3D Visualization of the separated fluid flows

For the detailed investigation of the 3D unsteady incompressible viscous separated fluid flows around a sphere (for 200≤Re≤700) and a circular cylinder (for 200≤Re≤400) the direct numerical simulation and 3D visualization are used. For 3D visualization of the fluid flows around a sphere the definition of vortex core as a connected region containing two negative eigenvalues of theS ²+Ω ² tensor is used (whereS _i,j andΩ _ij are the rate of strain and the rate of rotation tensors). The formation mechanism of vortices in the sphere wake for Re=500 is described in detail. For 3D visualization of the fluid flows around a circular cylinder the 3D isosurfaces of the streamwise component of vorticity ω _x are used.     

Conservation laws for a vortex in a compressible nonequilibrium medium

The problem of conservation of magnitudes is considered for a vortex in a relaxing compressible medium. Heat release due to the relaxation of a nonequilibrium medium leads to the propagation of compression waves, which remove material. Traditional integrals of motion are inapplicable in this case. We pro-pose the concept of integral quantity, which is conserved with an arbitrary degree of accuracy despite the fact that waves cross the boundary of the integration domain. Based on this concept, a broad class of conservation laws is derived for axisymmetric disturbances of columnar vortices, including conservation of the circulation and total angular momentum of the vortex. For nonaxisymmetric disturbances, it is shown that the total angular momentum and properly defined energy integral are conserved. Numerical verification of the derived conservation laws is performed and the perspectives for using these conservation laws in numerical simulations are discussed.     

Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials

It is known that optical-lattice (OL) potentials can stabilize solitons and solitary vortices against the critical collapse, generated by cubic attractive nonlinearity in the 2D geometry. We demonstrate that OLs can also stabilize various species of fundamental and vortical solitons against the supercritical collapse, driven by the double-attractive cubic-quintic nonlinearity (however, solitons remain unstable in the case of the pure quintic nonlinearity). Two types of OLs are considered, producing similar results: the 2D Kronig-Penney “checkerboard”, and the sinusoidal potential. Soliton families are obtained by means of a variational approximation, and as numerical solutions. The stability of all families, which include fundamental and multi-humped solitons, vortices of oblique and straight types, vortices built of quadrupoles, and supervortices, strictly obeys the Vakhitov-Kolokolov criterion. The model applies to optical media and BEC in “pancake” traps.     

Viscoelastic effects on asymmetric two‐dimensional vortex patterns in a strongly coupled dusty plasma

Strongly coupled dusty plasma medium is often described as a viscoelastic fluid that retains its memory. In a flowing dusty plasma medium, vortices of different sizes appear when the flow does not remain laminar. The vortices also merge to transfer energy between different scales. In the present work, we study the effect of viscoelasticity and compressibility over a localized vortex structure and multiple rotational vortices in a strongly coupled viscoelastic dusty plasma medium. In case of single rotating vortex flow, a transverse wave is generated from the localized vortex source and the evolution time of generated waves is found to be reduced due to finite viscoelasticity and compressibility of the medium. It is found that the viscoelasticity suppresses the dispersion of vorticity. In the presence of multiple vortices, we find, the vortex mergers get highly affected in the presence of memory effect of the fluid, and thus the dynamics of the medium gets completely altered compared to a non‐viscoelastic fluid. For a compressible fluid, viscoelasticity dampens the energy in the sonic waves generated in the medium. Thus a highly viscoelastic and compressible fluid, in some cases, behaves similarly to an incompressible viscoelastic fluid. The wave‐front like rings propagate in elliptical orbits keeping the footprint of the earlier position of the point‐vortex. The rings collide with each other even within the patch vortex region forming regions of high vorticity at the point of intersection and pass through each other.     

Statistics of two-dimensional point vortices and high-energy vortex states

Results from the theory ofU-statistics are used to characterize the microcanonical partition function of theN-vortex system in a rectangular region for largeN, under various boundary conditions, and for neutral, asymptotically neutral, and nonneutral systems. Numerical estimates show that the limiting distribution is well matched in the region of major probability forN larger than 20. Implications for the thermodynamic limit are discussed. Vortex clustering is quantitatively studied via the average interaction energy between negative and positive vortices. Vortex states for which clustering is generic (in a statistical sense) are shown to result from two modeling processes: the approximation of a continuous inviscid fluid by point vortex configurations; and the modeling of the evolution of a continuous fluid at high Reynolds number by point vortex configurations, with the viscosity represented by the annihilation of close positive-negative vortex pairs. This last process, with the vortex dynamics replaced by a random walk, reproduces quite well the late-time features seen in spectral integration of the 2d Navier-Stokes equation.     

