem of gasdynamics is investigated, in which the wave is radiated by a piston executing a single cycle of harmonic oscillation into an inviscid perfect gas. The method of analysis is based on the simple-wave theory up to the shock formation time, and beyond that time on the numerical calculation by a high-resolution TVD upwind scheme. The initial sinusoid-like wave profile is rapidly distorted as the wave propagates, and this leads to the formation of head and tail shocks. The main effects of strong nonlinearity may be listed as follows: (i) entropy production at shock fronts, (ii) the existence of waves reflected from shocks, (iii) an asymmetric wave profile stemming from the boundary condition at the source of the strongly nonlinear problem. As the result, the strongly nonlinear wave possesses the following remarkable distinctive features, in contrast to its counterpart in the weakly nonlinear regime. The tail shock is not formed at the tail of the wave, and the expansion wave behind the head shock has non-uniform intensity. The N (-like) wave propagates with some excess mass. Thereby a region with low density, associated with the entropy production, appears in the vicinity of the source.
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Wang, Xiao, and W. E. Cooke. "Wave-function shock waves." Physical Review A 46, no. 7 (1992): 4347–53. http://dx.doi.org/10.1103/physreva.46.4347.
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Huete, C., J. G. Wouchuk, B. Canaud, and A. L. Velikovich. "Analytical linear theory for the shock and re-shock of isotropic density inhomogeneities." Journal of Fluid Mechanics 700 (April 30, 2012): 214–45. http://dx.doi.org/10.1017/jfm.2012.126.
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AbstractWe present an analytical model that describes the linear interaction of two successive shocks launched into a non-uniform density field. The re-shock problem is important in different fields, inertial confinement fusion among them, where several shocks are needed to compress the non-uniform target. At first, we present a linear theory model that studies the interaction of two successive shocks with a single-mode density perturbation field ahead of the first shock. The second shock is launched after the sonic waves emitted by the first shock wave have vanished. Therefore, in the case considered in this work, the second shock only interacts with the entropic and vortical perturbations left by the first shock front. The velocity, vorticity and density fields are later obtained in the space behind the second shock. With the results of the single-mode theory, the interaction with a full spectrum of random-isotropic density perturbations is considered by decomposing it into Fourier modes. The model describes in detail how the second shock wave modifies the turbulent field generated by the first shock wave. Averages of the downstream quantities (kinetic energy, vorticity, acoustic flux and density) are easily obtained either for two-dimensional or three-dimensional upstream isotropic spectra. The asymptotic limits of very strong shocks are discussed. The study shown here is an extension of previous works, where the interaction of a planar shock wave with random isotropic vorticity/entropy/acoustic spectra were studied independently. It is also a preliminary step towards the understanding of the re-shock of a fully turbulent flow, where all three of the modes, vortical, entropic and acoustic, might be present.
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Harutyunyan, G. A., A. A. Muradyan, A. R. Aramyan, et al. "Analysis of shock wave propagation in the atmosphere through generated sound waves." Journal of Instrumentation 19, no. 06 (2024): C06012. http://dx.doi.org/10.1088/1748-0221/19/06/c06012.
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Abstract The paper presents the results of studies of shock waves propagating in the atmosphere. These results were obtained by recording sound waves generated by a shock wave. It has been shown that it takes approximately two seconds for a shock wave to form. The frequency of the sound wave generated by the shock wave depends on the speed of propagation of the shock wave. It was found that the shock wave accelerates as it propagates upward. This phenomenon can be used as a method for determining the velocities of shock waves or supersonic moving bodies.
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Harris, S. E. "Sonic shocks governed by the modified Burgers' equation." European Journal of Applied Mathematics 7, no. 2 (1996): 201–22. http://dx.doi.org/10.1017/s0956792500002291.
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In this paper, we investigate the evolution of N-waves in a medium governed by the modified Burgers' equation. It is shown that the general behaviour when the nonlinearity is of arbitrary odd integer order is the same as for the cubic case. For an N-wave of zero mean displacement, a shock is formed immediately to prevent a multi-valued solution and a second shock is formed at later times. At a finite time, the second shock satisfies a sonic condition and this state persists. The Taylor-type shock structure ceases to be the appropriate description, and instead we have a shock which matches only algebraically to the outer wave on one side. At a larger time still, the other shock is affected but the two shocks remain distinct until the wave dies under linear mechanisms. The behaviour of N-waves of non-zero mean is also examined and it is shown that in some cases, a purely one-signed profile remains.
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Hang, Peng, and Yao Wenjin. "Propagation characteristics of explosion shock waves in air under different temperature and pressure conditions." Journal of Physics: Conference Series 2891, no. 5 (2024): 052011. https://doi.org/10.1088/1742-6596/2891/5/052011.
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Abstract In order to study the propagation characteristics of explosion shock waves in air under different temperature and pressure conditions, stress wave theory and detonation wave theory were first used to analyze the propagation characteristics of shock waves. Combined with numerical simulation results, the propagation characteristics of explosion shock waves were comprehensively analyzed and verified. The following conclusion was drawn: the higher the pressure, the larger the peak value of shock waves at the same spatial position, and the greater the specific impulse of shock waves, Shortening of shock wave propagation distance; The higher the temperature, the less the peak pressure changes at the same spatial position, the smaller the specific impulse of the shock wave, and the longer the propagation distance of the shock wave.
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BROWN, B. P., and B. M. ARGROW. "Two-dimensional shock tube flow for dense gases." Journal of Fluid Mechanics 349 (October 25, 1997): 95–115. http://dx.doi.org/10.1017/s0022112097006575.
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Non-stationary oblique shock wave reflections for fluids in the dense gas regime are examined for selected cases. A time-accurate predictor-corrector TVD scheme with reflective boundary conditions for solving the Euler equations simulates the evolution of a wave field for an inviscid van der Waals gas near the thermodynamic critical point. The simulated cases involve shock tube flows with compressive wedges and circular arcs. Non-classical phenomena, such as disintegrating shocks, expansion shocks, composite waves, etc., demonstrate significant differences from perfect gas flow fields over similar geometries. Detailed displays of wave field structures and thermodynamic states for the dense gas flow fields are presented and analysed.
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Kai, Y., W. Garen, T. Schlegel, and U. Teubner. "A novel shock tube with a laser–plasma driver." Laser and Particle Beams 35, no. 4 (2017): 610–18. http://dx.doi.org/10.1017/s0263034617000635.
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AbstractA novel method to generate shock waves in small tubes is demonstrated. A femtosecond laser is applied to generate an optical breakdown an aluminum film as target. Due to the sudden appearance of this non-equilibrium state of the target, a shock wave is induced. The shock wave is further driven by the expanding high-pressure plasma (up to 10 Mbar), which serves as a quasi-piston, until the plasma recombines. The shock wave then propagates further into a glass capillary (different square capillaries with hydraulic diameter D down to 50 µm are applied). Shock wave propagation is investigated by laser interferometry. Although the plasma is an unsteady driver, due to the geometrical confinement of the capillaries, rather strong micro shocks can still propagate as far as 35 times D. In addition to the experiments, the initial conditions of this novel method are investigated by hydrocode simulations using MULTI-fs.
