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1
ONG, LAWRENCE, and JAMES M. WALLACE. "Joint probability density analysis of the structure and dynamics of the vorticity field of a turbulent boundary layer." Journal of Fluid Mechanics 367 (July 25, 1998): 291–328. http://dx.doi.org/10.1017/s002211209800158x.
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An experimental study of a turbulent boundary layer at Rθ≈1070 and Rτ≈543 was conducted. Detailed measurements of the velocity vector and the velocity gradient tensor within the near-wall region were performed at various distances from the wall, ranging from approximately y+=14 to y+=89. The measured mean statistical properties of the fluctuating velocity and vorticity components agree well with previous experimental and numerically simulated data. These boundary layer measurements were used in a joint probability density analysis of the various component vorticity and vorticity–velocity gradient products that appear in the instantaneous vorticity and enstrophy transport equations. The vorticity filaments that contribute most to the vorticity covariance Ω[bar]xΩ [bar]y in this region were found to be oriented downstream with angles of inclination to the wall, when projected on the streamwise (x, y)-plane, that decrease with distance moving from the buffer to the logarithmic layer. When projected on the planview (x, z)- and cross-stream (y, z)-planes, the vorticity filaments that most contribute to the vorticity covariances Ω [bar]xΩ [bar]z and Ω [bar]yΩ [bar]z have angles of inclination to the z-ordinate axis that increase with distance from it. All the elements of the ΩiΩj ∂Ui/∂xj term in the enstrophy transport equation, i.e. the term that describes the rate of increase or decrease of the enstrophy by vorticity filament stretching or compression by the strain-rate field, have been examined. On balance, the average stretching of the vorticity filaments is greater than compression at all y+ locations examined here. However, some individual velocity gradient components compress the vorticity filaments, on average, more than they stretch them.
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Ostrikov, N. N., and E. M. Zhmulin. "Vortex dynamics of viscous fluid flows. Part 1. Two-dimensional flows." Journal of Fluid Mechanics 276 (October 10, 1994): 81–111. http://dx.doi.org/10.1017/s0022112094002478.
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The method of product integration is applied to the vortex dynamics of two-dimensional incompressible viscous media. In the cases of both unbounded and bounded flows under the no-slip boundary condition, the analytic solutions of the Cauchy problem are obtained for the Helmholtz equation in the form of linear and nonlinear product integrals. The application of product integrals allows the generalization in a natural way of the vortex dynamics concept to the case of viscous flows. However, this new approach requires the reconsideration of some traditional notions of vortex dynamics. Two lengthscales are introduced in the form of a micro- and a macro-scale. Elementary ‘vortex objects’ are defined as two types of singular vortex filaments with equal but opposite intensities. The vorticity is considered as the macro-value proportional to the concentration of elementary vortex filaments inhabiting the micro-level. The vortex motion of a viscous medium is represented as the stochastic motion of an infinite set of elementary vortex filaments on the micro-level governed by the stochastic differential equations, where the stochastic velocity component of every filament simulates the viscous diffusion of vorticity, and the regular component is the macro-value induced according to the Biot–Savart law and simulates the convective transfer of vorticity.In flows with boundaries, the production of elementary vortex filaments at the boundary is introduced to satisfy the no-slip condition. This phenomenon is described by the application of the generalized Markov processes theory. The integral equation for the production intensity of elementary vortex filaments is derived and solved using the no-slip condition reformulated in terms of vorticity. Additional conditions on this intensity are determined to avoid the many-valuedness of the pressure in a multi-connected flow domain. This intensity depends on the vorticity in the flow and the boundary velocity at every time instant, together with boundary acceleration.As a result, the successive and accurate application of the product-integral method allows the study of vortex dynamics in a viscous fluid according to the concepts of Helmholtz and Kelvin.
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KIMURA, Y., and J. R. HERRING. "Gradient enhancement and filament ejection for a non-uniform elliptic vortex in two-dimensional turbulence." Journal of Fluid Mechanics 439 (July 23, 2001): 43–56. http://dx.doi.org/10.1017/s0022112001004529.
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The axisymmetrization of a two-dimensional non-uniform elliptic vortex is studied in terms of the growth of palinstrophy, the squared vorticity gradient. First, it is pointed out that the equation for palinstrophy growth, if written in terms of the strain rate tensor, has a similar form to that of enstrophy growth in three-dimensions – the vortex-stretching equation. Then palinstrophy production is analysed, particularly for non-uniform elliptic vortices. It is shown analytically and verified numerically that a non-uniform elliptic vortex in general has a quadrupole structure for palinstrophy production, and that in the positive production regions, vortex filaments are ejected following the gradient enhancement process for vorticity. Numerical simulations are conducted for two different initial conditions, compact support and Gaussian vorticity distributions. These are characterized by distinctly different features of filament ejection and energy spectra. For both cases, the total palinstrophy production is a good indicator of the development of small-scale vorticity. In particular for the compact support case, a possible intermittency mechanism in the filament ejection process is proposed.
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Klein, Rupert, and Omar M. Knio. "Asymptotic vorticity structure and numerical simulation of slender vortex filaments." Journal of Fluid Mechanics 284 (February 10, 1995): 275–321. http://dx.doi.org/10.1017/s002211209500036x.
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A new asymptotic analysis of slender vortices in three dimensions, based solely on the vorticity transport equation and the non-local vorticity–velocity relation gives new insight into the structure of slender vortex filaments. The approach is quite different from earlier analyses using matched asymptotic solutions for the velocity field and it yields additional information. This insight is used to derive three different modifications of the thin-tube version of a numerical vortex element method. Our modifications remove an O(1) error from the node velocities of the standard thin-tube model and allow us to properly account for any prescribed physical vortex core structure independent of the numerical vorticity smoothing function. We demonstrate the performance of the improved models by comparison with asymptotic solutions for slender vortex rings and for perturbed slender vortex filaments in the Klein–Majda regime, in which the filament geometry is characterized by small-amplitude–short-wavelength displacements from a straight line. These comparisons represent a stringent mutual test for both the proposed modified thin-tube schemes and for the Klein–Majda theory. Importantly, we find a convincing agreement of numerical and asymptotic predictions for values of the Klein–Majda expansion parameter ε as large as ½. Thus, our results support their findings in earlier publications for realistic physical vortex core sizes.
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KUVSHINOV, B. N., V. P. LAKHIN, F. PEGORARO, and T. J. SCHEP. "Hamiltonian vortices and reconnection in a magnetized plasma." Journal of Plasma Physics 59, no. 4 (June 1998): 727–36. http://dx.doi.org/10.1017/s0022377898006655.
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Hamiltonian vortices and reconnection in magnetized plasmas are investigated analytically and numerically using a two-fluid model. The equations are written in the Lagrangian form of three fields that are advected with different velocities. This system can be considered as a generalization and extension of the two-dimensional Euler equation for an ordinary fluid. It is pointed out that these equations allow solutions in the form of singular current-vortex filaments, drift-Alfvén vortices and magnetic islands, and admit collisionless magnetic reconnection where magnetic flux is converted into electron momentum and ion vorticity.
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Li, Siran. "Regularity of Desingularized Models for Vortex Filaments in Incompressible Viscous Flows: A Geometrical Approach." Quarterly Journal of Mechanics and Applied Mathematics 73, no. 3 (May 20, 2020): 217–30. http://dx.doi.org/10.1093/qjmam/hbaa008.
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Summary We establish the regularity of weak solutions for the vorticity equation associated to a family of desingularized models for vortex filament dynamics in 3D incompressible viscous flows. These generalize the classical model ‘of an allowance for the thickness of the vortices’ due to Louis Rosenhead in 1930. Our approach is based on an interplay between the geometry of vorticity and analytic inequalities in Sobolev spaces.
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Dauhajre, Daniel P., and James C. McWilliams. "Diurnal Evolution of Submesoscale Front and Filament Circulations." Journal of Physical Oceanography 48, no. 10 (October 2018): 2343–61. http://dx.doi.org/10.1175/jpo-d-18-0143.1.