Soaring interfaces, vortices and vortex systems inside the internal waves wake past the horizontally moving cylinder in a continuously stratified fluid

The flow pattern around a horizontal cylinder towed at constant velocity along isopycnic plane in a continuously stratified liquid is visualized by conventional techniques of “Vertical slit-Foucault’s knife”, “Maksoutov’s slit-thread” and “horizontal slit-regular grating”. Using sensitive high-resolution methods allows detail studying such component of stratified flow structures as soaring interfaces, singular soaring vortices and vortex systems, which arise directly inside the internal waves field past the cylinder. These flow elements having high level of vorticity are separated from the downstream wake by a strip of fluid without any small-scale inhomogeneities. Formation of singular vortex dipoles on leading edges of soaring interfaces is investigated in details in a wide range of flow parameters.     

Comment on vortex mass and quantum tunneling of vortices

Vortex mass in Fermi superfluids and superconductors and its influence on quantum tunneling of vortices are discussed. The vortex mass is essentially enhanced due to the fermion zero modes in the core of the vortex: the bound states of the Bogoliubov quasiparticles localized in the core. These bound states form the normal component, which is nonzero even in the low-temperature limit. In the collisionless regime ω ₀ τ≫1 the normal component trapped by the vortex is unbound from the normal component in a bulk superfluid/superconductor and adds to the inertial mass of the moving vortex. In a d-wave superconductor the vortex mass has an additional factor of (B _c2/B)^1/2 due to the gap nodes. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 2, 201–206 (25 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Cherenkov interaction of vortices with a free surface

The interaction of vortex filaments in an ideal incompressible fluid with the free surface of the latter is investigated in the canonical formalism. A Hamiltonian formulation of the equations of motion is given in terms of both canonical and noncanonical Poisson brackets. The relationship between these two approaches is analyzed. The Lagrangian of the system and the Poisson brackets are obtained in terms of vortex lines, making it possible to study the dynamics of thin vortex filaments with allowance for finite thickness of the filaments. For two-dimensional flows exact equations of motion describing the interaction of point vortices and surface waves are derived by transformation to conformal variables. Asymptotic steady-state solutions are found for a vortex moving at a velocity lower than the minimum phase velocity of surface waves. It is found that discrete coupled states of surface waves above a vortex are possible by virtue of the inhomogeneous Doppler effect. At velocities higher than the minimum phase velocity the buoyant rise of a vortex as a result of Cherenkov radiation is described in the semiclassical limit. The instability of a vortex filament against three-dimensional kink perturbations due to interaction with the “image” vortex is demonstrated. Zh. éksp. Teor. Fiz. 115, 894–919 (March 1999)     

Magnetic vortices and thermoelectric effect in a hollow superconducting cylinder

The question of a surface barrier which determines the behavior of a vortex in a hollow superconducting cylinder of finite thickness in an external magnetic field is discussed, taking into account magnetic flux quantization in the cavity. The behavior of magnetic vortices in a hollow superconductor in the presence of a thermoelectric current is also considered. Pairs of magnetic vortices with opposite magnetic field orientations (vortex-antivortex pairs) are generated by this current near T _c. The thermoelectric current drives the antivortex (the vortex with oppositely directed field) out of the cylinder, whereas the vortex is ejected into the cavity and remains on the inside cylinder surface as a current. The number of magnetic flux quanta trapped inside the cylinder increases by one. The relation of this mechanism to the “giant” thermoelectric effect in hollow superconductors is discussed. Zh. éksp. Teor. Fiz. 111, 2175–2193 (June 1997)     

Hydrodynamic impulse in a compressible fluid

A suitable expression for hydrodynamic impulse in a compressible fluid is deduced. The development of appropriate impulse formulation for compressible Euler equations confirms the propriety of the hydrodynamic impulse expression for a compressible fluid given here. Implications of the application of this formulation to a compressible vortex ring are pointed out. Extension of Benjamin's variational characterization of a moving axisymmetric vortex system to a compressible fluid is explored.     