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Goyal, Eva, Guljot Singh, Vivek Sharma, Jaspreet Gill, and Gagandeep Gupta. "Extra Corporeal Shock Wave – A New Wave of Therapy." Dental Journal of Advance Studies 03, no. 03 (2015): 129–34. http://dx.doi.org/10.1055/s-0038-1672027.
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AbstractExtracorporeal shock wave therapy (ESWT) has been enormously used in medical practice, especially for the management of various orthopedic and musculoskeletal disorders. Extracorporeal shock wave therapy has favorable effects on stimulating callus formation, inducing angiogenesis and bone regeneration and relieving pain. Studies also indicated that extra corporeal shock waves have a significant bactericidal effect on bone- and implant-associated infections. The present article reviews the various applications of extra corporeal shock wave therapy in the field of dentistry and the possibility of inculcating the useful properties of shock waves in improving the treatment outcome.
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Kononov, D. A., D. V. Bisikalo, V. B. Puzin, and A. G. Zhilkin. "Transient Processes in a Binary System with a White Dwarf." Acta Polytechnica CTU Proceedings 2, no. 1 (2015): 46–49. http://dx.doi.org/10.14311/app.2015.02.0046.
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Using the results of 3D gas dynamic numerical simulations we propose a mechanism that can explain the quiescent multihumped shape of light curves of WZ Sge short-period cataclysmic variable stars. Analysis of the obtained solutions shows that in the modeled system an accretion disk forms. In the outer regions of the disk four shock waves occur: two arms of the spiral tidal shock; “hot line”, a shock wave caused by the interaction of the circum-disk halo and the stream from the inner Lagrangian point; and the bow-shock forming due to the supersonic motion of the accretor and disk in the gas of the circum-binary envelope. In addition, in our solutions we observe a spiral precessional density wave in the disk. This wave propagates from inside the disk down to its outer regions and almost rests in the laboratory frame in one orbital period. As a results every next orbital period each shock wave passes through the outer part of the density wave. Supplying these shocks with extra-density the precessional density wave amplifies them, which leads to enhanced energy release at each shock and may be observed as a brightening (or hump) in the light curve. Since the velocity of the retrograde precession is a little lower that the orbital velocity of the system, the same shock wave at every next orbital cycle interacts with the density wave later than at the previous cycle. This causes the observed shift of the humps over binary phases. The number of the shock waves, interacting with the density wave determines the largest number of humps that may be observed in one orbital period of a WZ Sge type star.
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Liu, Shuitao, and Gengyan Xing. "The History of Shock Wave Medicine Development in China." Journal of Regenerative Science 3, no. 2 (2023): 3–4. http://dx.doi.org/10.13107/jrs.2023.v03.i02.87.
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The development of shock wave medicine in China can be traced back to the 1980s. At that time, shock waves were applied to treat urinary tract stones with good results. In 1993, Professor Xing Gengyan pioneered the application of extracorporeal shock wave therapy for humeral epicondylitis, marking a significant milestone in the advancement of shock wave medicine in China. With the deepening of research on shock waves and technological advancements, the indications for shock wave medicine have been continuously expanded, achieving good results in treating bone tissue diseases such as delayed fracture healing and non-union. To further promote the experience of shock wave therapy, Professor Xing Gengyan successively held 8 national continuing education programs on “Extracorporeal Shock Wave Therapy for Bone and Muscle Disorders,” training thousands of doctors who mastered shock wave therapy techniques. With the conduct of numerous clinical studies and accumulation of data, the China National Medical Products Administration approved the domestic production of extracorporeal shock wave therapy machines for treating orthopedic diseases in August 2000, marking the official entry of shock wave medicine into a high-speed development phase in China. As clinical applications continue to advance and expand, Chinese scholars have begun to explore the mechanisms of action of shock waves. In 2004, Professor Xing Ganyan’s research on “Osteoblast Mechanochemical Signal Transduction and Related Gene Expression Following ESWT” was funded by the National Natural Science Foundation of China, resulting in a wealth of published findings. In 2007, Professor Xing Ganyan edited and published the first monograph on shock wave medicine, <Extracorporeal Shock Wave Therapy for Bone and Muscle Diseases (First Edition)>, which consists of two parts and eight chapters. This comprehensive summary of over a decade of clinical application experience and foundational research laid the foundation for shock wave medicine in China. With the rapid advancement of China’s medical level, Chinese scholars’ research on shock waves has gradually gained global recognition. A significant number of papers on shock waves published by Chinese scholars has been indexed, and their research achievements have been communicated at international conferences. Concurrently, as the depth of research on shock wave therapy increases and instruments advance, shock waves are no longer confined to treating urinary tract stones, non-unions, osteonecrosis, and tendinopathy [1-4]. They have also achieved promising results in treating myocardial infarction, skin ulcers, tumors, nerve injuries, and male dysfunction, among others. In December 2013, the Chinese Shock Wave Medicine Professional Committee was established in Beijing, with Professor Xing Gengyan serving as the inaugural Chairman. Since then, shock wave medicine has had an independent academic organization. Building on past experiences, in 2014, the <Expert Consensus on Extracorporeal Shock Wave Therapy for Bone and Muscle Diseases> was released [5], significantly advancing the scientific and standardized development of shock wave medicine. In 2015, the <Extracorporeal Shock Wave Therapy for Bone and Muscle Diseases (Second Edition)> was published, expanding the volume to 5 articles and 19 chapters, with a significant addition of numerous recent research findings. In July 2016, at the annual meeting of the international society for medical shock wave treatment (ISMST) held in Malaysia, Professor Xing Gengyan was elected as the President of the ISMST. China secured the hosting rights for the 22nd annual conference in 2019, signifying that China is at the forefront of shock wave medicine development worldwide. The year 2019 marked the most memorable year in the history of shock wave development in Chinese medicine. Building upon the previous two editions of the <Expert Consensus on Extracorporeal Shock Wave Therapy for Bone and Muscle Diseases>, Chinese scholars integrated evidence-based medical experiences and released the <Chinese Guidelines for Extracorporeal Shock Wave Therapy for Bone and Muscle Diseases (2019 Edition) [6], thereby standardizing and scientifically advancing the application of shock waves in China. In May of the same year, the ISMST 22nd International Congress on Medical Shock Waves convened in Beijing, attended by over 1,200 experts and scholars from nearly 30 countries. This was the largest-attended conference in the history of shock wave medicine, covering the broadest range of academic interests and delving into the most in-depth discussions on various research topics, significantly advancing the development of shock wave medicine in China. Currently, over 3,000 hospitals in China possess extracorporeal shock wave therapy systems, covering treatment fields such as orthopedics, urology, plastic surgery, cardiology, stomatology, oncology, and rehabilitation, treating millions of patients annually [7-9]. Concurrently, Chinese scholars in the field of shock wave therapy are continually innovating, integrating extracorporeal shock waves with techniques such as arthroscopy, stem cells, and nanomaterials to achieve synergistic therapeutic effects, resulting in favorable outcomes [10-12]. Each year, over 500 related research papers are published. Further, elucidating the biological mechanisms of shock waves in clinical efficacy at the organizational, cellular, and molecular levels will continuously expand the application scope of shock waves. In response to the relative lack of high-level evidence for shock wave research, the China Shock Wave Medical Association is organizing multi-center, large-sample clinical studies; standardized training for practitioners and accreditation of treatment institutions have also been put on the agenda. It is believed that in the near future, China’s shock wave medicine will witness a richer array of research achievements, bringing blessings to more patients.
