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Journal articles on the topic 'Isentropic gas motion'
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1
Alıyev, E., M. Rasulov, and M. Xalılov. "NUMERCIAL SOLUTION OF INITIAL-BOUNDARY VALUE PROBLEM FOR ONE-DIMENSIONAL GAS DYNAMICS IN THE CLASS OF DISCONTINUOUS FUNCTIONS." International independent scientific journal, no. 45 (December 6, 2022): 8–9. https://doi.org/10.5281/zenodo.7418270.
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<strong><em>Abstract</em></strong> <em>In this study, we will prepare a spatial auxiliary problem for the developed numerical method to solve the initial-boundary value problem for the first-order nonlinear partial differential system of equations that describes the one-dimensional motion of isentropic gas as follows</em>
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SAUER, NIKO. "THE DYNAMIC PISTON PROBLEM IN CLASSICAL NONLINEAR ACOUSTICS." Mathematical Models and Methods in Applied Sciences 21, no. 01 (2011): 149–67. http://dx.doi.org/10.1142/s0218202511005015.
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This paper discusses the effects of an applied external force on the motion of a piston in a tube and the motion of the gas in the tube. The equations under consideration are the recently proposed ones for nonlinear sonic disturbances in an isentropic gas.
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Yulmukhametova, Yu V. "Barochronous shear gas motion." Multiphase Systems 14, no. 4 (2019): 274–78. http://dx.doi.org/10.21662/10.21662/mfs2019.4.035.
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The equations of ideal gas dynamics admit an 11-dimensional Lie algebra of first-order differentiation operators. All subalgebras of this algebra are listed. Khabirov S.V. for all 48 types of 4-dimensional subalgebras, the bases of point invariants are calculated and three 4-dimensional subalgebras are considered that produce regular partially invariant solutions in Cartesian, cylindrical and spherical coordinates, respectively. In this paper, we pose the problem of finding the solution of 3-dimensional equations of gas dynamics in a Cartesian coordinate system with an arbitrary equation of state, built on invariants of a 4-dimensional subalgebra. The basic operators of the considered subalgebra are combinations of translations and Galilean transfers. The invariants of this subalgebra define a representation of the solution for unknown hydrodynamic functions. Speed components are linear functions in terms of spatial variables. Moreover, density and pressure depend only on time. After substituting the solution representation, we studied the compatibility of the resulting system of differential equations. The system is collaborative and has an exact solution. Such a solution describes the isentropic barochronous shear motion of a gas. The equations of the world lines of motion of gas particles are found. The moments of particle collapse are established. There were two of them. The equations of collapse surfaces are found and written. For the flat case, several statements about the nature of the motion of gas particles are proved.
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Chirkunov, Yu A. "Conservation laws and group properties of equations of isentropic gas motion." Journal of Applied Mechanics and Technical Physics 51, no. 1 (2010): 1–3. http://dx.doi.org/10.1007/s10808-010-0001-6.
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Makino, Tetu, and Shigeharu Takeno. "Initial boundary value problem for the spherically symmetric motion of isentropic gas." Japan Journal of Industrial and Applied Mathematics 11, no. 1 (1994): 171–83. http://dx.doi.org/10.1007/bf03167220.
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Deryabin, S. L., and A. S. Kiryanova. "Mathematical modeling of gravity-based fluid flows resulting from dam failure." Mathematical structures and modeling, no. 4 (2017): 73–85. http://dx.doi.org/10.24147/2222-8772.2017.4.73-85.
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The paper considers three-dimensional isentropic flows of a polytropic gas under gravity. A system of gas dynamics equations for a polytropic gas is used as a mathematical model. With the polytropic exponent $ \gamma = 7.02 $, this system describes the motion of water. An orthogonal curvilinear coordinate system is introduced into the system. To formulate the problem of the decay of a special discontinuity in the system, a degenerate change of variables is made, namely: the dependent and independent variables swap roles. In the new variables, an initial-boundary value problem with data on the sound characteristic and an additional condition is formulated for the system. The solution to the initial-boundary value problem is constructed in the form of power series. The convergence of the constructed series in the region from the surface of the weak discontinuity to the gas-vacuum boundary inclusive is proved. To determine the law of motion of the gas-vacuum boundary, a quasi-linear system of partial differential equations is written out, which is reduced to a system of ordinary differential equations using a characteristic parameter.