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AbstractThe local circulation of submesoscale fronts and filaments can be partly understood through a horizontal momentum balance of Coriolis, a horizontal pressure gradient, and vertical diffusivity in a turbulent boundary layer, known as the turbulent thermal wind balance (TTW or T2W). T2W often reproduces the instantaneous relative vorticity and divergence of submesoscale circulations in open-ocean and shelf settings. However, a diurnal cycle in submesoscale vorticity and divergence is characterized by a non-T2W phasing: a maximum in divergence magnitude lags the maximum in vertical diffusivity (with vorticity lagging divergence). Here, an idealized model is used to solve the transient turbulent thermal wind (T3W) equations and to investigate the diurnal evolution of front and filament circulation in a 2D plane. Relative to a steady-state circulation, transient evolution can cause both instantaneous strengthening and a weaker diurnal average of the secondary circulation. The primary mechanisms controlling the diurnal variability exist in a 1D Ekman layer that imprints onto the 2D circulation. In midlatitudes, acceleration during separate phases of the diurnal cycle (from night to day and from day to night) is dominated by distinct inertial oscillation and vertically diffusive mechanisms, respectively. However, the manifestation of these dual accelerations is sensitive to latitude, boundary layer depth, and the strength of the forcing. A simple 1D model predicts the diurnal phasing of submesoscale divergence and vorticity in realistic primitive equation simulations of the southwestern Pacific and coastal California.
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ANDERSEN, TIMOTHY D., and CHJAN C. LIM. "A length-scale formula for confined quasi-two-dimensional plasmas." Journal of Plasma Physics 75, no. 4 (August 2009): 437–54. http://dx.doi.org/10.1017/s0022377809008137.
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AbstractTypically a magnetohydrodynamical model for neutral plasmas must take into account both the ionic and the electron fluids and their interaction. However, at short time scales, the ionic fluid appears to be stationary compared to the electron fluid. On these scales, we need consider only the electron motion and associated field dynamics, and a single fluid model called the electron magnetohydrodynamical model which treats the ionic fluid as a uniform neutralizing background applies. Using Maxwell's equations, the vorticity of the electron fluid and the magnetic field can be combined to give a generalized vorticity field, and one can show that Euler's equations govern its behavior. When the vorticity is concentrated into slender, periodic, and nearly parallel (but slightly three-dimensional) filaments, one can also show that Euler's equations simplify into a Hamiltonian system and treat the system in statistical equilibrium, where the filaments act as interacting particles. In this paper, we show that, under a mean-field approximation, as the number of filaments becomes infinite (with appropriate scaling to keep the vorticity constant) and given that angular momentum is conserved, the statistical length scale, R, of this system in the Gibbs canonical ensemble follows an explicit formula, which we derive. This formula shows how the most critical statistic of an electron plasma of this type, its size, varies with angular momentum, kinetic energy, and filament elasticity (a measure of the interior structure of each filament) and in particular it shows how three-dimensional effects cause significant increases in the system size from a perfectly parallel, two-dimensional, one-component Coulomb gas.
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Ragone, Francesco, and Gualtiero Badin. "A study of surface semi-geostrophic turbulence: freely decaying dynamics." Journal of Fluid Mechanics 792 (March 4, 2016): 740–74. http://dx.doi.org/10.1017/jfm.2016.116.
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In this study we give a characterization of semi-geostrophic turbulence by performing freely decaying simulations for the case of constant uniform potential vorticity, a set of equations known as the surface semi-geostrophic approximation. The equations are formulated as conservation laws for potential temperature and potential vorticity, with a nonlinear Monge–Ampère type inversion equation for the streamfunction, expressed in a transformed coordinate system that follows the geostrophic flow. We perform model studies of turbulent surface semi-geostrophic flows in a domain doubly periodic in the horizontal and limited in the vertical by two rigid lids, allowing for variations of potential temperature at one of the boundaries, and we compare the results with those obtained in the corresponding surface quasi-geostrophic case. The results show that, while the surface quasi-geostrophic dynamics is dominated by a symmetric population of cyclones and anticyclones, the surface semi-geostrophic dynamics features a more prominent role of fronts and filaments. The resulting distribution of potential temperature is strongly skewed and peaked at non-zero values at and close to the active boundary, while symmetry is restored in the interior of the domain, where small-scale frontal structures do not penetrate. In surface semi-geostrophic turbulence, energy spectra are less steep than in the surface quasi-geostrophic case, with more energy concentrated at small scales for increasing Rossby number. The energy related to frontal structures, the lateral strain rate and the vertical velocities are largest close to the active boundary. These results show that the semi-geostrophic model could be of interest for studying the lateral mixing of properties in geophysical flows.
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Stout, Eric, and Fazle Hussain. "External turbulence-induced axial flow and instability in a vortex." Journal of Fluid Mechanics 793 (March 16, 2016): 353–79. http://dx.doi.org/10.1017/jfm.2016.123.
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External turbulence-induced axial flow in an incompressible, normal-mode stable Lamb–Oseen (two-dimensional) vortex column is studied via direct numerical simulations of the Navier–Stokes equations. Azimuthally oriented vorticity filaments, formed from external turbulence, advect radially towards or away from the vortex axis (depending on the filament’s swirl direction), resulting in a net induced axial flow in the vortex core; axial flow increases with increasing vortex Reynolds number ($Re=$ vortex circulation/viscosity). This contrasts the viscous mechanism for axial flow generation downstream of a lifting body, wherein an axial pressure gradient is produced by viscous diffusion of the swirl (Batchelor, J. Fluid Mech., vol. 20, 1964, pp. 645–658). Analysis of the self-induced motion of an arbitrarily curved external filament shows that any non-axisymmetric filament undergoes radial advection. We then studied the evolution of a vortex column starting with an imposed optimal transient growth perturbation. For a range of Re values, axial flow develops and initially grows as (time)$^{5/2}$ before decreasing after two turnover times; for $Re=10\,000$ – the highest computationally achievable – axial flow at late times becomes sufficiently strong to induce vortex instability. Contrary to a prior claim of a parent–offspring mechanism at the outer edge of the core, vorticity tilting within the core by axial flow is the underlying mechanism producing energy growth. Thus, external perturbations in practical flows (at $Re\sim 10^{7}$) produce destabilizing axial flow, possibly leading to the sought-after vortex breakup.
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Tsujino, Satoki, and Hung-Chi Kuo. "Potential Vorticity Mixing and Rapid Intensification in the Numerically Simulated Supertyphoon Haiyan (2013)." Journal of the Atmospheric Sciences 77, no. 6 (May 26, 2020): 2067–90. http://dx.doi.org/10.1175/jas-d-19-0219.1.
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Abstract The inner-core dynamics of Supertyphoon Haiyan (2013) undergoing rapid intensification (RI) are studied with a 2-km-resolution cloud-resolving model simulation. The potential vorticity (PV) field in the simulated storm reveals an elliptical and polygonal-shaped eyewall at the low and middle levels during RI onset. The PV budget analysis confirms the importance of PV mixing at this stage, that is, the asymmetric transport of diabatically generated PV to the storm center from the eyewall and the ejection of PV filaments outside the eyewall. We employ a piecewise PV inversion (PPVI) and an omega equation to interpret the model results in balanced dynamics. The omega equation diagnosis suggests eye dynamical warming is associated with the PV mixing. The PPVI indicates that PV mixing accounts for about 50% of the central pressure fall during RI onset. The decrease of central pressure enhances the boundary layer (BL) inflow. The BL inflow leads to contraction of the radius of the maximum tangential wind (RMW) and the formation of a symmetric convective PV tower inside the RMW. The eye in the later stage of the RI is warmed by the subsidence associated with the convective PV towers. The results suggest that the pressure change associated with PV mixing, the increase of the symmetric BL radial inflow, and the development of a symmetric convective PV tower are the essential collaborating dynamics for RI. An experiment with 500-m resolution shows that the convergence of BL inflow can lead to an updraft magnitude of 20 m s−1 and to a convective PV tower with a peak value of 200 PVU (1 PVU = 10−6 K kg−1 m2 s−1).