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Kawamura, Yosuke, and Masafumi Nakagawa. "OS21-2 Experimental Study on the Oblique Shock Waves and Expansion Waves in the Supersonic Carbon Dioxide Two-phase Flow(Multiphase Shock Wave,OS21 Shock wave and high-speed gasdynamics,FLUID AND THERMODYNAMICS)." Abstracts of ATEM : International Conference on Advanced Technology in Experimental Mechanics : Asian Conference on Experimental Mechanics 2015.14 (2015): 260. http://dx.doi.org/10.1299/jsmeatem.2015.14.260.
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Vuorinen, Laura, Rami Vainio, Heli Hietala, and Terry Z. Liu. "Monte Carlo Simulations of Electron Acceleration at Bow Waves Driven by Fast Jets in the Earth’s Magnetosheath." Astrophysical Journal 934, no. 2 (2022): 165. http://dx.doi.org/10.3847/1538-4357/ac7f42.
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Abstract The shocked solar wind flows around the Earth’s magnetosphere in the magnetosheath downstream of the Earth’s bow shock. Within this region, faster flows of plasma, called magnetosheath jets, are frequently observed. These jets have been shown to sometimes exhibit supermagnetosonic speeds relative to the magnetosheath flow and to develop bow waves or shocks of their own. Such jet-driven bow waves have been observed to accelerate ions and electrons. We model electron acceleration by magnetosheath jet-driven bow waves using test-particle Monte Carlo simulations. Our simulations suggest that the energy increase of electrons with energies of a few hundred eV to 10 keV can be explained by a collapsing magnetic trap forming between the bow wave and the magnetopause with shock drift acceleration at the moving bow wave. Our simulations allow us to estimate the efficiency of acceleration as a function of different jet and magnetosheath parameters. Electron acceleration by jet-driven bow waves can increase the total acceleration in the parent shock environment, most likely also at shocks other than the Earth’s bow shock.
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Kewalramani, Jitendra, Zhenting Zou, Richard Marsh, Bruce Bukiet, and Jay Meegoda. "Nonlinear Behavior of High-Intensity Ultrasound Propagation in an Ideal Fluid." Acoustics 2, no. 1 (2020): 147–63. http://dx.doi.org/10.3390/acoustics2010011.
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In this paper, nonlinearity associated with intense ultrasound is studied by using the one-dimensional motion of nonlinear shock wave in an ideal fluid. In nonlinear acoustics, the wave speed of different segments of a waveform is different, which causes distortion in the waveform and can result in the formation of a shock (discontinuity). Acoustic pressure of high-intensity waves causes particles in the ideal fluid to vibrate forward and backward, and this disturbance is of relatively large magnitude due to high-intensities, which leads to nonlinearity in the waveform. In this research, this vibration of fluid due to the intense ultrasonic wave is modeled as a fluid pushed by one complete cycle of piston. In a piston cycle, as it moves forward, it causes fluid particles to compress, which may lead to the formation of a shock (discontinuity). Then as the piston retracts, a forward-moving rarefaction, a smooth fan zone of continuously changing pressure, density, and velocity is generated. When the piston stops at the end of the cycle, another shock is sent forward into the medium. The variation in wave speed over the entire waveform is calculated by solving a Riemann problem. This study examined the interaction of shocks with a rarefaction. The flow field resulting from these interactions shows that the shock waves are attenuated to a Mach wave, and the pressure distribution within the flow field shows the initial wave is dissipated. The developed theory is applied to waves generated by 20 KHz, 500 KHz, and 2 MHz transducers with 50, 150, 500, and 1500 W power levels to explore the effect of frequency and power on the generation and decay of shock waves. This work enhances the understanding of the interactions of high-intensity ultrasonic waves with fluids.
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GUARDONE, ALBERTO. "Three-dimensional shock tube flows for dense gases." Journal of Fluid Mechanics 583 (July 4, 2007): 423–42. http://dx.doi.org/10.1017/s0022112007006313.
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The formation process of a non-classical rarefaction shock wave in dense gas shock tubes is investigated by means of numerical simulations. To this purpose, a novel numerical scheme for the solution of the Euler equations under non-ideal thermodynamics is presented, and applied for the first time to the simulation of non-classical fully three-dimensional flows. Numerical simulations are carried out to study the complex flow field resulting from the partial burst of the shock tube diaphragm, a situation that has been observed in preliminary trials of a dense gas shock tube experiment. Beyond the many similarities with the corresponding classical flow, the non-classical wave field is characterized by the occurrence of anomalous compression isentropic waves and rarefaction shocks propagating past the leading rarefaction shock front. Negative mass flow through the rarefaction shock wave results in a limited interaction with the contact surface close to the diaphragm, a peculiarity of the non-classical regime. The geometrical asymmetry does not prevent the formation of a single rarefaction shock front, though the pressure difference across the rarefaction wave is predicted to be weaker than the one which would be obtained by the complete burst of the diaphragm.
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Nakagawa, Atsuhiro, Yasuko Kusaka, Takayuki Hirano, et al. "Application of shock waves as a treatment modality in the vicinity of the brain and skull." Journal of Neurosurgery 99, no. 1 (2003): 156–62. http://dx.doi.org/10.3171/jns.2003.99.1.0156.
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Object. Shock waves have not previously been used as a treatment modality for lesions in the brain and skull because of the lack of a suitable shock wave source and concerns about safety. Therefore, the authors have performed experiments aimed at developing both a new, compact shock wave generator with a holmium:yttrium-aluminum-garnet (Ho:YAG) laser and a safe method for exposing the surface of the brain to these shock waves. Methods. Twenty male Sprague—Dawley rats were used in this study. In 10 rats, a single shock wave was delivered directly to the brain, whereas the protective effect of inserting a 0.7-mm-thick expanded polytetrafluoroethylene (ePTFE) dural substitute between the dura mater and skull before applying the shock wave was investigated in the other 10 rats. Visualizations on shadowgraphy along with pressure measurements were obtained to confirm that the shock wave generator was capable of conveying waves in a limited volume without harmful effects to the target. The attenuation rates of shock waves administered through a 0.7-mm-thick ePTFE dural substitute and a surgical cottonoid were measured to determine which of these materials was suitable for avoiding propagation of the shock wave beyond the target. Conclusions. Using the shock wave generator with the Ho:YAG laser, a localized shock wave (with a maximum overpressure of 50 bar) can be generated from a small device (external diameter 15 mm, weight 20 g). The placement of a 0.7-mm-thick ePTFE dural substitute over the dura mater reduces the overpressure of the shock wave by 96% and eliminates damage to surrounding tissue in the rat brain. These findings indicate possibilities for applying shock waves in various neurosurgical treatments such as cranioplasty, local drug delivery, embolysis, and pain management.
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Kravchenko, Denis S., Elena V. Kustova, and Maksim Yu Melnik. "Higher criteria for the regularity of a one-dimensional local field." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 9, no. 3 (2022): 426–39. http://dx.doi.org/10.21638/spbu01.2022.304.