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Song, Yukun, Shuai Chen, and Fengming Liu. "The well-posedness of solution to a compressible non-Newtonian fluid with self-gravitational potential." Open Mathematics 16, no. 1 (2018): 1466–77. http://dx.doi.org/10.1515/math-2018-0122.
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AbstractWe study the initial boundary value problem of a compressible non-Newtonian fluid. The system describes the motion of the compressible viscous isentropic gas flow driven by the non-Newtonian self-gravitational force. The existence of strong solutions are derived in one dimensional bounded intervals by constructing a semi-discrete Galerkin scheme. Moreover, the uniqueness of solutions are also investigated. The main point of the study is that the viscosity term and potential term are fully nonlinear, and the initial vacuum is allowed.
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Liu, Jianli, Ziyi Qin, and Manwai Yuen. "Formation of Singularity for Isentropic Irrotational Compressible Euler Equations." Symmetry 16, no. 4 (2024): 454. http://dx.doi.org/10.3390/sym16040454.
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The domain of science and engineering relies heavily on an in-depth comprehension of fluid dynamics, given the prevalence of fluids such as water, air, and interstellar gas in the universe. Euler equations form the basis for the study of fluid motion. This paper is concerned with the Cauchy problem of isentropic compressible Euler equations away from the vacuum. We use the integration method with the general test function f=f(r), proving that there exist the corresponding blowup results of C1 irrotational solutions for Euler equations and Euler equations with time-dependent damping in Rn (n≥2), provided the density-independent initial functional is sufficiently large. We also provide two simple and explicit test functions f(r)=r and f(r)=1+r, to demonstrate the blowup phenomenon in the one-dimensional case. In particular, our results are applicable to the non-radial system.
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Chirkunov, Yu A. "Non-local conservation laws for the equations of the irrotational isentropic plane-parallel gas motion." Journal of Applied Mathematics and Mechanics 76, no. 2 (2012): 199–204. http://dx.doi.org/10.1016/j.jappmathmech.2012.05.011.
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Zhou, Mingxue, Cheng Wu, Fengjiang An, et al. "Acceleration Characteristics of Discrete Fragments Generated from Explosively-Driven Cylindrical Metal Shells." Materials 13, no. 9 (2020): 2066. http://dx.doi.org/10.3390/ma13092066.
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The acceleration characteristics of fragments generated from explosively-driven cylindrical shells are important issues in warhead design. However, there is as yet no reasonable theory for predicting the acceleration process of a specific metallic shell; existing approaches either ignore the effects of shell disintegration and the subsequent gas leakage on fragment acceleration or treat them in a simplified manner. In this paper, a theoretical model was established to study the acceleration of discrete fragments under the combined effect of shell disintegration and gas leakage. Firstly, an equation of motion was developed, where the acceleration of a cylindrical shell and the internal detonation gas was determined by the motive force impacting the inner surface of the metallic cylinder. To account for the force decrease induced by both the change in fragment area after the shell disintegrates and the subsequent drop in gas pressure due to gas leakage, the equation of motion was then associated with an equation for the locally isentropic expansion of the detonation gas and a modified gas-leakage equation. Finally, theoretical analysis was conducted by solving the associated differential equations. The proposed model showed good agreement with experimental data and numerical simulations, indicating that it was suitable for predicting the acceleration of discrete fragments generated from a disintegrated warhead shell. In addition, this study facilitated a better understanding of the complicated interaction between fragment acceleration and gas outflow.
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Prust, Logan J., Hila Glanz, Lars Bildsten, Hagai B. Perets, and Friedrich K. Röpke. "Morphology and Mach Number Dependence of Subsonic Bondi–Hoyle Accretion." Astrophysical Journal 966, no. 1 (2024): 103. http://dx.doi.org/10.3847/1538-4357/ad3732.
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Abstract We carry out three-dimensional computations of the accretion rate onto an object (of size R sink and mass m) as it moves through a uniform medium at a subsonic speed v ∞. The object is treated as a fully absorbing boundary (e.g., a black hole). In contrast to early conjectures, we show that for an accretor with R sink ≪ R A = 2 Gm / v ∞ 2 in a gaseous medium with adiabatic index γ = 5/3, the accretion rate is independent of Mach number and is determined only by m and the gas entropy. Our numerical simulations are conducted using two different numerical schemes via the Athena++ and Arepo hydrodynamics solvers, which reach nearly identical steady-state solutions. We find that pressure gradients generated by the isentropic compression of the flow near the accretor are sufficient to suspend much of the surrounding gas in a near-hydrostatic equilibrium, just as predicted from the spherical Bondi–Hoyle calculation. Indeed, the accretion rates for steady flow match the Bondi–Hoyle rate, and are indicative of isentropic flow for subsonic motion where no shocks occur. We also find that the accretion drag may be predicted using the Safronov number, Θ = R A /R sink, and is much less than the dynamical friction for sufficiently small accretors (R sink ≪ R A ).