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Morvan, Mathieu, Pierre L'Hégaret, Xavier Carton, Jonathan Gula, Clément Vic, Charly de Marez, Mikhail Sokolovskiy, and Konstantin Koshel. "The life cycle of submesoscale eddies generated by topographic interactions." Ocean Science 15, no. 6 (November 22, 2019): 1531–43. http://dx.doi.org/10.5194/os-15-1531-2019.
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Abstract. Persian Gulf Water and Red Sea Water are salty and dense waters flowing at intermediate depths in the Gulf of Oman and the Gulf of Aden, respectively. Their spreading pathways are influence by mesoscale eddies that dominate the surface flow in both semi-enclosed basins. In situ measurements combined with altimetry indicate that Persian Gulf Water is stirred in the form of filaments and submesoscale structures by mesoscale eddies. In this paper, we study the formation and the life cycle of intense submesoscale vortices and their potential impact on the spreading of Persian Gulf Water and Red Sea Water. We use a primitive-equation three-dimensional hydrostatic model at a submesoscale-resolving resolution to study the evolution of submesoscale vortices. Our configuration idealistically mimics the dynamics in the Gulf of Oman and the Gulf of Aden: a zonal row of mesoscale vortices interacting with north and south topographic slopes. Intense submesoscale vortices are generated in the simulations along the continental slopes due to two different mechanisms. First, intense vorticity filaments are generated over the continental slope due to frictional interactions of the background flow with the sloping topography. These filaments are shed into the ocean interior and undergo horizontal shear instability that leads to the formation of submesoscale coherent vortices. The second mechanism is inviscid and features baroclinic instabilities arising at depth due to the weak stratification. Submesoscale vortices subsequently drift away, merge and form larger vortices. They can also pair with opposite-signed vortices and travel across the domain. They eventually dissipate their energy via several mechanisms, in particular fusion into the larger eddies or erosion on the topography. Since no submesoscale flow clearly associated with the fragments of Persian Gulf Water was observed in situ, we modeled Persian Gulf Water as Lagrangian particles. Particle patches are advected and sheared by vortices and are entrained into filaments. Their size first grows as the square root of time: a signature of the merging processes. Then, it increases linearly with time, corresponding to their ballistic advection by submesoscale eddies. On the contrary, without intense submesoscale eddies, particles are mainly advected by mesoscale eddies; this implies a weaker dispersion of particles than in the previous case. This shows the potentially important role of submesoscale eddies in spreading Persian Gulf Water and Red Sea Water.
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Morvan, Mathieu, Xavier Carton, Stéphanie Corréard, and Rémy Baraille. "Submesoscale Dynamics in the Gulf of Aden and the Gulf of Oman." Fluids 5, no. 3 (August 28, 2020): 146. http://dx.doi.org/10.3390/fluids5030146.
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We have investigated the surface and subsurface submesoscale dynamics in the Gulf of Aden and the Gulf of Oman. Our results are based on the analyses of regional numerical simulations performed with a primitive equation model (HYCOM) at submesoscale permitting horizontal resolution. A model zoom for each gulf was embedded in a regional mesoscale-resolving simulation. In the Gulf of Aden and the Gulf of Oman, the interactions of mesoscale structures and fronts instabilities form submesoscale eddies and filaments. Rotational energy spectra show that the Gulf of Aden has a higher ratio of submesoscale to mesocale energy than the Gulf of Oman. Fast waves (internal gravity waves, tidal waves, Kelvin waves) and slow waves (Rossby waves) were characterized via energy spectra of the divergent velocity. Local upwelling systems which shed cold filaments, coastal current instabilities at the surface, and baroclinic instability at capes in subsurface were identified as generators of submesocale structures. In particular, the Ras al Hamra and Ras al Hadd capes in the Gulf of Oman, and the Cape of Berbera in the Gulf of Aden, are loci of submesoscale eddy generation. To determine the instability mechanisms involved in these generations, we diagnosed the Ertel potential vorticity and the energy conversion terms: the horizontal and vertical Reynolds stresses and the vertical buoyancy flux. Finally, the impacts of the subsurface submesoscale eddy production at capes on the diffusion and fate of the Red Sea Water (in the Gulf of Aden) and the Persian Gulf Water (in the Gulf of Oman) are highlighted.
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Hussain, Fazle, and Eric Stout. "Self-limiting and regenerative dynamics of perturbation growth on a vortex column." Journal of Fluid Mechanics 718 (February 8, 2013): 39–88. http://dx.doi.org/10.1017/jfm.2012.580.
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AbstractWe study the mechanisms of centrifugal instability and its eventual self-limitation, as well as regenerative instability on a vortex column with a circulation overshoot (potentially unstable) via direct numerical simulations of the incompressible Navier–Stokes equations. The perturbation vorticity (${\boldsymbol{\omega} }^{\prime } $) dynamics are analysed in cylindrical ($r, \theta , z$) coordinates in the computationally accessible vortex Reynolds number, $\mathit{Re}({\equiv }\mathrm{circulation/viscosity} )$, range of 500–12 500, mostly for the axisymmetric mode (azimuthal wavenumber $m= 0$). Mean strain generates azimuthally oriented vorticity filaments (i.e. filaments with azimuthal vorticity, ${ \omega }_{\theta }^{\prime } $), producing positive Reynolds stress necessary for energy growth. This ${ \omega }_{\theta }^{\prime } $ in turn tilts negative mean axial vorticity, $- {\Omega }_{z} $ (associated with the overshoot), to amplify the filament, thus causing instability. (The initial energy growth rate (${\sigma }_{r} $), peak energy (${G}_{\mathit{max}} $) and time of peak energy (${T}_{p} $) are found to vary algebraically with $\mathit{Re}$.) Limitation of vorticity growth, also energy production, occurs as the filament moves the overshoot outward, hence lessening and shifting $\vert {- }{\Omega }_{z} \vert $, while also transporting the core $+ {\Omega }_{z} $, to the location of the filament. We discover that a basic change in overshoot decay behaviour from viscous to inviscid occurs at $Re\sim 5000$. We also find that the overshoot decay time has an asymptotic limit of 45 turnover times with increasing $\mathit{Re}$. After the limitation, the filament generates negative Reynolds stress, concomitant energy decay and hence self-limitation of growth; these inviscid effects are enhanced further by viscosity. In addition, the filament transports angular momentum radially inward, which can produce a new circulation overshoot and renewed instability. Energy decays at the $\mathit{Re}$ studied, but, at higher $\mathit{Re}$, regenerative growth of energy is likely due to the renewed mean shearing. New generation of overshoot and Reynolds stress is examined using a helical ($m= 1$) perturbation. Regenerative energy growth, possibly resulting in even vortex breakup, can be triggered by this new overshoot at practical $\mathit{Re}$ (${\sim }1{0}^{6} $ for trailing vortices), which are currently beyond the computational capability.
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Danioux, E., J. Vanneste, P. Klein, and H. Sasaki. "Spontaneous inertia-gravity-wave generation by surface-intensified turbulence." Journal of Fluid Mechanics 699 (April 24, 2012): 153–73. http://dx.doi.org/10.1017/jfm.2012.90.