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A coupled problem of gasdynamics, vibrational relaxation, and dissociation in the flow of oxygen behind reflected shock waves is studied. The detailed state-to-state kinetic approach is used, which is based on a coupled solution of the momentum and energy conservation equations with the balance equations for molecular vibrational state populations and concentrations of oxygen atoms. Initial conditions corresponding to recent experiments in shock tubes are considered. For different models of physicochemical processes, a comparison is made with experimental data; varying the model parameters yields satisfactory agreement of all gas-dynamic parameters with the measured ones. The key feature of the proposed approach is the allowance for partial vibrational-chemical relaxation in the time interval between the incident and reflected shock waves. When relaxation between the shocks is not frozen, the reflected shock wave propagates through a vibrationally nonequilibrium gas, which significantly affects kinetics and gas dynamics. Accounting for partial relaxation ensures good agreement between the pressure calculated behind the front of the reflected shock wave and the pressure measured in the experiment. On the other hand, comparison with the vibrational temperature calculated indirectly from spectroscopic experimental data under the assumption of frozen relaxation shows noticeable differences near the shock wave front. We conclude that the technique for extracting gas-dynamic parameters fromspectroscopic data has to be improved by taking into account vibrational excitation before the reflected shock wave.
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Bohdan, Artem, Aaron Tran, Lorenzo Sironi, and Lynn B. Wilson. "Electrostatic Waves and Electron Holes in Simulations of Low-Mach Quasi-perpendicular Shocks." Astrophysical Journal 974, no. 1 (2024): 37. http://dx.doi.org/10.3847/1538-4357/ad6b0c.
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Abstract Collisionless low-Mach-number shocks are abundant in astrophysical and space plasma environments, exhibiting complex wave activity and wave–particle interactions. In this paper, we present 2D Particle-in-Cell (PIC) simulations of quasi-perpendicular nonrelativistic (v sh ≈ (5500–22000) km s−1) low-Mach-number shocks, with a specific focus on studying electrostatic waves in the shock ramp and precursor regions. In these shocks, an ion-scale oblique whistler wave creates a configuration with two hot counterstreaming electron beams, which drive unstable electron acoustic waves (EAWs) that can turn into electrostatic solitary waves (ESWs) at the late stage of their evolution. By conducting simulations with periodic boundaries, we show that the EAW properties agree with linear dispersion analysis. The characteristics of ESWs in shock simulations, including their wavelength and amplitude, depend on the shock velocity. When extrapolated to shocks with realistic velocities (v sh ≈ 300 km s−1), the ESW wavelength is reduced to one-tenth of the electron skin depth and the ESW amplitude is anticipated to surpass that of the quasi-static electric field by more than a factor of 100. These theoretical predictions may explain a discrepancy, between PIC and satellite measurements, in the relative amplitude of high- and low-frequency electric field fluctuations.
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Yan, Dong, Jinchang Zhao, and Shaoqing Niu. "Normal Reflection Characteristics of One-Dimensional Unsteady Flow Shock Waves on Rigid Walls from Pulse Discharge in Water." Shock and Vibration 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/6958085.
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Strong shock waves can be generated by pulse discharge in water, and the characteristics due to the shock wave normal reflection from rigid walls have important significance to many fields, such as industrial production and defense construction. This paper investigates the effects of hydrostatic pressures and perturbation of wave source (i.e., charging voltage) on normal reflection of one-dimensional unsteady flow shock waves. Basic properties of the incidence and reflection waves were analyzed theoretically and experimentally to identify the reflection mechanisms and hence the influencing factors and characteristics. The results indicated that increased perturbation (i.e., charging voltage) leads to increased peak pressure and velocity of the reflected shock wave, whereas increased hydrostatic pressure obviously inhibited superposition of the reflection waves close to the rigid wall. The perturbation of wave source influence on the reflected wave was much lower than that on the incident wave, while the hydrostatic pressure obviously affected both incident and reflection waves. The reflection wave from the rigid wall in water exhibited the characteristics of a weak shock wave, and with increased hydrostatic pressure, these weak shock wave characteristics became more obvious.
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MARCHANT, T. R., and NOEL F. SMYTH. "APPROXIMATE TECHNIQUES FOR DISPERSIVE SHOCK WAVES IN NONLINEAR MEDIA." Journal of Nonlinear Optical Physics & Materials 21, no. 03 (2012): 1250035. http://dx.doi.org/10.1142/s021886351250035x.
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Many optical and other nonlinear media are governed by dispersive, or diffractive, wave equations, for which initial jump discontinuities are resolved into a dispersive shock wave. The dispersive shock wave smooths the initial discontinuity and is a modulated wavetrain consisting of solitary waves at its leading edge and linear waves at its trailing edge. For integrable equations the dispersive shock wave solution can be found using Whitham modulation theory. For nonlinear wave equations which are hyperbolic outside the dispersive shock region, the amplitudes of the solitary waves at the leading edge and the linear waves at the trailing edge of the dispersive shock can be determined. In this paper an approximate method is presented for calculating the amplitude of the lead solitary waves of a dispersive shock for general nonlinear wave equations, even if these equations are not hyperbolic in the dispersionless limit. The approximate method is validated using known dispersive shock solutions and then applied to calculate approximate dispersive shock solutions for equations governing nonlinear optical media, such as nematic liquid crystals, thermal glasses and colloids. These approximate solutions are compared with numerical results and excellent comparisons are obtained.
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Johnson, Jerome B. "Simple model of shock-wave attenuation in snow." Journal of Glaciology 37, no. 127 (1991): 303–12. http://dx.doi.org/10.1017/s0022143000005724.
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AbstractA simple momentum model, assuming that snow compacts along a prescribed pressure–density curve, is used to calculate the pressure attenuation of shock waves in snow. Four shock-loading situations are examined: instantaneously applied pressure impulses for one-dimensional, cylindrical and spherical shock-wave geometries, and a one-dimensional pressure impulse of finite duration. Calculations show that for an instantaneously applied impulse the pressure attenuation for one-dimensional, cylindrical and spherical shock waves is determined by the pressure density (P–ρ) compaction curve of snow. The maximum attenuation for a one-dimensional shock wave is proportional to (Xf–X0)−1.5for the multi-stage (P–ρ) curve and (Xf–X0)−2when compaction occurs in a single step (single-stage compaction), where (Xf–X0) is the shock-wave propagation distance. Cylindrical waves have a maximum attenutation that varies from (R–R0)−2for single-stage compaction and (R–R0)−1.5for multi-stage compaction, when (R–R0) ≪R0, whereRis the propagation radius andR0is the interior radius over which a pressure impulse is applied, toR−4when (R–R0) ≫R0Spherical waves have a maximum attenuation that varies from (R–R0)−2for single-stage compaction and (R–R0)−1.5for multi-stage compaction toR−6when 〈R–R0〉 ≫R0.The shock-wave pressure in snow for a finite-duration pressure impulse is determined by the pressure impulse versus time profile during the time interval of the impulse. After the pressure impulse ends, shock-wave pressure attenuation is the same as for an instantaneously applied pressure impulse containing the same total momentum. Pressure attenuation near a shock-wave source, where the duration of the shock wave is relatively short, is greater than for a shock wave farther from a source where the shock wave has a relatively long duration. Shock-wave attenuation in snow can be delayed or reduced by increasing the duration of a finite-duration pressure impulse. A sufficiently long-duration impulse may result in no shock-wave pressure attenuation in a shallow snow cover.
