Anisotropic geophysical vortices

A survey is made of many types of coherent vortices in the Earth's ocean and atmosphere. These vortices often occur with strong, environmentally induced anisotropy in their velocity and vorticity fields. We propose a definition of the essential characteristics of coherent vortices and formulate hypotheses concerning their dynamical role in complex, anisotropic fluid motions. Finally, we analyze numerical solutions both for uniformly rotating, stably stratified three-dimensional flow and for two-dimensional flow for the phenomena of enstrophy cascade and dissipation, intermittency, isotropy in the appropriate coordinate frame, coherent vortex emergence, vortex population dynamics, and approach to a nonturbulent end state.     

Horseshoe vortices in inhomogeneous flows

The formation of a horseshoe-shaped vortex from an initial straight cylindrical vortex occurring in the viscous layer of a retarding fluid flow in a channel with a nonuniform cross section is studied experimentally. The spatial bends of the vortex filament and the effect of the ambient fluid pressure first form an arch with supports at the bottom of the channel, then a horseshoe-shaped vortex, and finally a circular vortex with the destruction of the supports.     

Drift waves and counter rotating vortices in pair-ion plasmas

Linear dispersion relation has been found for drift and acoustic waves in pair-ion-electron plasmas. The stationary solution in the form of counter rotating vortices has been obtained in the presence of equilibrium potential profile. It is noticed that the speed of nonlinear structures is reduced with the increase of electrons concentration in pair-ion plasmas. Linear instability condition has also been found in the presence of shear flow. It is pointed out that the present results can be useful for future pair-ion plasma experiments.     

Dominant vortices in impinging jet flows

A novel method of flow visualization by dye was used in conjunction with numerical solutions to investigate the formation stages of large stationary vortical motions located in the “trajectory bend” centers of impinging jet flows. The vortices dominate the flowfield and were found to have profound influence on the wall transport phenomena. Depending on the value of Reynolds number, four regimes were identified with different flow character.     

Dust vortices, clouds, and jets in nuclear-induced plasmas

The collective movement of dust particles in a plasma formed during deceleration of decay products of californium nuclei in neon is investigated experimentally. For the first time, compact vortex structures containing a large number of coagulating dust particles and dense dust clouds evolving in time are observed. Dust formations have clearly defined boundaries and particles in them form ordered liquid-type structures. Under steady-state conditions, dust structures exist from several minutes to hours. An increase in the voltage applied to the high-voltage electrode leads to the formation of dust particle jets. A change in the electric field configuration transforms the structures from one type to another. A strong recombination of electrons and ions at dust particles is observed. The momentum transfer from ions drifting in an external field to gas molecules is studied using the Monte Carlo method. It is shown that the transferred momentum is so large that it may cause a gas flow. The characteristic features of vortex flow in neon and in air are explained.     

Formation and dynamics of dark solitons and vortices in quantum electron plasmas

We present simulation studies of the formation and dynamics of dark solitons and vortices in quantum electron plasmas. The electron dynamics in the latter is governed by a pair of equations comprising the nonlinear Schr?dinger and Poisson system of equations, which conserves the number of electrons as well as their momentum and energy. The present governing equations in one spatial dimension admit stationary solutions in the form a dark envelope soliton. The dynamics of the latter reveals its robustness. Furthermore, we numerically demonstrate the existence of cylindrically symmetric two-dimensional quantum electron vortices, which survive during collisions. The nonlinear structures presented here may serve the purpose of transporting information at quantum scales in ultracold micromechanical systems and dense plasmas, such as those created during intense laser-matter interactions.     

On the stability of geophysical flows

Summary The stability of the solution of two-dimensional stationary Euler equations for rotating flows with a constant Coriolis force is studied. An Arnold theorem in which some sufficient conditions for the stability are given was used for this purpose. This theorem can be applied to a large class of geophysical flows.