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AbstractThe spontaneous generation of inertia-gravity waves (IGWs) by surface-intensified, nearly balanced motion is examined using a high-resolution simulation of the primitive equations in an idealized oceanic configuration. At large scale and mesoscale, the dynamics, which is driven by baroclinic instability near the surface, is balanced and qualitatively well described by the surface quasi-geostrophic model. This however predicts an increase of the Rossby number with decreasing spatial scales and, hence, a breakdown of balance at small scale; the generation of IGWs is a consequence of this breakdown. The wave field is analysed away from the surface, at depths where the associated vertical velocities are of the same order as those associated with the balanced motion. Quasi-geostrophic relations, the omega equation in particular, prove sufficient to separate the IGWs from the balanced contribution to the motion. A spectral analysis indicates that the wave energy is localized around dispersion relation for free IGWs, and decays only slowly as the frequency and horizontal wavenumber increase. The IGW generation is highly intermittent in time and space: localized wavepackets are emitted when thin filaments in the surface density are formed by straining, leading to large vertical vorticity and correspondingly large Rossby numbers. At depth, the IGW field is the result of a number of generation events; away from the generation sites it takes the form of a relatively homogeneous, apparently random wave field. The energy of the IGW field generated spontaneously is estimated and found to be several orders of magnitude smaller than the typical IGW energy in the ocean.
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ELOY, CHRISTOPHE, and STÉPHANE LE DIZÈS. "Three-dimensional instability of Burgers and Lamb–Oseen vortices in a strain field." Journal of Fluid Mechanics 378 (January 10, 1999): 145–66. http://dx.doi.org/10.1017/s0022112098003103.
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The linear stability of Burgers and Lamb–Oseen vortices is addressed when the vortex of circulation Γ and radius δ is subjected to an additional strain field of rate s perpendicular to the vorticity axis. The resulting non-axisymmetric vortex is analysed in the limit of large Reynolds number RΓ=Γ/v and small strain s[Lt ]Γ/δ2 by considering the approximations obtained by Moffatt et al. (1994) and Jiménez et al. (1996) for each case respectively. For both vortices, the TWMS instability (Tsai & Widnall 1976; Moore & Saffman 1975) is shown to be active, i.e. stationary helical Kelvin waves of azimuthal wavenumbers m=1 and m=−1 resonate and are amplified by the external strain in the neighbourhood of critical axial wavenumbers which are computed. The additional effects of diffusion for the Lamb–Oseen vortex and stretching for the Burgers vortex are proved to limit in time the resonance. The transient growth of the helical waves is analysed in detail for the distinguished scaling s∼Γ/ (δ2R1/2Γ). An amplitude equation describing the resonance is obtained and the maximum gain of the wave amplitudes is calculated. The effect of the vorticity profile on the instability characteristic as well as of a time-varying stretching rate are analysed. In particular the stretching rate maximizing the instability is calculated. The results are also discussed in the light of recent observations in experiments and numerical simulations. It is argued that the Kelvin waves resonance mechanism could explain various dynamical behaviours of vortex filaments in turbulence.
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Zhao, Yaomin, Yue Yang, and Shiyi Chen. "Evolution of material surfaces in the temporal transition in channel flow." Journal of Fluid Mechanics 793 (March 23, 2016): 840–76. http://dx.doi.org/10.1017/jfm.2016.152.
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We report a Lagrangian study on the evolution of material surfaces in the Klebanoff-type temporal transitional channel flow. Based on the Eulerian velocity field from the direct numerical simulation, a backward-particle-tracking method is applied to solve the transport equation of the Lagrangian scalar field, and then the isosurfaces of the Lagrangian field can be extracted as material surfaces in the evolution. Three critical issues for Lagrangian investigations on the evolution of coherent structures using material surfaces are addressed. First, the initial scalar field is uniquely determined based on the proposed criteria, so that the initial material surfaces can be approximated as vortex surfaces, and remain invariant in the initial laminar state. Second, the evolution of typical material surfaces initially from different wall distances is presented, and then the influential material surface with the maximum deformation is identified. Large vorticity variations with the maximum curvature growth of vortex lines are also observed on this surface. Moreover, crucial events in the transition can be characterized in a Lagrangian approach by conditional statistics on the material surfaces. Finally, the influential material surface, which is initially a vortex surface, is demonstrated as a surrogate of the vortex surface before significant topological changes of vortical structures. Therefore, this material surface can be used to elucidate the continuous temporal evolution of vortical structures in transitional wall-bounded flows in a Lagrangian perspective. The evolution of the influential material surface is divided into three stages: the formation of a triangular bulge from an initially disturbed streamwise–spanwise sheet, rolling up of the vortex sheet near the bulge ridges with the vorticity intensification and the generation and evolution of signature hairpin-like structures with self-induced dynamics of vortex filaments.
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Hou, Thomas Y. "Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier–Stokes equations." Acta Numerica 18 (May 2009): 277–346. http://dx.doi.org/10.1017/s0962492906420018.
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Whether the 3D incompressible Euler and Navier–Stokes equations can develop a finite-time singularity from smooth initial data with finite energy has been one of the most long-standing open questions. We review some recent theoretical and computational studies which show that there is a subtle dynamic depletion of nonlinear vortex stretching due to local geometric regularity of vortex filaments. We also investigate the dynamic stability of the 3D Navier–Stokes equations and the stabilizing effect of convection. A unique feature of our approach is the interplay between computation and analysis. Guided by our local non-blow-up theory, we have performed large-scale computations of the 3D Euler equations using a novel pseudo-spectral method on some of the most promising blow-up candidates. Our results show that there is tremendous dynamic depletion of vortex stretching. Moreover, we observe that the support of maximum vorticity becomes severely flattened as the maximum vorticity increases and the direction of the vortex filaments near the support of maximum vorticity is very regular. Our numerical observations in turn provide valuable insight, which leads to further theoretical breakthrough. Finally, we present a new class of solutions for the 3D Euler and Navier–Stokes equations, which exhibit very interesting dynamic growth properties. By exploiting the special nonlinear structure of the equations, we prove nonlinear stability and the global regularity of this class of solutions.
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Gay-Balmaz, François, and Cesare Tronci. "The helicity and vorticity of liquid-crystal flows." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2128 (October 6, 2010): 1197–213. http://dx.doi.org/10.1098/rspa.2010.0309.
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We present explicit expressions of the helicity conservation in nematic liquid-crystal flows, for both the Ericksen–Leslie and Landau–de Gennes theories. This is done by using a minimal coupling argument that leads to an Euler-like equation for a modified vorticity involving both velocity and structure fields (e.g. director and alignment tensor). This equation for the modified vorticity shares many relevant properties with ideal fluid dynamics, and it allows for vortex-filament configurations, as well as point vortices, in two dimensions. We extend all these results to particles of arbitrary shape by considering systems with fully broken rotational symmetry.
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Golovina, V. V., E. A. Shakhova, and P. P. Rymkevich. "Condition equation of polymer filaments." Scientific and Technical Journal of Information Technologies, Mechanics and Optics 20, no. 6 (November 1, 2020): 877–82. http://dx.doi.org/10.17586/2226-1494-2020-20-6-877-882.
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Picone, J. M., and J. P. Boris. "Vorticity generation by shock propagation through bubbles in a gas." Journal of Fluid Mechanics 189 (April 1988): 23–51. http://dx.doi.org/10.1017/s0022112088000904.
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We present a new theoretical model of ‘late-time’ phenomena related to the interaction of a planar shock with a local, discrete inhomogeneity in an ambient gas. The term ‘late-time’ applies to the evolution of the inhomogeneity and the flow field after interaction with the incident shock has ceased. Observations of a shock propagating through a bubble or a spherical flame have exhibited or implied the formation of vortex structures and have showed continual distortion of the bubble or flame. Our theory shows that this is due to the generation of long-lived vorticity at the edge of the discrete inhomogeneity. The vorticity interacts with itself through the medium of the fluid, and, depending on the geometry of the discrete inhomogeneity, can roll up into vortex filaments or vortex rings. To verify and amplify this theoretical description, we use numerical solutions of the fluid equations for conservation of mass, momentum, and energy to study the interaction of a weak shock with a cylindrical or spherical bubble. The simulated bubble has either a higher or lower density than the ambient gas. In this way, the calculations provide insights into the effects of both geometry and distortion of the local sound speed. The Mach number of the shock is 1.2, the ambient gas is air, and the pressure is 1 atmosphere. Because of the simple geometry of each bubble, the vorticity generated at the boundary rolls up into a vortex filament pair (cylindrical bubble) or a vortex ring (spherical bubble). The structural features and timescales of the phenomena observed in the calculations agree closely with recent experiments of Haas & Sturtevant, in which helium and Freon bubbles were used to provide the local departures from ambient density. The discussion of results includes a survey of alternative numerical methods, sources of uncertainty in velocities of interfaces or structures, as derived from the laboratory and numerical experiments, and the relationship of our analysis to other theories.
