Random sound waves in a weakly stratified atmosphere

The influence of random mass density and velocity fields on the frequencies and amplitudes of the sound waves that propagate along a constant gravity field is examined in the limit of weak random fields, small amplitude oscillations and a weakly stratified medium. Using a perturbative method, we derive dispersion relations from which we conclude that the effect of a space-dependent random mass density field is to attenuate sound waves. Frequencies of these waves are higher than in the case of a coherent medium. A time-dependent random mass density field increases frequencies and amplifies the sounds waves. On the other hand, a space-dependent random flow reduces the wave frequencies and attenuates the sound waves. The time-dependent random flow raises the frequencies of the sound waves and amplifies their amplitudes. In the limit of the gravity-free medium the above results are in an agreement with the former findings.     

Three-dimensional vortex visualization in stratified spin-up

Abstract  

We present the results of three-dimensional time-dependent numerical simulations of incremental spin-up of a thermally stratified fluid. The fluid inside a vertical cylindrical container of radius R and height 2H is water characterized by the kinematic viscosity ν and thermal diffusivity κ. Initially, its density (temperature) varies linearly with height and is characterized by a constant buoyancy frequency N, which is proportional to the density gradient. The system undergoes an abrupt change in the rotation rate from its initial value Ω_i, when the fluid is in a solid-body rotation state, to the final value Ω_f. The aim of this contribution is to show the formation of columnar vortices in a high Rossby number spin-up flow.     

Traces of a tsunamigenic earthquake in a rotating stratified ocean

In the framework of the linear long-wave theory, we derive a system of equations that describe the potential and vortex residual hydrodynamic fields that arise in a rotating stratified (two-layer) ocean during tsunami generation by coseismic deformations of the ocean bottom. For the model case of a cylindrically symmetric ocean bottom deformation, we find an approximate analytical solution of the problem. Based on this solution, we analyze the specific features of residual fields due to the presence of stratification for conditions that are typical of real tsunami sources.     

Instabilities of Taylor columns in a rotating stratified fluid

We numerically solve for the flow in a differentially rotating spherical shell, with a stable stratification imposed along the rotation axis. The axisymmetric basic state evolves from a Stewartson layer in the unstratified limit to a Taylor column in the strongly stratified limit. For the Taylor columns, we next compute the linear onset of non-axisymmetric instabilities, and show that small (0.1) and large (10) Prandtl numbers yield very different results. For Pr=10, positive and negative differential rotations also yield fundamentally different instabilities.     

Bose-Einstein condensates with a bent vortex in rotating traps

We consider a 3D dilute Bose-Einstein condensate at thermal equilibrium in a rotating harmonic trap. The condensate wavefunction is a local minimum of the Gross-Pitaevskii energy functional and we determine it numerically with the very efficient conjugate gradient method. For single vortex configurations in a cigar-shaped harmonic trap we find that the vortex line is bent, in agreement with the numerical prediction of Garcia-Ripoll and Perez-Garcia [Phys. Rev. A 63, 041603 (2001)]. We derive a simple energy functional for the vortex line in a cigar-shaped condensate which allows to understand physically why the vortex line bends and to predict analytically the minimal rotation frequency required to stabilize the bent vortex line. This analytical prediction is in excellent agreement with the numerical results. It also allows to find in a simple way a saddle point of the energy, where the vortex line is in a stationary configuration in the rotating frame but not a local minimum of energy. Finally we investigate numerically the effect of thermal fluctuations on the vortex line for a condensate with a straight vortex: we can predict what happens in a single realization of the experiment by a Monte Carlo sampling of an atomic field quasi-distribution function of the density operator of the gas at thermal equilibrium in the Bogoliubov approximation. Received 28 March 2002 / Received in final form 13 September 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: yvan.castin@lkb.ens.fr     

Three-dimensional dynamics of a vortex array in rotating superfluid

This work studies numerically three-dimensional formation of a vortex array in a rotating cylindrical vessel. The formation process and the resulting equilibrium pattern are affected by pinning sites on the vessel’s bottom.     

Spontaneous rotating vortex lattices in a pumped decaying condensate

Injection and decay of particles in an inhomogeneous quantum condensate can significantly change its behavior. We model trapped, pumped, decaying condensates by a complex Gross-Pitaevskii equation and analyze the density and currents in the steady state. With homogeneous pumping, rotationally symmetric solutions are unstable. Stability may be restored by a finite pumping spot. However if the pumping spot is larger than the Thomas-Fermi cloud radius, then rotationally symmetric solutions are replaced by solutions with spontaneous arrays of vortices. These vortex arrays arise without any rotation of the trap, spontaneously breaking rotational symmetry.     