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Chen, Yi-Hao, and Sebastian Heinz. "AGN Jets, Bubbles, and Heat Pumps." Proceedings of the International Astronomical Union 14, S342 (2018): 149–53. http://dx.doi.org/10.1017/s1743921318005379.
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AbstractRadio-mode feedback from relativistic jets is one of the prominent heating mechanisms in clusters of galaxies. We present a long-term evolution of high-resolution MHD simulation of jets interacting with an environment modeled to represent the Perseus cluster. We investigate the thermodynamics of the ICM due to the gas motion triggered by the action of the jets and show that low-entropy gas is lifted efficiently in the wake of the inflating radio lobe. We look into the uplift mechanism and estimate the energy budget and the rate of thermal conduction. The redistribution of entropy suggests that heat conduction can play a more significant role in the thermal evolution of the cluster core in the presence of jets, which act effectively as a heat pump, thus heating the ICM more efficiently than jets would by themselves in an isentropic cluster.
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Deryabin, S. L., and A. P. Sadov. "Mathematical modeling of self-gravitating gas flows using nonstationary self-similar variables." Herald of the Ural State University of Railway Transport, no. 3 (2022): 15–22. http://dx.doi.org/10.20291/2079-0392-2022-3-15-22.
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The paper considers one-dimensional isentropic flows of an ideal gas gravitating by Newton. As a mathematical model, the system of equations of gas dynamics is used, taking into account the effect of gravity according to Newton. In the system of gas dynamics equations, a self-similar feature is introduced into the variable x, and for the resulting system, the Cauchy problem with data on the sound characteristic is solved. The solution of the initial boundary value problem is constructed in the form of a convergent power series. Some of the coefficients of the series are found when solving algebraic equations, the rest of the coefficients of the series are found when integrating ordinary differential equations. Then, in the form of the system of ordinary differential equations, the law of motion of the gas-vacuum boundary is written out. The obtained analytical solutions can be used to develop new approximations of boundary and initial conditions for numerical simulation of a gravitational rarefaction wave for a long period of time.
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Akiki, M., and J. Majdalani. "Compressible integral representation of rotational and axisymmetric rocket flow." Journal of Fluid Mechanics 809 (November 9, 2016): 213–39. http://dx.doi.org/10.1017/jfm.2016.654.
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This work focuses on the development of a semi-analytical model that is appropriate for the rotational, steady, inviscid, and compressible motion of an ideal gas, which is accelerated uniformly along the length of a right-cylindrical rocket chamber. By overcoming some of the difficulties encountered in previous work on the subject, the present analysis leads to an improved mathematical formulation, which enables us to retrieve an exact solution for the pressure field. Considering a slender porous chamber of circular cross-section, the method that we follow reduces the problem’s mass, momentum, energy, ideal gas, and isentropic relations to a single integral equation that is amenable to a direct numerical evaluation. Then, using an Abel transformation, exact closed-form representations of the pressure distribution are obtained for particular values of the specific heat ratio. Throughout this effort, Saint-Robert’s power law is used to link the pressure to the mass injection rate at the wall. This allows us to compare the results associated with the axisymmetric chamber configuration to two closed-form analytical solutions developed under either one- or two-dimensional, isentropic flow conditions. The comparison is carried out assuming, first, a uniformly distributed mass flux and, second, a constant radial injection speed along the simulated propellant grain. Our amended formulation is consequently shown to agree with a one-dimensional solution obtained for the case of uniform wall mass flux, as well as numerical simulations and asymptotic approximations for a constant wall injection speed. The numerical simulations include three particular models: a strictly inviscid solver, which closely agrees with the present formulation, and both $k$–$\unicode[STIX]{x1D714}$ and Spalart–Allmaras computations.
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NAKAMURA, TOHRU, SHINYA NISHIBATA, and SHIGENORI YANAGI. "LARGE-TIME BEHAVIOR OF SPHERICALLY SYMMETRIC SOLUTIONS TO AN ISENTROPIC MODEL OF COMPRESSIBLE VISCOUS FLUID IN A FIELD OF POTENTIAL FORCES." Mathematical Models and Methods in Applied Sciences 14, no. 12 (2004): 1849–79. http://dx.doi.org/10.1142/s0218202504003842.