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Fan, M., Y. Wenren, W. Dietz, M. Xiao, and J. Steinhoff. "Computing Blunt Body Flows on Coarse Grids Using Vorticity Confinement." Journal of Fluids Engineering 124, no. 4 (December 1, 2002): 876–85. http://dx.doi.org/10.1115/1.1517573.
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Over the last few years, a new flow computational methodology, vorticity confinement, has been shown to be very effective in treating concentrated vortical regions. These include thin vortex filaments which can be numerically convected over arbitrary distances on coarse Eulerian grids, while requiring only ∼2 grid cells across their cross section. They also include boundary layers on surfaces “immersed” in nonconforming uniform Cartesian grids, with no requirement for grid refinement or complex logic near the surface. In this paper we use vorticity confinement to treat flow over blunt bodies, including attached and separating boundary layers, and resulting turbulent wakes. In the wake it serves as a new, simple effective large-eddy simulation (LES). The same basic idea is applied to all of these features: At the smallest scales (∼2 cells) the vortical structures are captured and treated, effectively, as solitary waves that are solutions of nonlinear discrete equations on the grid. The method does not attempt to accurately discretize the Euler/Navier-Stokes partial differential equations (pde’s) for these small scales, but, rather, serves as an implicit, nonlinear model of the structures, directly on the grid. The method also allows the boundary layer to be effectively “captured.” In the turbulent wake, where there are many scales, small structures represent an effective small scale energy sink. However, they do not have the unphysical spreading due to numerical diffusion at these scales, which is present in conventional computational methods. The basic modeling idea is similar to that used in shock capturing, where intrinsically discrete equations are satisfied in thin, modeled regions. It is argued that, for realistic high Reynolds number flows, this direct, grid-based modeling approach is much more effective than first formulating model pde’s for the small scale, turbulent vortical regions and then discretizing them. Results are presented for three-dimensional flows over round and square cylinders and a realistic helicopter landing ship. Comparisons with experimental data are given. Finally, a new simpler formulation of vorticity confinement is given together with a related formulation for confinement of passive scalar fields.
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Demontis, F., G. Ortenzi, and C. van der Mee. "Exact solutions of the Hirota equation and vortex filaments motion." Physica D: Nonlinear Phenomena 313 (December 2015): 61–80. http://dx.doi.org/10.1016/j.physd.2015.09.009.
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Gabbay, Michael, Edward Ott, and Parvez N. Guzdar. "Reconnection of vortex filaments in the complex Ginzburg-Landau equation." Physical Review E 58, no. 2 (August 1, 1998): 2576–79. http://dx.doi.org/10.1103/physreve.58.2576.
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Jordan, S. A., and S. A. Ragab. "A Large-Eddy Simulation of the Near Wake of a Circular Cylinder." Journal of Fluids Engineering 120, no. 2 (June 1, 1998): 243–52. http://dx.doi.org/10.1115/1.2820640.
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The formation and the downstream transport of the Strouhal vortices in the near wake of a circular cylinder are investigated using the large-eddy simulation (LES) method. The governing equations are formulated in curvilinear coordinates to accommodate a nonorthogonal grid with formal development of a dynamic model to account for the subgrid turbulent scales. Results were produced with and without use of the model. The focus of the investigation is at a subcritical Reynolds number of 5600. Using the dynamic model, the LES results compared best to the published experimental data in terms of both the global and local wake characteristics such as the drag and base pressure coefficients, shedding and detection frequencies, peak vorticity, and the downstream mean velocity-defect and Reynolds stresses. The results further showed streamwise filaments that connect subsequent Strouhal vortices. Qualitatively, the time-averaged Reynolds stresses of the formation region revealed similar symmetric characteristics over the range 525 ≤ Re ≤ 140,000.
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Bembenek, Eric, Francis J. Poulin, and Michael L. Waite. "Realizing Surface-Driven Flows in the Primitive Equations." Journal of Physical Oceanography 45, no. 5 (May 2015): 1376–92. http://dx.doi.org/10.1175/jpo-d-14-0097.1.
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AbstractThe surface quasigeostrophic (SQG) model describes flows with surface buoyancy perturbations with no interior quasigeostrophic potential vorticity at small Rossby number Ro and O(1) Burger number, where quasigeostrophic dynamics are expected to hold. Numerical simulations of SQG dynamics have shown that vortices are frequently generated at small scales, which may have O(1) Rossby numbers and therefore may be beyond the limits of SQG. This paper examines the dynamics of an initially geostrophically balanced elliptical surface buoyancy perturbation in both the SQG model and the nonhydrostatic Boussinesq primitive equations (PE). In the case of very small Rossby number, it is confirmed that both models agree, as expected. For larger Ro, non-SQG effects emerge and as a result the solution of the PE deviates significantly from that of SQG. In particular, an increase in the Rossby number has the following effects: (i) the buoyancy filaments at the surface are stabilized in that they generate fewer secondary vortices; (ii) the core of the vortex experiences inertial instability, which results in a uniform buoyancy profile in its interior; (iii) the divergent part of the energy spectrum increases in magnitude; (iv) the PE model has significantly more gravity waves that are radiated from the vortex; (v) the magnitude of the vertical velocity increases; and (vi) in the mature stages of evolution, there are gravitational instabilities that develop because of the complicated dynamics inside the vortex. It is demonstrated that significant non-SQG effects are evident when the large-scale Rossby number of the initial flow is about 0.05 and the local Rossby number is O(1).
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Keener, J. P. "Knotted vortex filaments in an ideal fluid." Journal of Fluid Mechanics 211 (February 1990): 629–51. http://dx.doi.org/10.1017/s0022112090001732.
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Knotted closed-curve solutions of the equation of self-induced vortex motion are studied. It is shown that there are invariant torus knots which translate and rotate as rigid bodies. The general motion of ‘small-amplitude’ torus knots and iterated (cabled) torus knots is described and found to be almost periodic in time, and for some, but not all, initial data, the topology of the knot is shown to be invariant.
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Rousseau, Guillaume, Hugues Chaté, and Raymond Kapral. "Twisted vortex filaments in the three-dimensional complex Ginzburg–Landau equation." Chaos: An Interdisciplinary Journal of Nonlinear Science 18, no. 2 (June 2008): 026103. http://dx.doi.org/10.1063/1.2940439.
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Gabbay, Michael, Edward Ott, and Parvez N. Guzdar. "Motion of Scroll Wave Filaments in the Complex Ginzburg-Landau Equation." Physical Review Letters 78, no. 10 (March 10, 1997): 2012–15. http://dx.doi.org/10.1103/physrevlett.78.2012.
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Zou, Jing, Ying Chen Zhang, J. N. Huang, Hong Yan Wu, and Y. P. Qiu. "Preparation and Properties of PP/PLA /Multiwall Carbon Nanotube Composites Filaments Obtained by Melt Compounding." Materials Science Forum 620-622 (April 2009): 465–68. http://dx.doi.org/10.4028/www.scientific.net/msf.620-622.465.
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The present paper studied the thermal and mechanical properties of atmospheric pressure plasma jet (APPJ) treated multiwall carbon nanotubes/polypropylene/polylactic acid nanocomposite filaments. The experiments included tensile tests, differential scanning calorimeter (DSC), Scanning electron microscopy (SEM) experiments. DSC studies showed that there were a distinct shift in Tg and a relatively moderate change in Tm for different systems. The activation volumes of CNTs/PP/PLA nanocomposite filaments have been calculated to describe strain rate sensitive behavior of CNTs/PP/PLA nanocomposite filaments by following Eyring’s equation based on the tensile test results.