Partially coherent vortex beams propagation in a turbulent atmosphere

Based on the Rytov approximation and the cross-spectral density approximation for the mutual coherence function of the partially coherent field, the propagation properties of the partially coherent beams with optical vortices in turbulent atmosphere are discussed. The average intensity and the mutual coherence function of the partially coherent vortex beams propagation in weak turbulent atmosphere are obtained.It is shown that the vortex structure of the average cross-spectral density of partially coherent beams has the same helicoidally shape as that of the phase of the fully coherent Laguerre-Gauss beams in free space and the relative intensity of the beam is degraded by optical vortex.     

Over-reflection of travelling internal waves in a rotating stratified fluid

Summary It has been known for many years that waves of different kind propagating in a fluid and incident on a mean flow localized shear layer can exhibit, in the linear theory, a reflection coefficient larger than unity. When this phenomenon takes place the wave is said to be over-reflected at the shear layer. In this paper the over-reflection of inertial-gravity waves in a stratified rotating fluid in horizontal sheared motion is studied by making use of the constancy of the net vertical energy flux associated with the wave field. It is found that over-reflection can take place if some physical conditions, explicitly evaluated, are locally satisfied in the fluid. Such conditions are discussed and a comparison is carried out with the same phenomenon in a nonrotating system.

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Riassunto Si sa da molti anni che la teoria lineare di onde di diversa natura, propagantesi in un fluido ed interagenti con uno strato localizzato di shear, prevede, in alcuni casi, un coefficiente di riflessione maggiore dell'unità. Questo fenomeno prende il nome di super riflessione. In questo articolo si studia la super riflessione delle onde gravito-inerziali in un fluido stratificato in moto orizzontale con la velocità dipendente dalla sola coordinata verticale. Lo studio è portato a termine servendosi della condizione di continuità e costanza del flusso netto verticale di energia associata al campo d'onda. Si trova che la super riflessione avviene se sono soddisfatte alcune condizioni fisiche che sono esplicitamente determinate: tali condizioni sono inoltre discusse in dettaglio ed i risultati sono confrontati con quelli, classici, relativi alla propagazione di onde interne nei fluidi stratificati in assenza di rotazione.

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Резюме В течение многих лет известно, что линейная теория волн различной природы, которые распространяются в жидкости и взаимодействуют с локализованным пограничным слоем, предсказывает, что в некоторых случаях коэффициенты отражения могут превьщать единицу. Зто явление носит название супер-отражения (сверх-отражение) на пограничном слое. В этой статье исследуется супер-отражение инерциальной гравитационной волны в стратифицированной вращающейся жидкости в случаэ горизонтального движения со скоростью, зависящей только от вертикальной координаты. При рассмотрении учитывается постоянство результирующей вертикальной энергии, связанной с полем волны. Получено, что сверх-отражение может иметь место, если локально в жидкости выполняются некоторые физические условия. Проводится обсуждение этих условий и полученные результаты сравниваются с классическими результатами по распространению внутренних волн в стратифицированной жидкости в отсутствии вращения.

     

Nonlinear waves in a rotating plasma cylinder

Previous work on exact cylindrical surface waves in a nonneutral cold-electron plasma bounded by a dielectric is extended to include plasma rotation. A set of nonlinear rate equations describing the temporal behavior of the system is derived by first determining an appropriate spatial wave structure. Physically relevant periodic solutions are obtained     

Formation of a vortex lattice in a rotating BCS Fermi gas

We investigate theoretically the formation of a vortex lattice in a superfluid two-spin component Fermi gas in a rotating harmonic trap, in a BCS-type regime of condensed non-bosonic pairs. Our analytical solution of the superfluid hydrodynamic equations, both for the 2D BCS equation of state and for the 3D unitary quantum gas, predicts that the vortex free gas is subject to a dynamic instability for fast enough rotation. With a numerical solution of the full time dependent BCS equations in a 2D model, we confirm the existence of this dynamic instability and we show that it leads to the formation of a regular pattern of quantum vortices in the gas.     