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Riassunto Si è studiata la stabilità delle soluzioni per le equazioni di Eulero stazionarie bidimensionali nel caso di un flusso in rotazione con una forza di Coriolis costante. A tal fine si è fatto uso di un teorema, dovuto ad Arnold, nel quale sono date le condizioni sufficienti per la stabilità del moto. Questo teorema può essere applicato ad una vasta classe di flussi geofisici.

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Work supported by a CNR grant. Progetto Finalizzato Oceanografia.     

Convection driven zonal flows and vortices in the major planets

The dynamical properties of convection in rotating cylindrical annuli and spherical shells are reviewed. Simple theoretical models and experimental simulations of planetary convection through the use of the centrifugal force in the laboratory are emphasized. The model of columnar convection in a cylindrical annulus not only serves as a guide to the dynamical properties of convection in rotating sphere; it also is of interest as a basic physical system that exhibits several dynamical properties in their most simple form. The generation of zonal mean flows is discussed in some detail and examples of recent numerical computations are presented. The exploration of the parameter space for the annulus model is not yet complete and the theoretical exploration of convection in rotating spheres is still in the beginning phase. Quantitative comparisons with the observations of the dynamics of planetary atmospheres will have to await the consideration in the models of the effects of magnetic fields and the deviations from the Boussinesq approximation.     

Zonal flows in tokamak plasmas with toroidal rotation

Zonal flows in tokamak plasmas with toroidal rotation are theoretically investigated. It is found that the low-frequency branch of zonal flows, which is linearly stable in a nonrotating system, becomes linearly unstable in a rotating tokamak, and that the high-frequency branch of zonal flows, the geodesic acoustic mode, can propagate in the poloidal direction with the frequency significantly lower than the frequency of the standing wave geodesic acoustic mode in the nonrotating system.     

Spin vortices and stationary spin flows in a normal Fermi liquid

We solve the equations for the collisionless spin dynamics of a normal Fermi liquid, which describe structures resembling spin vortices coherently precessing in a uniform magnetic field. We examine their stability and relaxation, and consider various regimes of stationary magnetization transport along a channel. Zh. éksp. Teor. Fiz. 114, 1266–1283 (October 1998)     

Is the Abrikosov model applicable for describing electronic vortices in plasmas?

A new model of electronic vortices in plasma is studied. The model assumes that the profile of the Lagrangian invariant I, equal to the ratio I=Ω/n of the electronic vorticity to the electron density, is given. The proposed approach takes into account the magnetic Debye scale r _B ≃B/4πen, which leads to breakdown of plasma quasineutrality. It is shown that the Abrikosov singular model cannot be used to describe electron vortices in plasmas because of the fundamental limitation on the electron vorticity on the axis of a vortex in a plasma. Analysis of the equations shows that in the model considered for the electronic vorticity, the total magnetic flux decreases when the size r ₀ of the region in which I≠0 becomes less than c/ω_pe (ω_pe is the electron plasma frequency). For ω _pe r ₀/c≪1, an electronic vortex is formed in which the magnetic flux decreases as r ₀ ² and the inertial component predominates in the electronic vorticity. The structure arising as ω _pe r ₀/c⇒0 is a narrow “hole” in the electron density, which can be identified from the spectrum of electromagnetic waves in this region. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 461–466 (10 April 1998)     

Geodesic acoustic modes and zonal flows in toroidally rotating tokamak plasmas

The effect of equilibrium toroidal rotation on the rotational eigen-modes in large aspect ratio tokamak is studied. The case of equilibrium with uniform plasma density on magnetic surfaces is considered. It is shown that the toroidal rotation results in a frequency up-shift of ordinary Geodesic Acoustic Modes. A new unstable low frequency branch of the continuum modes is found. This mode appears as a consequence of the non-uniform plasma pressure created by the centrifugal force on the magnetic surfaces. This mode represents a linear eigen-mode counterpart of Zonal Flow modes. It is shown that the growth rate of such a mode increases with the increase of the angular velocity of toroidal rotation.     