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Zhu, Hai Yan, Ying Chen Zhang, Jing Zou, Hong Yan Wu, and Y. P. Qiu. "The Microstructural Deformation of the Montmorillonite Particles/Polypropylene/Polylactic Acid Nanocomposite Filaments Infused with Plasma Treated Montmorillonite." Materials Science Forum 620-622 (April 2009): 469–72. http://dx.doi.org/10.4028/www.scientific.net/msf.620-622.469.
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The purpose of the present work is to investigate the microstructural deformation of the montmorillonite (MMT) particles/polypropylene (PP)/polylactic acid (PLA) nanocomposite filaments infused with plasma treated MMT. The activation volumes of the MMT/PP/PLA nanocomposite filaments ranging from 31.4572 to 151.2100 (nm)3 estimated by the Eyring’s equation quantitatively revealed that the plasma treated MMT acted as obstacles to dislocation motion during microstructural plastic deformation mechanisms. DSC analysis showed marked increases in glass transition temperature (Tg), indicating the plasma treated MMT could effectively help resist the free crankshaft movement of the macromolecular chain in the nanocomposite filaments. In addition, the MMT/PP/PLA nanocomposite filaments developed intercalated structures which had been examined by SEM.
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Zhang, Ying Chen, Jian Fei Xie, Hong Yan Wu, and Y. P. Qiu. "Crystallization and Mechanical Properties of Nano ZnO/PP/PLA Composite Filaments." Materials Science Forum 620-622 (April 2009): 485–88. http://dx.doi.org/10.4028/www.scientific.net/msf.620-622.485.
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In the present work, the effect of plasma treated ZnO nanoparticle on crystallization behavior and properties of polypropylene（PP）/ polylactic acid （PLA）composites filaments has been intensively researched. Our results show that, although the interfacial interaction between PP/PLA and nano ZnO is very weak, addition of nano ZnO and the proportional relations of PP/PLA in composites induced the increase of percent crystallinity. Tensile results showed that nano ZnO /PP/PLA nanocomposites filaments were strain rate sensitive materials and the activation volumes of the nano ZnO /PP/PLA nanocomposite filaments by following Eyring’s equation could be evaluated.
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Zhang, Ying Chen, Hai Yan Zhu, Hong Yan Wu, and Y. P. Qiu. "Nano Effects of Helium-Plasma Treatment Nano-SiO2 Sol-Gel Coating UHMWPE Filaments." Materials Science Forum 610-613 (January 2009): 714–21. http://dx.doi.org/10.4028/www.scientific.net/msf.610-613.714.
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The effects of helium-plasma treatment on tensile deformation of nano-SiO2 sol-gel coating UHMWPE filaments (HONSUHMWPE) were studied and a new concept for the nano-structural interphase between fiber surface and nano-coating was provided. The tensile test results showed that in addition to the enhanced ductility of UHMWPE filaments by nano-SiO2 sol-gel coating UHMWPE filaments treated by helium-plasma, the activation volumes of UHMWPE filaments untreated and treated with helium-plasma ranging from 1101.875 to 16603.07(nm)3 by following Eyring’s equation were important descriptors for the properties of the nano-structural interphase between fiber surface and nano-coating, From the results of SEM and FTIR, it was observed that the remarkable uniform dispersion of the nano-SiO2 coating of the UHMWPE filaments modified with helium plasma not only introduced the activated functional groups, but also formed a protective layer on the fiber surfaces.
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BESSAIH, H., and F. FLANDOLI. "LIMIT BEHAVIOUR OF A DENSE COLLECTION OF VORTEX FILAMENTS." Mathematical Models and Methods in Applied Sciences 14, no. 02 (February 2004): 189–215. http://dx.doi.org/10.1142/s0218202504003209.
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The understanding of vortex structures in 3D turbulent fluids is a basic problem. One of the questions is whether some large scale structure can emerge as the macroscopic result of the self-organization of small scale vortex filaments, similarly to the 2D case of point vortices. This paper gives a first step in this direction: a mean field result is proved for a dense collection of vortex filaments. The filaments considered here are described by stochastic processes, including Brownian motion. Under a special rescaling of the energy, a mean field result is proved for a model of 3D vortex filaments described by stochastic processes, including Brownian motion, Brownian bridge, fractional Brownian motion and other semimartingales. Propagation of chaos, variational characterization of the limit Gibbs density h and an equation for h are proved.
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Gabbay, Michael, Edward Ott, and Parvez N. Guzdar. "The dynamics of scroll wave filaments in the complex Ginzburg-Landau equation." Physica D: Nonlinear Phenomena 118, no. 3-4 (July 1998): 371–95. http://dx.doi.org/10.1016/s0167-2789(97)00321-7.
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Manzoor, Rubab, M. Adeel, and M. Saeed. "Dynamics of collapsing stellar filament and exotic matter." International Journal of Modern Physics D 29, no. 05 (March 11, 2020): 2050036. http://dx.doi.org/10.1142/s0218271820500364.
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This paper studies the collapse of stellar filaments in the presence of dark matter (DM). We use [Formula: see text] gravity to involve DM in the collapse. We apply Darmois junction conditions (DJCs) on the surface of collapsing boundary [Formula: see text] and obtain the collapse equation. The radial pressure associated with the seen matter is found to be nonzero at [Formula: see text]. We then use Starobinsky model, [Formula: see text], as a candidate of DM to obtain stability criteria (SC) of the collapsing body. It is found that the stability of filamentary structure relates radial pressure of baryonic directly with the gravitational effects of DM. Stability of polytropic family of filaments are studied by applying polytropic equation of state to baryonic contribution. For all polytropic stable filaments, it turns out that the visible matter density is exponentially linked to effects of DM. Finally, we discuss connection between exotic terms and gravitational waves (GW). It is theoretically indicated that the presence of DM can affect the GW propagation.
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Li, Lei, Harishankar Manikantan, David Saintillan, and Saverio E. Spagnolie. "The sedimentation of flexible filaments." Journal of Fluid Mechanics 735 (October 29, 2013): 705–36. http://dx.doi.org/10.1017/jfm.2013.512.
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AbstractThe dynamics of a flexible filament sedimenting in a viscous fluid are explored analytically and numerically. Compared with the well-studied case of sedimenting rigid rods, the introduction of filament compliance is shown to cause a significant alteration in the long-time sedimentation orientation and filament geometry. A model is developed by balancing viscous, elastic and gravitational forces in a slender-body theory for zero-Reynolds-number flows, and the filament dynamics are characterized by a dimensionless elasto-gravitation number. Filaments of both non-uniform and uniform cross-sectional thickness are considered. In the weakly flexible regime, a multiple-scale asymptotic expansion is used to obtain expressions for filament translations, rotations and shapes. These are shown to match excellently with full numerical simulations. Furthermore, we show that trajectories of sedimenting flexible filaments, unlike their rigid counterparts, are restricted to a cloud whose envelope is determined by the elasto-gravitation number. In the highly flexible regime we show that a filament sedimenting along its long axis is susceptible to a buckling instability. A linear stability analysis provides a dispersion relation, illustrating clearly the competing effects of the compressive stress and the restoring elastic force in the buckling process. The instability travels as a wave along the filament opposite the direction of gravity as it grows and the predicted growth rates are shown to compare favourably with numerical simulations. The linear eigenmodes of the governing equation are also studied, which agree well with the finite-amplitude buckled shapes arising in simulations.
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GRINSTEIN, FERNANDO F. "Vortex dynamics and entrainment in rectangular free jets." Journal of Fluid Mechanics 437 (June 22, 2001): 69–101. http://dx.doi.org/10.1017/s0022112001004141.