Analysis of the merger between plasma vortices in a Penning trap

In the paper, the interaction between a finite-size vortex of constant density and a weak, pointlike vortex in a Penning trap is studied analytically. A suitable Fourier representation for the contour of the finite vortex is considered and a model for small perturbations, which is linear with respect to the Fourier coefficients, is deduced. The resonance condition for the surface modes and a sufficient condition for the merger of the vortices not to occur are obtained. The validity of the analytic results is checked with a contour dynamics code making use of a new methodology developed by the authors. Numerical results referred to a case of strongly-interacting vortices are also reported.Received: 18 April 2003, Published online: 12 August 2003PACS: 52.27.Jt Nonneutral plasmas - 52.35.We Plasma vorticity - 47.32.Cc Vortex dynamicsA. DAngola: Present address: Universitá della Basilicata, Dipartimento di Ingegneria e Fisica dellambiente, Contrada Macchia Romana, 85100 Potenza, Italy.     

Visualization of two-dimensional vortex flows in thin oscillating liquid films

A possibility of visualizing flows using random inhomogeneities of film thicknesses of different colors as particles for visualization is shown on an example of a vortex flow structure in an oscillating thin liquid film. Formation of vortex flows in a thin liquid film containing surface-active substances is investigated in experiments. The film is fixed horizontally along the edges of the cell vibrating in the vertical direction. Spatially homogeneous oscillations of the liquid film can excite different types of waves that generate two-dimensional vortex flows due to nonlinearity. We present results of experimental investigation of the structure of vortex flows in a thin film (0.5–10 μm) with rectangular boundaries. It has been revealed that, if the horizontal size of an inhomogeneous region is much smaller than the size of vortices, the inhomogeneities are transported by vortices and their interference pattern can be used for visualization of vortex flows.     

可压缩流动离散涡方法

推导了可压缩流动旋涡动力学基本方程,并分析了其基本性质。如同不可压流动,在可压缩流动中旋涡同样具有场与物质两重特征。得出了可压缩流中的旋涡诱导速度公式,对Ｂｉｏｔ－Ｓａｖａｒｔ方程进行了可压缩修正。基于Ｌａｇｒａｎｇｉａｎ框架下的粒子方法,求解可压缩流中的胀量项,从而用离散涡模型求解了非定常、不稳定、可压缩流场。数值实验验证了提议的计算方法有效性。并分析了可压缩流动中旋涡运动的特征,与不可压流动的差别。     

Fluid particle advection in the vicinity of the Föppl vortex system

Fluid particle advection in the vicinity of the Föppl vortex system is considered. Due to periodic motion of vortices about the Föppl equilibrium, fluid particles within the vortex atmosphere, the fluid region with a velocity field being induced by the vortices, can move chaotic in the sense of exponential divergence of near trajectories. This chaotic motion leads to the vortex atmosphere particles to be carried away from the atmosphere to the exterior flow. In this Letter, the part of the carried away fluid particles is numerically assessed and the dynamics of the fluid release from the vortex atmosphere is demonstrated.     

Anisotropy of the vortex structure and resistivity in the basal plane of YBa<Subscript>2</Subscript>Cu<Subscript>4</Subscript>O<Subscript>8</Subscript> single crystals

The vortex lattice of the YBa₂Cu₄O₈ high-temperature superconductor is studied in the basal plane of monocrystalline samples using the decoration technique in a field interval of 40–600 Oe. Vortex lattice anisotropy (field-independent “compression” of a regular hexagonal vortex cell in the poorly conducting direction by a factor of about 1.3) is detected. Resistivity anisotropy ρ _a /ρ _b measured at temperatures from T _c to room temperature is 16–9. Possible reasons for the discrepancy between our results and the available data are discussed.     

Distributed two-dimensional boundary-layer receptivity to non-stationary vortical disturbances in the presence of surface roughness