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We study the large-time behavior of a spherically symmetric motion of isentropic and compressible viscous gas in a field of potential force over an unbounded exterior domain in ℝn(n≥2). First, we show the unique existence of a stationary solution satisfying an adhesion boundary condition and a positive spatial asymptotic condition. Then, it is shown that the stationary solution becomes a time asymptotic state to the initial boundary value problem with the same boundary and spatial asymptotic conditions. Here, the initial data can be chosen arbitrarily large if it belongs to the suitable Sobolev space. Moreover, if the external force is attractive to the center of a sphere, it can also be taken arbitrarily large. The proof of the stability theorem is based on computations, executed by using the Lagrangian coordinate. In the proof, it is the essential step to obtain the pointwise estimate for the density. It is derived through employing a representation formula of the density with the aid of the standard energy method. The Hölder regularity of the initial data is also required for translating the results in the Lagrangian coordinate to those in the Eulerian coordinate.
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Avola, Calogero, Colin Copeland, Alessandro Romagnoli, Richard Burke, and Pavlos Dimitriou. "Attempt to correlate simulations and measurements of turbine performance under pulsating flows for automotive turbochargers." Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 233, no. 2 (2017): 174–87. http://dx.doi.org/10.1177/0954407017739123.
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The paper attempts to correlate simulations and measurements of turbine performance under pulsating flows for automotive turbochargers. Under real automotive powertrain conditions, turbochargers are subjected to pulsating flows, due to the motion of the engine’s valves. Experiments on a purpose-built 2.2 L diesel engine gas-stand have allowed the quantification of unsteady pulsating turbine performance. Temperature, pressure and mass flow measurements are fundamental for the characterisation of turbine performance. An adequate sampling frequency of the instruments and acquisition rates are highly important for the quantification of unsteady turbomachine performance. In the absence of fast, responsive sensors for monitoring mass flow and temperature, however, appropriate considerations would have to be taken into account when making estimates of turbine performance under pulsating flows. A 1D model of the engine gas-stand has been developed and validated against experimental data. A hybrid unsteady/quasi-steady turbine model has been adopted to identify unsteadiness at the turbine inlet and outlet. To evaluate isentropic turbine efficiency and reduce the influence of external heat transfer upon measurements, the turbine inlet temperature has been measured experimentally in the vicinity of the turbine rotor in the inlet section, upstream of the turbine tongue. The hybrid unsteady/quasi-steady turbine model considers the presence of unsteady flows in the turbine inlet and outlet, leaving the rest of the turbine to react quasi-steadily. Virtual sensors and thermocouples have been implemented in a 1D model to correlate experimental time-averaged temperature measurements.
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PARK, JUN SANG, and JAE MIN HYUN. "Transient response of a compressible fluid in a rapidly rotating circular pipe." Journal of Fluid Mechanics 427 (January 25, 2001): 275–97. http://dx.doi.org/10.1017/s002211200000238x.
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The transient adjustment process of a compressible fluid in a rapidly rotating pipe is studied. The system Ekman number E is small, and the assumptions of small Mach number and the heavy-gas limit (γ = 1.0) are invoked. Fluid motion is generated by imposing a step-change perturbation in the temperature at the pipe wall Tw. Comprehensive analytical solutions are obtained by deploying the matched asymptotic technique with proper timescales O(E−1/2) and O(E−1). These analytical solutions are shown to be consistent with corresponding full numerical solutions. The detailed profiles of major variables are delineated, and evolution of velocity and temperature fields is portrayed. At moderate times, the entire flow field can be divided into two regions. In the inner inviscid region, thermo-acoustic compression takes place, and the process is isothermal–isentropic with the angular momentum being conserved. In the outer viscous region, diffusion of angular momentum occurs. The principal dynamic mechanisms are discussed, and physical rationalizations are offered. The essential differences between the responses of a compressible and an incompressible fluid are highlighted.The issue of stability of the analytically obtained flow is addressed by undertaking a formal stability analysis. It is illustrated that, within the range of parameters of present concern, the flow is stable when ε ∼ O(E).
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Tanner, Scott D., D. J. Douglas, and J. B. French. "Gas and Ion Dynamics of a Three-Aperture Vacuum Interface for Inductively Coupled Plasma-Mass Spectrometry." Applied Spectroscopy 48, no. 11 (1994): 1373–78. http://dx.doi.org/10.1366/0003702944028137.