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Simulations of low-aspect-ratio, rectangular free jets are presented. The investigations focus on the entrainment and transitional vortex dynamics in compressible (subsonic) jets initialized with laminar conditions, a thin vortex sheet with slightly rounded-off corner regions, and uniform initial momentum thickness. A monotonically integrated large-eddy simulation approach based on the solution of the unsteady flow equations with high-resolution monotone algorithms is used. Inherent uncertainties in the jet entrainment measurement process are addressed using the database from laboratory experiments and simulations. Vorticity geometries characterizing the near flow field of low aspect-ratio (A) rectangular jets are demonstrated, involving: (i) self-deforming and (ii) splitting vortex rings; interacting ring and braid (rib) vortices including (iii) single ribs aligned with corner regions (A [ges ] 2) and (iv) rib pairs aligned with the corners (A = 1); (v) a more disorganized flow regime in the far jet downstream, where the rotational-fluid volume is occupied by a relatively weak vorticity background with strong, slender tube-like filament vortices filling a small fraction of the domain – as observed in fully developed turbulent flows. The near field entrainment properties of low-A rectangular jets are shown to be largely determined by the characteristic A-dependent coupling geometry of interacting rib and ring vortices and by vortex-ring axis-switching times.
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Deng, Jian Qi, Xiu Qing Zhang, Shu Zhen Shang, Zu Xin Zhao, and Yi Fu Ye. "Deformation Processing and Mechanical Properties of Cu-10Cr-0.4Zr In Situ Composite Microwires." Materials Science Forum 682 (March 2011): 89–95. http://dx.doi.org/10.4028/www.scientific.net/msf.682.89.
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The Cu-10Cr-0.4Zr in situ composite microwires were prepared by cast and cold drawing procedure. Deformation processing and mechanical properties of Cu-10Cr-0.4Zr composites were investigated. The results showed that the additional 0.4wt. %Zr in the Cu-10Cr in situ composite microwires gave birth to smaller as-cast Cr phases, which led to refined filaments in the matrix at higher drawing strains. As the drawing strains increased, the Cr filaments were constrained to fold or twist (even overlapped together) on longitudinal sections, and the Cr filaments become homogeneity and refinement at the longitudinal sections at the same time. At η=6.2, the thickness of Cr filaments reached 250-300nm, and the ultimate strength of Cu-10Cr-0.4Zr composites reached 1089 MPa. And the predicted strength using Hall-Petch equation was 1037 MPa, which was in reasonably good agreement with the observed strength (1089 MPa).
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BRACCO, ANNALISA, and JAMES C. MCWILLIAMS. "Reynolds-number dependency in homogeneous, stationary two-dimensional turbulence." Journal of Fluid Mechanics 646 (March 8, 2010): 517–26. http://dx.doi.org/10.1017/s0022112009993661.
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Turbulent solutions of the two-dimensional Navier–Stokes equations are a paradigm for the chaotic space–time patterns and equilibrium distributions of turbulent geophysical and astrophysical ‘thin’ flows on large horizontal scales. Here we investigate how homogeneous, stationary two-dimensional turbulence varies with the Reynolds number (Re) in stationary solutions with large-scale, random forcing and viscous diffusion, also including hypoviscous diffusion to limit the inverse energy cascade. This survey is made over the computationally feasible range in Re ≫ 1, approximately between 1.5 × 103 and 5.6 × 106. For increasing Re, we witness the emergence of vorticity fine structure within the filaments and vortex cores. The energy spectrum shape approaches the forward-enstrophy inertial-range form k−3 at large Re, and the velocity structure function is independent of Re. All other statistical measures investigated in this study exhibit power-law scaling with Re, including energy, enstrophy, dissipation rates and the vorticity structure function. The scaling exponents depend on the forcing properties through their influences on large-scale coherent structures, whose particular distributions are non-universal. A striking result is the Re independence of the intermittency measures of the flow, in contrast with the known behaviour for three-dimensional homogeneous turbulence of asymptotically increasing intermittency. This is a consequence of the control of the tails of the distribution functions by large-scale coherent vortices. Our analysis allows extrapolation towards the asymptotic limit of Re → ∞, fundamental to geophysical and astrophysical regimes and their large-scale simulation models where turbulent transport and dissipation must be parameterized.
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Dyachenko, S., A. C. Newell, A. Pushkarev, and V. E. Zakharov. "Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation." Physica D: Nonlinear Phenomena 57, no. 1-2 (June 1992): 96–160. http://dx.doi.org/10.1016/0167-2789(92)90090-a.
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Wang, Fumei, Fei Gu, and Bugao Xu. "Elastic Strain of PTT/PET Self-Crimping Fibers." Journal of Engineered Fibers and Fabrics 8, no. 2 (June 2013): 155892501300800. http://dx.doi.org/10.1177/155892501300800206.
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This paper studies the relationship between crimp curvatures and elastic strains of two series of PTT (Polytrimethylene terephthalate)/ PET (Polyethylene terephthalate) self-crimping fibers produced with two different spinnerets which merge PTT and PET fluids at different points. The crimp curvature is estimated based on fiber cross-sectional parameters and the polymer properties. The elastic strain, the strain associated with crimp removal, is measured directly from the stress-strain curves of the fibers. It was found that the crimp curvatures of the PTT/PET filaments in the two series increased with their PTT contents. The elastic strains of the PTT/PET filaments in each series showed a linear positive correlation with the estimated crimp curvatures. A linear equation (R=0.979) was established to predict the elastic stain from the calculated curvature for fibers in different series. This prediction equation can help to determine appropriate fiber cross section, composite ratio and distribution of the two components in the design stage of filament. The paper also shows a color image of dyed PTT/PET filaments, which is helpful in examining the interfacial morphology of the two components. Thus, the spinning method has a certain influence on the interfacial morphology of the fiber cross-section.
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Biktashev, V. N. "A Three-Dimensional Autowave Turbulence." International Journal of Bifurcation and Chaos 08, no. 04 (April 1998): 677–84. http://dx.doi.org/10.1142/s0218127498000474.
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Autowave vortices are topological defects in autowave fields in nonlinear active media of various natures and serve as centers of self-organization in the medium. In three-dimensional media, the topological defects are lines, called vortex filaments. Evolution of three-dimensional vortices, in certain conditions, can be described in terms of evolution of their filaments, analogously to that of hydrodynamical vortices in LIA approximation. In the motion equation for the filament, a coefficient called filament tension, plays a principal role, and determines qualitative long-time behavior. While vortices with positive tension tend to shrink and so either collapse or stabilize to a straight shape, depending on boundary conditions, vortices with negative tension show internal instability of shape. This is an essentially three-dimensional effect, as two-dimensional media with the same parameters do not possess any peculiar properties. In large volumes, the instability of filaments can lead to propagating, nondecremental activity composed of curved vortex filaments that multiply and annihilate in an apparently chaotic manner. This may be related to a mechanism of cardiac fibrillation.
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Zhou, Yingjie, Zhenyu Wu, Yisheng Liu, Zhong Xiang, and Xudong Hu. "Numerical and experimental study on the joint forming mechanism in the pneumatic splicing process." Textile Research Journal 89, no. 21-22 (March 18, 2019): 4512–25. http://dx.doi.org/10.1177/0040517519837731.
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This study presents an investigation on the joint forming mechanism of pneumatic splicing by numerical and experimental methods. A one-way coupling numerical model concerning interaction between fluid and filaments was established to simulate the complex motion of a flexible body in a spiral flow field. The airflow field in the splicing chamber, which contributes to longitudinal and normal aerodynamic force along a filament regarded as a digital chain composed of a series of interconnected rods, was obtained by a two-equation turbulent computational fluid dynamics model. Contact-friction behavior within filaments was also taken into consideration. An iterative algorithm was adopted to update the displacement of filaments and the corresponding aerodynamic force. A high-speed visualization test bench was built to record the sequence motion of filaments in the splicing process. The splicing mechanism within flexible filaments was identified by comparison between the experimental data and numerical results. The filament portion located in the homolateral rotating channel with respect to orifice is blown to bent by the jet airflow. It contributes to a frontal area in the axial airflow direction, causing the filament to be retracted toward its fixed end. Meanwhile, the portion in the contralateral rotating channel tries to wrap around the opposite filaments due to the spiral airflow. The interaction between filaments generates the contact force and related friction force, which commonly resists the retracting force exerted on the homolateral filament portion. The competition between the two forces determines whether the joint can be formed. Furthermore, the influence of the overlapping length on splicing behavior was discussed.
