Spiral density wave generation by vortices in Keplerian flows

We examine accretion disk flow under combined radial and vertical stratification utilizing a local Cartesian (or " shearing box ") approximation. We investigate both axisymmetric and nonaxisymmetric disturbances with the Boussinesq approximation. Under axisymmetric disturbances, a new dispersion relation is derived. It reduces to the Solberg–Ho¨ıland criterion in the case without vertical stratification. It shows that, asymptotically, stable radial and vertical stratification cannot induce any linear instability; Keplerian flow is accordingly stable. Previous investigations strongly suggested that the so-called bypass concept of turbulence (i.e., that fine-tuned disturbances of any inviscid smooth shear flow can reach arbitrarily large transient growth) can also be applied to Keplerian disks. We present an analysis of this process for three-dimensional plane-wave disturbances comoving with the shear flow of a general rotating shear flow under combined stable radial and vertical rotation. We demonstrate that large transient growth occurs for K 2 /k 1 1 and k 3 = 0 or k 1 ∼ k 3 , where k 1 , K 2 , and k 3 are the azimuthal, radial, and vertical components of the initial wave vector, respectively. By using a generalized " wave–vortex " decomposition of the disturbance, we show that the large transient energy growth in a Keplerian disk is mainly generated by the transient dynamics of the vortex mode. The analysis of the power spectrum of total (kinetic+potential) energy in the azimuthal or vertical directions shows that the contribution coming from the vortex mode is dominant at large scales, while the contribution coming from the wave mode is important at small scales. These findings may be confirmed by appropriate numerical simulations in the high Reynolds number regime.

Journal of Physics A: Mathematical and General, 1987

Numerical studies of two-dimensional turbulence show the importance of localised structures, both in the small scales where intermittent transfers occur and in the large scales dominated by coherent vortices. This work is an attempt to establish a more appropriate theoretical framework than the usual Fourier representation. We present a dual representation, mixing continuous field and point vortices. The difficulties arising from the redundancy of the representation are solved through a hypothesis of mutual advection. The resulting equations conserve the natural invariants of the system. As a first application, we show that introducing a weakly charged point vortex in a continuous field with quasiperiodic behaviour induces a purely Lagrangian chaos. As the point vortex grows in intensity, it becomes quasistationary and the induced phase mixing dominates the behaviour of the continuous field.

The Astrophysical Journal, 2018

Linear disturbances superposed on steady flows in nonadiabatic plasmas are analyzed. In addition to the potential modes resulting (two sound waves and a thermal mode) that are Doppler shifted, a rotational mode appears identified as an entropy-vortex wave (evw) which is carried along by the gas flow. In adiabatic flows, as well as in nonadiabatic flows, the evw always shows a null pressure disturbance. But in the second case, the wave number of the evw disturbance is fixed for the particular thermal conditions of the gas. The above holds for optically thin gases, as well as for radiating flows, if the dynamical effects of the radiation field are neglected in a first approximation. The above results allow us to calculate the dimensions of the vortex elements that are expected to be formed in nonadiabatic gas flows, particularly in hot ionized plasmas of interest in astrophysics.

Physics of Fluids, 2001

We extend the spiral vortex solution of Lundgren ͓Phys. Fluids 25, 2193 ͑1982͔͒ to compressible turbulent flows with a perfect gas. This model links the dynamical and the spectral properties of incompressible flows, providing a k Ϫ5/3 Kolmogorov energy spectrum. In so doing, a compressible spatiotemporal transformation is derived, reducing the dynamics of three-dimensional vortices, stretched by an axisymmetric incompressible strain, into a two-dimensional compressible vortex dynamics. It enables us to write the three-dimensional spectra of the incompressible and compressible square velocities in terms of, respectively, the two-dimensional spectra of the enstrophy and of the square velocity divergence, by the use of a temporal integration. Numerical results are presented from decaying direct simulations performed with 512 2 grid points; initially, the rms Mach number is 0.23, with local values up to 0.9, the Reynolds number is 700, and the ratio between compressible and incompressible square velocities is 0.1. A k Ϫ5/3 inertial behavior is seen to result from the dynamical evolution for both the compressible and incompressible three-dimensional spectra.