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The equations describing the pressure, density, and temperature characteristics of isentropic flow and of the formation of a shock structure due to the sudden termination of the directed motion of a flowing plasma are reviewed. The results are applied to describe the flow characteristics of a novel ICP-MS vacuum interface which consists of three apertures: a conventional sampler and skimmer and a third aperture contained in a blunt support which is normal to (or nearly normal to) the axis of the primary expansion through the sampler and skimmer. The flow through the interface apertures is characterized as continuum, effusive, or transitional, and the impact of these forms of expansion on the ion dynamics (kinetic energies and plasma neutrality) is examined. A shock wave may form in front of the third aperture. The effect of this flow disturbance on the gas and ion dynamics in the vicinity of the aperture is discussed. Experimental neutral and ion flow results are compared to the theoretical predictions. It is concluded that the plasma retains its charge neutrality as it flows through the sampler and skimmer and, under the conditions studied, also through the shock and subsequent expansion through the third aperture. The gas behind the shock flows across the surface of the blunt tip of the third aperture, and the aperture itself may be offset from the axis of the original expansion to eliminate clogging of the aperture by unvaporized particles and condensed salts from the plasma and to prevent source plasma photons from contributing to the background signal continuum. The reduction in the ion current introduced into the ion optics region of the mass spectrometer reduces the magnitude of the space charge field and results in a gain in ion transmission efficiency which offsets the reduction of the ion flow.
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Moore, D. W., and D. I. Pullin. "The compressible vortex pair." Journal of Fluid Mechanics 185 (December 1987): 171–204. http://dx.doi.org/10.1017/s0022112087003136.
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We consider the steady self-propagation with respect to the fluid at infinity of two equal symmetrically shaped vortices in a compressible fluid. Each vortex core is modelled by a region of stagnant constant-pressure fluid bounded by closed constant-pressure, constant-speed streamlines of unknown shape. The external flow is assumed to be irrotational inviscid isentropic flow of a perfect gas. The flow is therefore shock free but may be locally supersonic. The nonlinear free-boundary problem for the vortex-pair flow is formulated in the hodograph plane of compressible-flow theory, and a numerical solution method based on finite differences is described. Specific results are presented for a range of parameters which control the flow, namely the Mach number of the pair translational motion and the fluid speed on each vortex bounding streamline. Perturbation-theory predictions are developed, valid for vortices of small core radius when the pair Mach number is much less than unity. These are in good agreement with the hodograph-plane calculations. The numerical and the perturbation-theory results together confirm the recently discovered (Barsony-Nagy, Er-El & Yungster 1987) existence of continuous shock-free transonic compressible flows with embedded vortices. For the vortex-pair geometry studied, solution branches corresponding to physically acceptable flows that could be calculated using the present hodograph-plane numerical method were found to be terminated when either the flow on the streamline of symmetry separating the vortiqes tends to become superonic or when limiting lines appear in the hodograph plane giving a locally multivalued mapping to the physical plane.
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Bozem, Heiko, Peter Hoor, Daniel Kunkel, et al. "Characterization of transport regimes and the polar dome during Arctic spring and summer using in situ aircraft measurements." Atmospheric Chemistry and Physics 19, no. 23 (2019): 15049–71. http://dx.doi.org/10.5194/acp-19-15049-2019.