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MATSUO, YUTAKA. "HOPF TERM, LOOP ALGEBRAS AND THREE-DIMENSIONAL NAVIER-STOKES EQUATION." Modern Physics Letters A 08, no. 28 (September 14, 1993): 2677–86. http://dx.doi.org/10.1142/s0217732393003068.
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The dynamics of the three-dimensional perfect fluid is equivalent to the motion of vortex filaments or "strings." We study the action principle and find that it is described by the Hopf term of the nonlinear sigma model. The Poisson bracket structure is described by the loop algebra, for example, the Virasoro algebra or the analog of O(3) current algebra. As a string theory, it is quite different from the standard Nambu-Goto string in its coupling to the extrinsic geometry. We also analyze briefly the two-dimensional case and give some emphasis on the w1+∞ structure.
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Jones, Bernard J. T., and Rien van de Weygaert. "The structural elements of the cosmic web." Proceedings of the International Astronomical Union 11, S308 (June 2014): 219–35. http://dx.doi.org/10.1017/s1743921316009923.
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AbstractIn 1970 Zel'dovich published a far-reaching paper presenting a simple equation describing the nonlinear growth of primordial density inhomogeneities. The equation was remarkably successful in explaining the large scale structure in the Universe that we observe: a Universe in which the structure appears to be delineated by filaments and clusters of galaxies surrounding huge void regions. In order to concretise this impression it is necessary to define these structural elements through formal techniques with which we can compare the Zel'dovich model and N-body simulations with the observational data.We present an overview of recent efforts to identify voids, filaments and clusters in both the observed galaxy distribution and in numerical simulations of structure formation. We focus, in particular, on methods that involve no fine-tuning of parameters and that handle scale dependence automatically. It is important that these techniques should result in finding structures that relate directly to the dynamical mechanism of structure formation.
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Mohamed, M. G. A., HyungWon Kim, and Tae-Won Cho. "Modeling of Memristive and Memcapacitive Behaviors in Metal-Oxide Junctions." Scientific World Journal 2015 (2015): 1–16. http://dx.doi.org/10.1155/2015/910126.
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Memristive behavior has been clearly addressed through growth and shrinkage of thin filaments in metal-oxide junctions. Capacitance change has also been observed, raising the possibility of using them as memcapacitors. Therefore, this paper proves that metal-oxide junctions can behave as a memcapacitor element by analyzing its characteristics and modeling its memristive and memcapacitive behaviors. We develop two behavioral modeling techniques: charge-dependent memcapacitor model and voltage-dependent memcapacitor model. A new physical model for metal-oxide junctions is presented based on conducting filaments variations, and its effect on device capacitance and resistance. In this model, we apply the exponential nature of growth and shrinkage of thin filaments and use Simmons’ tunneling equation to calculate the tunneling current. Simulation results show how the variations of practical device parameters can change the device behavior. They clarify the basic conditions for building a memcapacitor device with negligible change in resistance.
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JIA, LAI-BING, FANG LI, XIE-ZHEN YIN, and XIE-YUAN YIN. "Coupling modes between two flapping filaments." Journal of Fluid Mechanics 581 (May 22, 2007): 199–220. http://dx.doi.org/10.1017/s0022112007005563.
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The flapping coupling between two filaments is studied theoretically and experimentally in this paper. A temporal linear instability analysis is carried out based on a simplified hydrodynamic model. The dispersion relationship between the eigen-frequency ω and wavenumber k is expressed by a quartic equation. Two special cases of flapping coupling, i.e. two identical filaments having the same length and two filaments having different lengths, are studied in detail. In the case of two identical filaments, the theoretical analysis predicts four coupling modes, i.e. the stretched-straight mode, the antisymmetrical in-phase mode, the symmetrical out-of-phase mode and the indefinite mode. The theory also predicts the existence of an eigenfrequency jump during transition between the in-phase and out-of-phase modes, which has been observed in previous experiments and numerical simulations. In the case of two filaments having different lengths, four modes similar to those in the former case are identified theoretically. The distribution of coupling modes for both the cases is shown in two planes. One is a dimensionless plane of S vs. U, where S is the density ratio of solid filament to fluid and U2 is the ratio of fluid kinetic energy to solid elastic potential energy. The other is a dimensional plane of the half-distance (h) between two filaments vs. the filament length (L). Relevant experiments are carried out in a soap-film tunnel and the stable and unstable modes are observed. Theory and experiment are compared in detail. It should be noted that the model used in our analysis is a very simplified one that can provide intuitional analytical results of the coupling modes as well as their qualitative distributions. The factors neglected in our model, such as vortex shedding, viscous and nonlinear effects, do not allow the model to predict results precisely consistent with the experiments. Moreover, the Strouhal numbers of the flapping filaments are found to be generally around a fixed value in the experiments for both cases, implying that the filaments try to maintain a lower potential energy state.
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Affes, H., Z. Xiao, and A. T. Conlisk. "The boundary-layer flow due to a vortex approaching a cylinder." Journal of Fluid Mechanics 275 (September 25, 1994): 33–57. http://dx.doi.org/10.1017/s0022112094002272.
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The three-dimensional unsteady boundary layer induced by a vortex filament moving outside a circular cylinder is considered. In the present paper, we focus attention on the situation where the inviscid flow is fully three-dimensional but is symmetric with respect to the top centreline of the cylinder. The motion of the vortex toward the cylinder leads to separation of the boundary layer; in the present work a large unsteady adverse pressure gradient develops as well. Results for the three-dimensional streamlines, the vorticity distribution, and the velocity component normal to the cylinder indicate the presence of a region of unsteady three-dimensional secondary flow structure of rather complex shape located deep within the boundary layer. Within this three-dimensional secondary flow the fluid is progressively squeezed into a narrow region under the main vortex and it is expected that a local three-dimensional jet will develop sending boundary-layer fluid out into the main stream. It is pointed out that such three-dimensional eruptive behaviour has been observed in experiments. The results indicate the development of a three-dimensional singularity in the boundary-layer equations.
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Goldsmith, K. J. A., and J. M. Pittard. "The isothermal evolution of a shock-filament interaction." Monthly Notices of the Royal Astronomical Society 491, no. 4 (December 4, 2019): 4783–801. http://dx.doi.org/10.1093/mnras/stz3320.
Full textAbstract:
ABSTRACT Studies of filamentary structures that are prevalent throughout the interstellar medium are of great significance to a number of astrophysical fields. Here, we present 3D hydrodynamic simulations of shock-filament interactions where the equation of state has been softened to become almost isothermal. We investigate the effect of such an isothermal regime on the interaction (where both the shock and filament are isothermal), and we examine how the nature of the interaction changes when the orientation of the filament, the shock Mach number, and the filament density contrast are varied. We find that only sideways-oriented filaments with a density contrast of 102 form a three-rolled structure, dissimilar to the results of a previous study. Moreover, the angle of orientation of the filament plays a large role in the evolution of the filament morphology: the greater the angle of orientation, the longer and less turbulent the wake. Turbulent stripping of filament material leading to fragmentation of the core occurs in most filaments; however, filaments orientated at an angle of 85° to the shock front do not fragment and are longer lived. In addition, values of the drag time are influenced by the filament length, with longer filaments being accelerated faster than shorter ones. Furthermore, filaments in an isothermal regime exhibit faster acceleration than those struck by an adiabatic shock. Finally, we find that the drag and mixing times of the filament increase as the angle of orientation of the filament is increased.