Dynamics of Atmospheres and Oceans, 2002

A complete theory of the linear initial-value problem for Rossby waves on a class of smooth circular vortices in both f-plane and polar-region geometries is presented in the limit of small and large Rossby deformation radius. Although restricted to the interior region of barotropically stable circular vortices possessing a single extrema in tangential wind, the theory covers all azimuthal wavenumbers. The non-dimensional evolution equation for perturbation potential vorticity is shown to depend on only one parameter, G, involving the azimuthal wavenumber, the basic state radial potential vorticity gradient, the interior deformation radius, and the interior Rossby number.

IUTAM Bookseries, 2008

An analytical theory is presented for the motion of a localized vortex in the presence of a zonal Rossby wave on the β-plane. In the framework of the equivalent-barotropic quasi-geostrophic model, the analytical method developed by Sutyrin and Flierl [Sutyrin G.G., Flierl G.R., 1994. Intense vortex motion on the β-plane: development of the beta gyres. J. Atmos. Sci. 51, 773-790] for intense vortices with piecewiseconstant potential vorticity is generalized to take into account a slowly propagating Rossby wave which modifies the background potential vorticity. The predictions of these asymptotic expansions are compared with the results of numerical simulations. The theory describes the vortex advection by the wave and the vortex drift due to the background potential vorticity gradient. The net vortex drift speed due to the wave is found to be smaller than the maximum wave velocity; this is due to the baroclinic ␤-effect and to the periodic structure of the background potential vorticity gradient. Besides known elliptical core deformations, triangular deformations are generated by the wave on the core boundary. Additionally, the planetary ␤-effect provides a predominantly westward vortex drift with nearly the same speed as the wave propagation speed. The asymptotic theory is shown to agree well the results of a numerical pseudo-spectral, high-resolution biperiodic model when the vortex velocity is much larger than the wave velocity. Both meridional and zonal vortex drifts are slightly overestimated when the wave velocity is comparable with the vortex velocity. Vortex size is shown to be more influential on vortex trajectory than the Rossby wave length. In particular, smaller vortices drift westward farther and faster than large ones. Vortex core deformations typically contain modes 2 and 3 with a stronger mode 3 component for more intense Rossby waves as predicted by theory.

2020

Dusty plasma experiments can be performed quite easily in a strong coupling regime. In our previous work [V. S. Dharodi, S. K. Tiwari, and A. Das, Physics of Plasmas 21, 073705 (2014)]PHPAEN1070-664X10.1063/1.4888882, we numerically explored such plasmas with constant density and observed the transverse shear (TS) waves from the rotating vortex. Laboratory dusty plasmas are good examples of homogeneous plasmas; however, heterogeneity (e.g., density, temperature, and charge) may be due to the existence of voids, different domains with different orientations, presence of external forces like magnetic and/or electric, size or charge imbalance, etc. Here, we examine how the density heterogeneity in dusty plasmas responds to the circularly rotating vortex monopoles, specifically, smooth and sharp cutoff. For this purpose, we have carried out a series of two-dimensional fluid simulations in the framework of the incompressible generalized hydrodynamics fluid model. The rotating vortices ar...

Physics of Plasmas, 1998

Physical Review Letters, 1999

The effect of weak inhomogeneity on spiral wave dynamics is studied within the framework of the two-dimensional complex Ginzburg-Landau equation description. The inhomogeneity gives spatial dependence to the frequency of spiral waves. This provides a mechanism for the formation of a dominant spiral domain that suppresses other spiral domains. The spiral vortices also slowly drift in the inhomogeneity, and results for the velocity are given. [S0031-9007(98)08283-0]

2008