Post-solitons and electron vortices generated by femtosecond intense laser interacting with uniform near-critical-density plasmas

Generation of nonlinear structures, such as stimulated Raman side scattering waves, post-solitons and electron vortices, during ultra-short intense laser pulse transportation in near-critical-density (NCD) plasmas is studied by using multi-dimensional particle-in-cell (PIC) simulations. In two-dimensional geometries, both P- and S-polarized laser pulses are used to drive these nonlinear structures and to check the polarization effects on them. In the S-polarized case, the scattered waves can be captured by surrounding plasmas leading to the generation of post-solitons, while the main pulse excites convective electric currents leading to the formation of electron vortices through Kelvin-Helmholtz instability (KHI). In the P-polarized case, the scattered waves dissipate their energy by heating surrounding plasmas. Electron vortices are excited due to the hosing instability of the drive laser. These polarization dependent physical processes are reproduced in two different planes perpendicular to the laser propagation direction in three-dimensional simulation with linearly polarized laser driver. The current work provides inspiration for future experiments of laser-NCD plasma interactions.     

Slow integral manifolds for Lagrangian fluid dynamics in unsteady geophysical flows

The authors consider Lagrangian motion of fluid particles in unsteady gravity currents in geophysical flows. The vertical motion of fluid particles, especially the induced vertical mixing in these currents, is partially responsible for the ocean thermohaline circulation, and thus plays a role in the global climate dynamics.First, a reduced dynamic system for slow variables is derived for a nonautonomous multiscale system. The reduced system, still nonautonomous, is the original system restricted to a centre-like nonautonomous invariant manifold (so-called slow manifold) which holds slow motions of the system. An algorithm is also presented to obtain an approximation of the nonautonomous slow manifold. A novelty here is that the reduction principle applies to nonautonomous multiscale systems which satisfy conditions that are true only locally in space (as in many physical cases). This makes the reduction principle applicable to real physical systems.Then, this invariant manifold reduction principle is applied to an approximate conceptual Lagrangian model of gravity currents and a reduced nonautonomous system for slow vertical motion is obtained. This reduced system may be useful as a conceptual tractable tool for understanding some features of vertical mixing in unsteady gravity currents.     

Spatial resolution analysis of planar PIV measurements to characterise vortices in turbulent flows

The effects of spatial resolution of planar particle image velocimetry (PIV) on vortex size, swirling strength, circulation and population density characterisation are analysed using a series of experimental and numerical databases. The databases comprise a PIV database of an adverse-pressure-gradient turbulent boundary layer (APG TBL), a PIV database of a zero-pressure-gradient (ZPG) TBL in streamwise-wall-normal planes and streamwise-wall-normal slices of a direct numerical simulation (DNS) of a ZPG TBL. The effects of interrogation window and mesh sizes on the vortex parameters are analysed in the outer region of these flows using different qualitative and quantitative approaches. The quantitative analysis mainly capitalises on the possibility of mimicking the PIV data-sets with the DNS one. These approaches allow us to not only isolate the effects of mesh size and the interrogation window size but also to deduce the combined effects of other measurement errors in PIV. Typical values of mesh size and interrogation window size (0.01–0.03 of the boundary layer thickness) and typical levels of measurement uncertainties have significant effects on the vortex parameters. Moreover, each PIV error source affects the vortex parameters in different and frequently opposite manners. Hence, an optimal selection of measurement parameters such as the interrogation window size is indispensable in order to minimise the effects of spatial resolution and other measurement errors on the vortex parameters. Guidelines are presented in the Conclusions section of this paper. Finally, it is found that all the vortex parameters, when averaged across the outer region, are reasonably comparable in the ZPG and APG TBLs despite the fact that these are very different flows.     

Nonlinear generation of sheared flows and zonal magnetic fields by electron whistlers in plasmas

The nonlinear generation of shear field and flow in whistler waves is considered. It is shown that a coherent parametric process leads to modulational instability of four waves whistler interaction. Growth rates for the flow/field are compared with published simulation results.