Excitation spectroscopy of vortex lattices in a rotating Bose-Einstein condensate

Excitation spectroscopy of vortex lattices in rotating Bose-Einstein condensates is described. We numerically obtain the Bogoliubov-de Gennes quasiparticle excitations for a broad range of energies and analyze them in the context of the complex dynamics of the system. Our work is carried out in a regime in which standard hydrodynamic assumptions do not hold, and includes features not readily contained within existing treatments.     

Counter rotating vortex pair structure in a reacting jet in crossflow

This paper analyzes the time averaged flow structure of a reacting jet in cross flow (RJICF), emphasizing the structure of the counter-rotating vortex pair (CVP) by using simultaneous tomographic particle image velocimetry (TPIV) and hydroxyl radical planar laser induced fluorescence (OH-PLIF). It was performed to determine the extent to which heat release, and the associated effects of gas expansion and baroclinic vorticity production, impact the structure of the CVP. These results show the clear presence of a CVP in the time averaged flow field, whose trajectory lies below the jet centerline on either side of the centerplane. Consistent with other measurements of high momentum flux ratio JICF in nonreacting flows, there is significant asymmetry in strength of the two vortex cores. The strength and structure of the CVP was quantified with vorticity and swirling strength (λ_ci), showing that some regions of the flow with high shear are not necessarily accompanied by large scale bulk flow rotation and vice-versa. The OH PLIF measurement allows for correlation of the flame position with the dominant vortical structures, showing that the leeward flame branch lies slightly above, as well as, in the region between the CVP cores.     

The stability of rotating vortex patches

In this paper we examine the nonlinear and linear stability of variousrotating vortex patches. These patches include the Kirchhoff ellipse, the Kelvin waves, and the co-rotating uniformm vortices. These are achieved by using relative variational methods and spectral analysis. Thus, we extend Arnol'd's idea for stability problems in [1965, 1969] to a non-smooth symmetric setting and also relate that to the usual linear stability analysis.Supported by National Science Foundation under grant DMS-8501746Dedicated to the memory of my grandmother, Lang-Chang Lee Wan     

Nonlinear internal waves in a stratified fluid in a closed basin

Summary The problem of two layers of homogeneous inviscid incompressible fluid of density ϱ₁ and ϱ₂ (ϱ₁>ϱ₂) separated by a free surface in a closed basin is studied via a variational principle. A system of ordinary differential equations in the time variable, which approximate the original problem, is derived and discussed.

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Riassunto Si usa un principio variazionale per studiare il problema del moto di due fluidi omogenei incompressibili non viscosi di densità ϱ₁, ϱ₂ (ϱ₁>ϱ₂) separati da una superficie libera in un bacino chiuso. Dopo alcune approssimazioni si deriva e discute un sistema di equazioni differenziali ordinarie.

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Резюме С помоыью вариационного принципа исследуется проблема двух слоев однородной невязкой несжимаемой жидкости с плотностями ϱ₁ и ϱ₂ (ϱ₁>ϱ₂), раазделенных свободной поверхностью в замкнутом резервуаре. Выводится и обсуждается система обыкновенных дифференциальных уравнений по временной переменной, которая аппроксимирует исходную проблему.

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Work done under the auspices of C.N.R.-G.N.A.F.A.

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Partially supported by NSF under grant PHY77-18762.     

Finite vortex numbers and symmetric vortex structures in a rotating trapped Fermi gas in the BCS-BEC crossover

The ground state of a three-dimensional (3D) rotating trapped superfluid Fermi gas in the BCS-BEC crossover is mapped to finite N _v -body vortex states by a simple ansatz. The total vortex energy is measured from the ground-state energy of the system in the absence of the vortices. The vortex state is stable since the vortex potential and rotation energies are attractive while the vortex kinetic energy and interaction between vortices are repulsive. By combining the analytical and numerical works for the minimal vortex energy, the 2D configurations of N _v vortices are studied by taking into account of the finite size effects both on xy-plane and on z-direction. The calculated vortex numbers as a function of the interaction strength are appropriate to the renew experimental results by Zwierlein in [High-temperature superfluidity in a ultracold Fermi gas, Ph.D. thesis, Massachusetts Institute of Technology, 2006]. The numerical results show that there exist two types of vortex structures: the trap center is occupied and unoccupied by a vortex, even in the case of N _v < 10 with regular polygon and in the case of N _v ≥ 10 with finite triangle lattice. The rotation frequency dependent vortex numbers with different interaction strengths are also discussed.