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Johnson, Jerome B. "Simple model of shock-wave attenuation in snow." Journal of Glaciology 37, no. 127 (1991): 303–12. http://dx.doi.org/10.3189/s0022143000005724.
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AbstractA simple momentum model, assuming that snow compacts along a prescribed pressure–density curve, is used to calculate the pressure attenuation of shock waves in snow. Four shock-loading situations are examined: instantaneously applied pressure impulses for one-dimensional, cylindrical and spherical shock-wave geometries, and a one-dimensional pressure impulse of finite duration. Calculations show that for an instantaneously applied impulse the pressure attenuation for one-dimensional, cylindrical and spherical shock waves is determined by the pressure density (P–ρ) compaction curve of snow. The maximum attenuation for a one-dimensional shock wave is proportional to (Xf–X0)−1.5 for the multi-stage (P–ρ) curve and (Xf–X0)−2 when compaction occurs in a single step (single-stage compaction), where (Xf–X0) is the shock-wave propagation distance. Cylindrical waves have a maximum attenutation that varies from (R–R0)−2 for single-stage compaction and (R–R0)−1.5 for multi-stage compaction, when (R – R0) ≪ R0, where R is the propagation radius and R0 is the interior radius over which a pressure impulse is applied, to R−4 when (R – R0) ≫ R0 Spherical waves have a maximum attenuation that varies from (R – R0)−2 for single-stage compaction and (R – R0)−1.5 for multi-stage compaction to R−6 when 〈R – R0〉 ≫ R0.The shock-wave pressure in snow for a finite-duration pressure impulse is determined by the pressure impulse versus time profile during the time interval of the impulse. After the pressure impulse ends, shock-wave pressure attenuation is the same as for an instantaneously applied pressure impulse containing the same total momentum. Pressure attenuation near a shock-wave source, where the duration of the shock wave is relatively short, is greater than for a shock wave farther from a source where the shock wave has a relatively long duration. Shock-wave attenuation in snow can be delayed or reduced by increasing the duration of a finite-duration pressure impulse. A sufficiently long-duration impulse may result in no shock-wave pressure attenuation in a shallow snow cover.
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Lubchich, A. A., and I. V. Despirak. "Magnetohydrodynamic waves within the medium separated by the plane shock wave or rotational discontinuity." Annales Geophysicae 23, no. 5 (2005): 1889–908. http://dx.doi.org/10.5194/angeo-23-1889-2005.
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Abstract. Characteristics of small amplitude plane waves within the medium separated by the plane discontinuity into two half spaces are analysed. The approximation of the ideal one-fluid magnetohydrodynamics (MHD) is used. The discontinuities with the nonzero mass flux across them are mainly examined. These are fast or slow shock waves and rotational discontinuities. The dispersion equation for MHD waves within each of half space is obtained in the reference frame connected with the discontinuity surface. The solution of this equation permits one to determine the wave vectors versus the parameter cp, which is the phase velocity of surface discontinuity oscillations. This value of cp is common for all MHD waves and determined by an incident wave or by spontaneous oscillations of the discontinuity surface. The main purpose of the study is a detailed analysis of the dispersion equation solution. This analysis let us draw the following conclusions. (I) For a given cp, ahead or behind a discontinuity at most, one diverging wave can transform to a surface wave damping when moving away from the discontinuity. The surface wave can be a fast one or, in rare cases, a slow, magnetoacoustic one. The entropy and Alfvén waves always remain in a usual homogeneous mode. (II) For certain values of cp and parameters of the discontinuity behind the front of the fast shock wave, there can be four slow magnetoacoustic waves, satisfying the dispersion equation, and none of the fast magnetoacoustic waves. In this case, one of the four slow magnetoacoustic waves is incident on the fast shock wave from the side of a compressed medium. It is shown that its existence does not contradict the conditions of the evolutionarity of MHD shock waves. The four slow magnetoacoustic waves, satisfying the dispersion equation, can also exist from either side of a slow shock wave or rotational discontinuity. (III) The expressions determining the polarisation of the MHD waves are derived in the reference frame connected with the discontinuity surface. This form of presentation is much more convenient in investigating the interaction of small perturbations with MHD discontinuities. It is shown that the perturbations of the velocity and magnetic field associated with the surface magnetoacoustic wave have the elliptic polarisation. Usually the planes of polarisation for the perturbations of the velocity and magnetic field are not coincident with each other. Keywords. Space plasma physics (Discontinuities; Shock waves) – Interplanetary physics (Discontinuities; Interplanetary shocks) – Magnetospheric physics (Solar windmagnetosphere interactions)
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Haider, Jamil A., Sana Gul, Jamshaid U. Rahman, and Fiazud D. Zaman. "Travelling Wave Solutions of the Non-Linear Wave Equations." Acta Mechanica et Automatica 17, no. 2 (2023): 239–45. http://dx.doi.org/10.2478/ama-2023-0027.
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Abstract This article focuses on the exact periodic solutions of nonlinear wave equations using the well-known Jacobi elliptic function expansion method. This method is more general than the hyperbolic tangent function expansion method. The periodic solutions are found using this method which contains both solitary wave and shock wave solutions. In this paper, the new results are computed using the closed-form solution including solitary or shock wave solutions which are obtained using Jacobi elliptic function method. The corresponding solitary or shock wave solutions are compared with the actual results. The results are visualised and the periodic behaviour of the solution is described in detail. The shock waves are found to break with time, whereas, solitary waves are found to be improved continuously with time.
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Uddin, Sabur, Shazia Karim, F. S. Alshammari, et al. "Bifurcation Analysis of Travelling Waves and Multi-rogue Wave Solutions for a Nonlinear Pseudo-Parabolic Model of Visco-Elastic Kelvin-Voigt Fluid." Mathematical Problems in Engineering 2022 (September 27, 2022): 1–16. http://dx.doi.org/10.1155/2022/8227124.
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Through this article, we focus on the extension of travelling wave solutions for a prevalent nonlinear pseudo-parabolic physical Oskolkov model for Kevin-Voigt fluids by using two integral techniques. First of all, we explore the bifurcation and phase portraits of the model for different parametric conditions via a dynamical system approach. We derive smooth waves of the bright bell and dark bell, periodic waves, and singular waves of dark and bright cusps, in correspondence to homoclinic, periodic, and open orbits with cusp, respectively. Each orbit of the phase portraits is envisaged through various energy states. Secondly, with the help of a prevalent unified scheme, an inventive version of exact analytic solutions comprising hyperbolic, trigonometric, and rational functions can be invented with some collective parameters. The unified scheme is an excitably auspicious method to procure novel interacting travelling wave solutions and to obtain multipeaked bright and dark solitons, shock waves, bright bell waves with single and double shocks, combo waves of the bright-dark bell and dark-bright bell with a shock, dark bell into a double shock wave, and bright-dark multirogue type wave solutions of the model. The dynamics of the procured nonlinear wave solutions are also presented through 2-D, 3-D, and density plots with specified parameters.