The distributed (over the longitudinal coordinate) excitation of two-dimensional (2D) Tollmien — Schlichting (TS) waves by weak non-stationary free-stream vortices propagating along the edge of the laminar boundary layer developing over a surface with small-amplitude 2D roughness is examined. The vorticity vector of the free-stream vortices was oriented over the span of the model, i. e., did not depend on the transverse coordinate. The theoretical analysis of the excitation mechanism reported in [1] was refined to develop, around it, a procedure making it possible to experimentally determine the coefficients of distributed vortical receptivity of the flow and the coefficients of “vortex-roughness” receptivity by fitting the experimental distributions with analytical solutions. Under conditions with controllable excitation of disturbances, a detailed hot-wire study of free-stream disturbances and boundary-layer disturbances at several vortex frequencies and at several surface-roughness periods was performed, and the shape of the controllable surface roughness was measured. The point-source method was employed to experimentally examine the characteristics of linear three-dimensional (3D) stability of the flow to TS waves, necessary for determination of the coefficients of distributed receptivity. It was found that the free-stream vortices with transverse orientation of the vorticity vector excited boundary-layer TS waves via two receptivity mechanisms: (a) on the smooth surface (due to natural non-uniformity of the flow) and (b) during interaction of the vortices with the surface roughness. The developed approach was used to experimentally estimate the amplitudes and phases of the coefficients of both types of distributed vortical receptivity as dependent on problem parameters. The absolute values of both types of receptivity coefficients were found to rapidly grow in value with increasing vortex frequency. It is shown that the most efficient excitation of TS waves is observed in the situation with satisfied resonance conditions for streamwise vortex, surface-roughness, and TS-wave streamwise wavenumbers, resulting in strong deviation of the increments of the TS waves from the linear-stability increments. Under no-resonance conditions, only amplitude beats of boundary-layer disturbances were observed. This work was financialy supported by the Russian Foundation for Basic Research (Grant No. 03-01-00299).     

Relativistic vortex dynamics in axisymmetric stationary perfect fluid configuration

Relativistic formulation of Helmholtz’s vorticity transport equation is presented on the basis of Maxwell-like version of Euler’s equation of motion. Entangled characteristics associated with vorticity flux conservation in a vortex tube and in a stream tube are displayed on basis of Greenberg’s theory of spacelike congruence of vortex lines and \(1+1+(2)\) decomposition of the gradient of fluid’s 4-velocity. Vorticity flux surfaces are surfaces of revolution about the rotation axis and are rotating with fluid’s angular velocity due to gravitational isorotation in a stationary axisymmetric perfect fluid configuration. Fluid’s angular velocity, angular momentum per baryon, injection energy, and invariant rotational potential are constant on such vorticity flux surfaces. Gravitation causes distortion of coaxial cylindrical vorticity flux surfaces in the limit of post-Newtonian approximation. The rotation of the fluid with angular velocity relative to vorticity flux surfaces generates swirl which causes the stretching of material vortex lines being wrapped on vorticity flux surfaces. Fluid helicity which is conserved in the fluid’s rest frame does not remain conserved in a locally nonrotating frame because of the existence of swirl. Vortex lines are twist free in the absence of meridional circulations, but the twisting of spacetime due to dragging effect leads to the increase in vorticity flux in a vortex tube.     

Propagation of orifice- and nozzle-generated vortex rings in air

The effect of the exit geometry of a vortex ring generator was studied experimentally. Two types of exit geometries were chosen: an orifice and a nozzle. Vortex rings were generated by pushing a solenoid-valve-controlled, pressurized-air jet through the circular opening of the orifice or nozzle. Experiments were performed over a wide range of initial Reynolds number (450≤Re≤4580) and length-to-diameter ratio (0.7≤L/D≤7.0) of the air jet. The exit geometry was found to significantly influence the entire course of propagation of the vortex ring. The orifice-generated vortex ring had superior characteristics to that produced by the nozzle under the same conditions. The vorticity generated along the wall in the orifice exit plane had a negligible effect on the circulation of the vortex ring within the specified range of Reynolds number. Compared to the nozzle-generated vortex ring, the orifice-generated ring showed reduced initial vorticity losses and less diffusive entrainment of ambient fluid. The vortex rings produced by the orifice attained more circulation, less entrainment of ambient fluid and hence rapidly propagated through longer distances in comparison to the nozzle-generated rings.     

Physics of the amplification of vortex disturbances in shear flows

The physics of the linear mechanism of the amplification of vortex disturbances in shear flows, which is due to the nonorthogonality of the eigenfunctions of the problem in the linear dynamics, is described. To obtain the clearest and simplest picture, a parallel flow with a linear velocity shear is studied, and the vortex disturbances are represented in the form of plane waves — spatial Fourier harmonics. On this level our physical approach is consonant with the nonmodal mathematical analysis of linear processes in shear flows, which has been actively cultivated in the last few years. The physics presented explains the non-monotonic growth of vortex disturbances in time at the linear stage of evolution. Moreover, being universal, the “language” employed in this work can also be used to describe the amplification of potential (acoustic) disturbances. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 7, 517–522 (10 April 1996)