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Abstract. The springtime composition of the Arctic lower troposphere is to a large extent controlled by the transport of midlatitude air masses into the Arctic. In contrast, precipitation and natural sources play the most important role during summer. Within the Arctic region sloping isentropes create a barrier to horizontal transport, known as the polar dome. The polar dome varies in space and time and exhibits a strong influence on the transport of air masses from midlatitudes, enhancing transport during winter and inhibiting transport during summer. We analyzed aircraft-based trace gas measurements in the Arctic from two NETCARE airborne field campaigns (July 2014 and April 2015) with the Alfred Wegener Institute Polar 6 aircraft, covering an area from Spitsbergen to Alaska (134 to 17∘ W and 68 to 83∘ N). Using these data we characterized the transport regimes of midlatitude air masses traveling to the high Arctic based on CO and CO2 measurements as well as kinematic 10 d back trajectories. We found that dynamical isolation of the high Arctic lower troposphere leads to gradients of chemical tracers reflecting different local chemical lifetimes, sources, and sinks. In particular, gradients of CO and CO2 allowed for a trace-gas-based definition of the polar dome boundary for the two measurement periods, which showed pronounced seasonal differences. Rather than a sharp boundary, we derived a transition zone from both campaigns. In July 2014 the polar dome boundary was at 73.5∘ N latitude and 299–303.5 K potential temperature. During April 2015 the polar dome boundary was on average located at 66–68.5∘ N and 283.5–287.5 K. Tracer–tracer scatter plots confirm different air mass properties inside and outside the polar dome in both spring and summer. Further, we explored the processes controlling the recent transport history of air masses within and outside the polar dome. Air masses within the springtime polar dome mainly experienced diabatic cooling while traveling over cold surfaces. In contrast, air masses in the summertime polar dome were diabatically heated due to insolation. During both seasons air masses outside the polar dome slowly descended into the Arctic lower troposphere from above through radiative cooling. Ascent to the middle and upper troposphere mainly took place outside the Arctic, followed by a northward motion. Air masses inside and outside the polar dome were also distinguished by different chemical compositions of both trace gases and aerosol particles. We found that the fraction of amine-containing particles, originating from Arctic marine biogenic sources, is enhanced inside the polar dome. In contrast, concentrations of refractory black carbon are highest outside the polar dome, indicating remote pollution sources. Synoptic-scale weather systems frequently disturb the transport barrier formed by the polar dome and foster exchange between air masses from midlatitudes and polar regions. During the second phase of the NETCARE 2014 measurements a pronounced low-pressure system south of Resolute Bay brought inflow from southern latitudes, which pushed the polar dome northward and significantly affected trace gas mixing ratios in the measurement region. Mean CO mixing ratios increased from 77.9±2.5 to 84.9±4.7 ppbv between these two regimes. At the same time CO2 mixing ratios significantly decreased from 398.16 ± 1.01 to 393.81 ± 2.25 ppmv. Our results demonstrate the utility of applying a tracer-based diagnostic to determine the polar dome boundary for interpreting observations of atmospheric composition in the context of transport history.
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"The effect of compressibility on the speed of propagation of a vortex ring." Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 397, no. 1812 (1985): 87–97. http://dx.doi.org/10.1098/rspa.1985.0005.
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A circular vortex filament of radius R , cross sectional area π a 2 and circulation Г propagates steadily in an inviscid, calorically perfect gas. The flow outside the filament is assumed to be irrotational and isentropic. If it is further assumed that a/R ≪ 1, the cross section is approximately circular and the speed of propagation of the filament is shown to depend on the distribution of circulatory velocity v 0 and entropy s 0 within the core. If s 0 is constant and equal to its value in the isentropic exterior of the filament, the vortex ring is slowed down by compressibility effects, whatever the distribution of circulatory velocity. If the circulatory velocity corresponds to rigid rotation in the core cross section, the speed, U , of propagation is given by U = Γ/4π R [ln 8R/ a - ¼ - 5/12 M 2 + O ( M 4 )], where M is the Mach number Γ /2π ac ∞ and c ∞ is the sound speed far from the vortex ring. Numerical results for finite M are also given in this case. These results enable the cut-off theory of filament motion to be extended to compressible fluids.
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Si, Chenwei, Min Zhao, and Yuejin Zhu. "On the interaction between a detonation wave and an inert gas plug: A numerical investigation." Physics of Fluids 35, no. 12 (2023). http://dx.doi.org/10.1063/5.0176644.
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Employing inert gases to attenuate and obstruct the propagation of detonation waves has proven to be an effective strategy for mitigating potential damage in the realm of industrial safety, which involves complex physical and chemical mechanisms. This study utilizes an in-house solver built on the OpenFOAM platform to examine the interaction between a detonation wave and an inert gas plug of various lengths. The results reveal that as the length of the inert gas plug increases, various detonation states emerge downstream of the gas plug, and an exponential relationship is observed between the detonation re-initiation distance and the gas plug's length. In the process of detonation re-initiation, the non-isentropic process within the viscous boundary layer plays a crucial role in initiating the flames at the upper and lower channel walls. Later, the collision between flames initiates the detonation wave. Additionally, a localized detonation can also be triggered through the interaction between the compression wave and the wall. Notably, the impingements of the detonation wave and the transmitted shock wave induce the mixing and downstream motion of the gas plug. In the presence of the detonation re-initiation, the motion patterns of the left and right interfaces of the gas plug can be categorized into two distinct stages, which are mainly because of the impingement of backpropagation expansion waves and the hindrance of the high pressure generated by the detonation re-initiation, respectively. Also, as the length of the inert gas plug increases, the velocity difference between the two stages gradually decreases.