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Xi, Jin, Li Jie, Li Jin, Luo Hao, and Zhang Liheng. "Clinical Study on Appropriate Energy of Extracorporeal Shock Wave for Rotator Cuff Non-calcific Tendinopathy Treatment." Journal of Regenerative Science 3, no. 2 (2023): 47–51. http://dx.doi.org/10.13107/jrs.2023.v03.i02.103.
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Objective: This study aims to investigate the short-term clinical efficacy of extracorporeal shock waves with different energy levels on rotator cuff non-calcific tendinopathy. Materials and Methods: A total of 139 patients with rotator cuff rotator non-calcific tendinopathy were randomly divided into eight groups based on the different energy levels of the Dornier Aries smart focus shock wave therapy device: Level 5, 2000 shocks (0.062 mJ/mm2), Level 6, 2000 shocks (0.084 mJ/mm2), Level 7, 2000 shocks (0.096 mJ/mm2), Level 8, 2000 shocks (0.117 mJ/mm2), Level 5, 3000 shocks (0.062 mJ/mm2), Level 6, 3000 shocks (0.084 mJ/mm2), Level 7, 3000 shocks (0.096 mJ/mm2), and Level 8, 3000 shocks (0.117 mJ/mm2). Each group received shock wave treatment corresponding to the respective energy level and shock count. The visual analogue scale (VAS) and Constant-Murley score (CMS) were compared before and 1, 2, and 4 weeks after treatment to determine the short-term efficacy. Results: The VAS scores of all groups significantly decreased at 1, 2, and 4 weeks after treatment compared to before treatment. The VAS score of the Level 7, 2000 shocks (0.096 mJ/mm2) group was significantly lower than the other groups (P < 0.05). The CMS scores of all groups significantly increased at 1, 2, and 4 weeks after treatment compared to before treatment. The CMS score of the Level 7, 2000 shocks (0.096 mJ/mm2) group was significantly higher than the other groups (P < 0.05). There was significant statistical difference in the effective rate among the eight groups (P > 0.05). No serious adverse reactions were observed in any group before or after the treatment. Conclusion: Extracorporeal shock wave therapy for rotator cuff rotator non-calcific tendinopathy can alleviate shoulder joint pain, improve shoulder joint function, and enhance patients quality of life with good efficacy. The optimal therapeutic effect was observed at an energy level of 0.096 mJ/mm2 and 2000 shocks. Keywords: Rotator cuff injury, Rotator cuff non-calcific tendinopathy, Extracorporeal shock wave therapy
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Harutyunyan, V. G., A. R. Aramyan, G. R. Aramyan, et al. "Study of the Development of Sound Waves Generated by Shock Waves." Journal of Physics: Conference Series 2657, no. 1 (2023): 012008. http://dx.doi.org/10.1088/1742-6596/2657/1/012008.
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Abstract The work is devoted to studies of the time development of sound waves generated by shock waves. It is shown that the shock wave, propagating, generates an acoustic wave whose frequency changes over time. That change is related to the change in the speed of propagation of the shock wave.
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Bai, Chen-Yuan, and Zi-Niu Wu. "Size and shape of shock waves and slipline for Mach reflection in steady flow." Journal of Fluid Mechanics 818 (March 29, 2017): 116–40. http://dx.doi.org/10.1017/jfm.2017.139.
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For Mach reflection in steady supersonic flow, the slipline and reflected shock wave from the triple point are disturbed by secondary Mach waves generated over the slipline and by the expansion fan from the rear wedge corner. Analytical expressions for the shape of the curved slipline and reflected shock wave are derived in this paper. It is found that, due to transmitted expansion waves from the expansion fan, the slipline has a slope discontinuity at the turning point, i.e., the intersection point of the slipline and the leading characteristics of the transmitted expansion wave. The hypothetical shock wave calculated by considering this slope discontinuity as flow deflection angle matches a similar wave observed in numerical results by computational fluid dynamics, suggesting the existence of a weak shock wave from this turning point. The effects of the secondary Mach waves upstream of the turning point and of the turning point weak shock wave mutually cancel out approximately so that the transmitted Mach waves can be approximated as straight characteristic lines. This simplification leads to a fast analytical model which can predict the Mach stem height and shape of the slipline and reflected shock wave with increasing accuracy for the decreasing deflection angle of the slipline at the triple point. The slipline slope discontinuity at the turning point and the hypothetical turning point weak shock wave are new phenomena found in this work.
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Mahesh, Krishnan, Sangsan Lee, Sanjiva K. Lele, and Parviz Moin. "The interaction of an isotropic field of acoustic waves with a shock wave." Journal of Fluid Mechanics 300 (October 10, 1995): 383–407. http://dx.doi.org/10.1017/s0022112095003739.
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Moore's (1954) inviscid linear analysis of the interaction of a shock wave with a plane acoustic wave is evaluated by comparison to computation. The analysis is then extended to study the interaction of an isotropic field of acoustic waves with a normal shock wave. The evolution of fluctuating kinetic energy, sound level and thermodynamic fluctuations across the shock wave are examined in detail.The interaction of acoustic fluctuations with the shock is notably different from that of vortical fluctuations. The kinetic energy of the acoustic fluctuationsdecreasesacross the shock wave for Mach numbers between 1.25 and 1.8. For Mach numbers exceeding 3, the kinetic energy amplifies by levels that significantly exceed those found in the interaction of vortical fluctuations with the shock. Upon interacting with the shock wave, the acoustic waves generate vortical fluctuations whose contribution to the far-field kinetic energy increases with increasing Mach number. The level of sound increases across the shock wave. The rise in the sound pressure level across the shock varies from 5 to 20 dB for Mach number varying from 1.5 to 5. The fluctuations behind the shock wave are nearly isentropic for Mach number less than 1.5, beyond which the generation of entropy fluctuations becomes significant.
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Marinov, Assen. "Comparison of oblique shock wave angle in analytical and numerical solution." Aerospace Research in Bulgaria 31 (2019): 137–42. http://dx.doi.org/10.3897/arb.v31.e12.
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The drag of the subsonic aircraft is largely formed by the skin friction drag and lift-induced drag. At transonic flight occurs shock wave. Determination of shock wave angle is important part of design of every aircraft, which working in supersonic airflow regimes. Formation of shock waves cause formation the wave drag. The wave drag could account about 35% from total drag of aircraft. Shock wave angle is directly linked with the intensity of itself. This work compares shock wave angle calculations using analytical and numerical solving methods.
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Shi, Xiaofei, Terry Liu, Anton Artemyev, Vassilis Angelopoulos, Xiao-Jia Zhang, and Drew L. Turner. "Intense Whistler-mode Waves at Foreshock Transients: Characteristics and Regimes of Wave−Particle Resonant Interaction." Astrophysical Journal 944, no. 2 (2023): 193. http://dx.doi.org/10.3847/1538-4357/acb543.
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Abstract Thermalization and heating of plasma flows at shocks result in unstable charged-particle distributions that generate a wide range of electromagnetic waves. These waves, in turn, can further accelerate and scatter energetic particles. Thus, the properties of the waves and their implication for wave−particle interactions are critically important for modeling energetic particle dynamics in shock environments. Whistler-mode waves, excited by the electron heat flux or a temperature anisotropy, arise naturally near shocks and foreshock transients. As a result, they can often interact with suprathermal electrons. The low background magnetic field typical at the core of such transients and the large wave amplitudes may cause such interactions to enter the nonlinear regime. In this study, we present a statistical characterization of whistler-mode waves at foreshock transients around Earth’s bow shock, as they are observed under a wide range of upstream conditions. We find that a significant portion of them are sufficiently intense and coherent (narrowband) to warrant nonlinear treatment. Copious observations of background magnetic field gradients and intense whistler wave amplitudes suggest that phase trapping, a very effective mechanism for electron acceleration in inhomogeneous plasmas, may be the cause. We discuss the implications of our findings for electron acceleration in planetary and astrophysical shock environments.
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Markhotok, Anna. "The Post-Shock Nonequilibrium Relaxation in a Hypersonic Plasma Flow Involving Reflection off a Thermal Discontinuity." Plasma 6, no. 1 (2023): 181–97. http://dx.doi.org/10.3390/plasma6010014.
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The evolution in the post-shock nonequilibrium relaxation in a hypersonic plasma flow was investigated during a shock’s reflection off a thermal discontinuity. It was found that within a transitional period, the relaxation zone parameters past both the reflected and transmitted waves evolve differently compared to that in the incident wave. In a numerical example for the non-dissociating N2 gas heated to 5000 K/10,000 K across the interface and M = 3.5, the relaxation time determined for the transmitted wave is up to 50% shorter and the relaxation depth for both waves is significantly reduced, thus resulting in a weakened wave structure. The results of the extension into larger values of heating strength and the shock Mach numbers are discussed. The findings can be useful in the areas of research involving strong shocks interacting with optical discharges or other heated media on the scale where the shock structure becomes important.
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LEE, SANGSAN, SANJIVA K. LELE, and PARVIZ MOIN. "Interaction of isotropic turbulence with shock waves: effect of shock strength." Journal of Fluid Mechanics 340 (June 10, 1997): 225–47. http://dx.doi.org/10.1017/s0022112097005107.
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As an extension of the authors' work on isotropic vortical turbulence interacting with a shock wave (Lee, Lele & Moin 1993), direct numerical simulation and linear analysis are performed for stronger shock waves to investigate the effects of the upstream shock-normal Mach number (M1). A shock-capturing scheme is developed to accurately simulate the unsteady interaction of turbulence with shock waves. Turbulence kinetic energy is amplified across the shock wave, and this amplification tends to saturate beyond M1 = 3.0. An existing controversy between experiments and theoretical predictions on length scale change is thoroughly investigated through the shock-capturing simulation: most turbulence length scales decrease across the shock, while the dissipation length scale (ρq3/ε) increases slightly for shock waves with M1<1.65. Fluctuations in thermodynamic variables behind the shock wave are nearly isentropic for M1<1.2, and deviate significantly from isentropy for the stronger shock waves, due to the entropy fluctuation generated through the interaction.
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Hewitt, Paul. "SHOCK WAVE." Physics Teacher 58, no. 1 (2020): 4. http://dx.doi.org/10.1119/1.5141957.
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HALLUCIGENIA. "Shock wave." Geology Today 11, no. 3 (1995): 86–87. http://dx.doi.org/10.1111/j.1365-2451.1995.tb00919.x.
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Lowe, R. E., and D. Burgess. "The properties and causes of rippling in quasi-perpendicular collisionless shock fronts." Annales Geophysicae 21, no. 3 (2003): 671–79. http://dx.doi.org/10.5194/angeo-21-671-2003.
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Abstract. The overall structure of quasi-perpendicular, high Mach number collisionless shocks is controlled to a large extent by ion reflection at the shock ramp. Departure from a strictly one-dimensional structure is indicated by simulation results showing that the surface of such shocks is rippled, with variations in the density and all field components. We present a detailed analysis of these shock ripples, using results from a two-dimensional hybrid (particle ions, electron fluid) simulation. The process that generates the ripples is poorly understood, because the large gradients at the shock ramp make it difficult to identify instabilities. Our analysis reveals new features of the shock ripples, which suggest the presence of a surface wave mode dominating the shock normal magnetic field component of the ripples, as well as whistler waves excited by reflected ions.Key words. Space plasma physics (numerical simulation studies; shock waves; waves and instabilities)
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Coulouvrat, Francois. "Nonlinear acoustical transmission through a weak shock wave." Journal of the Acoustical Society of America 152, no. 4 (2022): A228. http://dx.doi.org/10.1121/10.0016098.
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Recent experiments (Ducousso et al., Phys. Rev. Appl., L051002, 2021) demonstrated the possibility to image weak shock propagation in solids by an ultrasonic probe wave. Wave interaction with a steady, ideal step shock in air has been previously described (Burgers, Selected Papers, Springer, 478–486, 1995—McKenzie and Westphal, Phys. Fluids, 11, 2350, 1968), without consideration for the particular case of a weak shock nor for the influence of the medium. The present paper considers a weak shock interacting in any inviscid fluid with an incident probe wave. No reflected wave arises. The transmitted wave, vortex and entropy modes behind the shock, and the shock front disturbance, are determined by the linearisation of the Rankine-Hugoniot relations. For a weak shock, entropy mode and energy jump relation can be omitted. The shock motion induces a Doppler effect dependant on the medium, air and water giving opposite trends. The transmitted wave amplitude is either increased or reduced through energy exchanges with the shock. For an incidence beyond the critical angle, instead of a total reflexion, an inversion of the direction of the transmitted wave occurs, propagating in the same direction as the shock. This phenomenon seems specific to weak shocks.
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Chen, Kaiyi. "High Energy Cosmic Generation Form Collisionless Shock Wave Acceleration." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 835–41. http://dx.doi.org/10.54097/hset.v38i.5967.
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The collision less shock wave one of the shock waves that is more likely to detect in the plasma that come from the magnetosphere, interplanetary space and so far. The most significance difference between other shock wave is the direct collision between particle is almost not exist. To be specific, the bow shock wave that occur by the interact of magnetosphere of an astrophysical object and solar wind is one of the collisions less shock wave. The collision-less shock wave in the universe could accelerate the particle in to high energy and form cosmic rays. In this essay, the basic reorganization of collision-less shock wave will be illustrated. On this basis, this paper is going to analysis a few mechanism of how the collision-less shock wave accelerate the particle and the recent experiment about the shock wave. According to the analysis, lots of state-of-art observations can be explained. These results shed light on guiding further exploration of high energy cosmic ray.
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Kato, Kaoruko, Miki Fujimura, Atsuhiro Nakagawa, et al. "Pressure-dependent effect of shock waves on rat brain: induction of neuronal apoptosis mediated by a caspase-dependent pathway." Journal of Neurosurgery 106, no. 4 (2007): 667–76. http://dx.doi.org/10.3171/jns.2007.106.4.667.
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Object Shock waves have been experimentally applied to various neurosurgical treatments including fragmentation of cerebral emboli, perforation of cyst walls or tissue, and delivery of drugs into cells. Nevertheless, the application of shock waves to clinical neurosurgery remains challenging because the threshold for shock wave–induced brain injury has not been determined. The authors investigated the pressure-dependent effect of shock waves on histological changes of rat brain, focusing especially on apoptosis. Methods Adult male rats were exposed to a single shot of shock waves (produced by silver azide explosion) at over-pressures of 1 or 10 MPa after craniotomy. Histological changes were evaluated sequentially by H & E staining and terminal deoxynucleotidyl transferase–mediated deoxyuridine triphosphate nick-end labeling (TUNEL). The expression of active caspase-3 and the effect of the nonselective caspase inhibitor N-benzyloxycarbonyl-Val-Ala-Asp-fluoromethylketone (Z-VAD-FMK) were examined to evaluate the contribution of a caspase-dependent pathway to shock wave–induced brain injury. High-overpressure (> 10 MPa) shock wave exposure resulted in contusional hemorrhage associated with a significant increase in TUNEL-positive neurons exhibiting chromatin condensation, nuclear segmentation, and apoptotic bodies. The maximum increase was seen at 24 hours after shock wave application. Low-overpressure (1 MPa) shock wave exposure resulted in spindle-shaped changes in neurons and elongation of nuclei without marked neuronal injury. The administration of Z-VAD-FMK significantly reduced the number of TUNEL-positive cells observed 24 hours after high-overpressure shock wave exposure (p < 0.01). A significant increase in the cytosolic expression of active caspase-3 was evident 24 hours after high-overpressure shock wave application; this increase was prevented by Z-VAD-FMK administration. Double immunofluorescence staining showed that TUNEL-positive cells were exclusively neurons. Conclusions The threshold for shock wave–induced brain injury is speculated to be under 1 MPa, a level that is lower than the threshold for other organs. High-overpressure shock wave exposure results in brain injury, including neuronal apoptosis mediated by a caspase-dependent pathway. This is the first report in which the pressure-dependent effect of shock wave on the histological characteristics of brain tissue is demonstrated.
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Faran, Tamar, Christopher D. Matzner, and Eliot Quataert. "Nonlinear Perturbations and Weak Shock Waves in Isentropic Atmospheres." Astrophysical Journal 976, no. 1 (2024): 97. http://dx.doi.org/10.3847/1538-4357/ad843c.
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Abstract Acoustic perturbations to stellar envelopes can lead to the formation of weak shock waves via nonlinear wave steepening. Close to the stellar surface, the weak shock wave increases in strength and can potentially lead to the expulsion of part of the stellar envelope. While accurate analytic solutions to the fluid equations exist in the limits of low-amplitude waves or strong shocks, connecting these phases generally requires simulations. We address this problem using the fact that the plane-parallel Euler equations, in the presence of a constant gravitational field, admit exact Riemann invariants when the flow is isentropic. We obtain exact solutions for acoustic perturbations and show that after they steepen into shock waves, Whitham’s approximation can be used to solve for the shock’s dynamics in the weak to moderately strong regimes, using a simple ordinary differential equation. Numerical simulations show that our analytic shock approximation is accurate up to moderate (∼few–15) Mach numbers, where the accuracy increases with the adiabatic index.
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Król, Piotr, Andrzej Franek, Jacek Durmała, et al. "Focused and Radial Shock Wave Therapy in the Treatment of Tennis Elbow: A Pilot Randomised Controlled Study." Journal of Human Kinetics 47, no. 1 (2015): 127–35. http://dx.doi.org/10.1515/hukin-2015-0068.
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AbstractThe purpose of this article was to evaluate and compare the efficacy of radial and focused shock wave therapies applied to treat tennis elbow. Patients with tennis elbow were randomized into two comparative groups: focused shock wave therapy (FSWT; n=25) and radial shock wave therapy (RSWT; n=25). Subjects in the FSWT and RSWT groups were applied with a focused shock wave (3 sessions, 2000 shocks, 4 Hz, 0.2 mJ/mm2) and a radial shock wave (3 sessions, 2000 + 2000 shocks, 8 Hz, 2.5 bar), respectively. The primary study endpoints were pain relief and functional improvement (muscle strength) one week after therapy. The secondary endpoint consisted of the results of the follow-up observation (3, 6 and 12 weeks after the study). Successive measurements showed that the amount of pain patients felt decreased in both groups. At the same time grip strength as well as strength of wrist extensors and flexors of the affected extremity improved significantly. Both focused and radial shock wave therapies can comparably and gradually reduce pain in subjects with tennis elbow. This process is accompanied by steadily improved strength of the affected extremity.
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Chen, Na, and Hanhua Ji. "Cardiac Shock Wave Therapy in Cardiovascular Diseases." Journal of Regenerative Science 3, no. 2 (2023): 81–86. http://dx.doi.org/10.13107/jrs.2023.v03.i02.115.
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Cardiovascular disease is one of the leading causes of death worldwide, placing a huge burden on patients and healthcare systems. Cardiac shock wave (CSW) technology is a non-invasive treatment method. In recent years, some scholars have discovered that extracorporeal shock wave can improve cardiovascular ischemic lesions. This article reviews the latest progress in basic research and clinical application of cardiac shock wave technology in cardiovascular medicine and reviews its efficacy and potential mechanisms in different diseases. First, the principle of shock waves and their application potential in cardiovascular medicine are introduced. Then, from the aspects of basic research and clinical application, the mechanism and clinical efficacy of shock waves in cardiovascular diseases such as coronary heart disease, myocardial ischemia-reperfusion injury, atrial fibrillation, atherosclerosis, and coronary artery calcification are discussed, as well as its advantages and limitations. Animal experiments and clinical studies have found that low-energy extracorporeal shock waves can upregulate the expression of vascular endothelial growth factors, promote angiogenesis, promote nitric oxide production, increase local blood perfusion, significantly reduce angina symptoms, and improve left ventricular function and remodeling. Finally, the future development trend of shock wave technology is prospected. This review provides an introduction to the properties, biomechanical effects, treatment mechanisms of cardiovascular diseases, research status and development prospects of extracorporeal shock waves. Keywords: Cardiac shock Wave Therapy, Cardiovascular diseases, ESWT
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Eliezer, Shalom, and Jose Maria Martinez Val. "The comeback of shock waves in inertial fusion energy." Laser and Particle Beams 29, no. 2 (2011): 175–81. http://dx.doi.org/10.1017/s0263034611000140.
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AbstractThe shock waves in laser plasma interaction have played an important role in the study of inertial fusion energy (IFE) since the 1970's and perhaps earlier. The interaction of laser, or any other high power beam, induced shock waves with matter was one of the foundations of the target design in IFE. Even the importance of shock wave collision was studied and its importance forgotten. In due course, the shock waves were taken as granted and became “second fiddle” in IFE scenario. The analysis of the shock wave in the context of IFE is revived in this paper. At the forefront of the past decade the concept of fast ignition was introduced. The different ideas of fast ignition are summarized with special emphasis on shock wave fast ignition. The ignition is achieved by launching a shock wave during the final stages of the implosion. In this paper, a possible instability in the propagation of the igniting shock wave is analyzed. The idea of combining the fast ignition fusion with an impact shock wave is suggested and analyzed. This is achieved by launching a shock wave by an accelerated foil during the final stage of the implosion in order to ignite the compressed fuel. In this scheme, like other fast ignition schemes, a significant reduction of the driver energy in comparison with standard IFE scenarios is required for the same high gain fusion.