[en] Time dependent vortex solutions for the Hasegawa-Mima equation with convection and viscous dissipation are presented. The exact solution with viscous dissipation shows a decay of vortex amplitude with time. The amplitude and size of the vortex are shown to decrease as a function of time using multiple time scale analysis. Finally a strained vortex solution is obtained considering a vortex which is embedded in an elliptical flow. The solutions exhibit features which are qualitatively similar to their counterpart in incompressible fluid-dynamics presented by Lundgren. The vortex scales are shown to be time dependent. Given a two-dimensional solution as an initial condition, solutions can be obtained as a function of stretched coordinates in time. The solution displays the evolution of vorticity in turbulent magnetized plasma-which may be a possible model for intermittency. (author). 5 refs

No abstract available

[en] Recent experiments and computer simulations have shown that the probability distribution function (PDF) of density and potential fluctuations associated with two-dimensional Rayleigh--Taylor turbulence in collisionless plasmas, may be exhibiting significant non-gaussian features. A possible interpretation of these results is that nonlinearly saturated coherent structures are formed which are however transient, because they are themselves unstable to fine scale secondary instabilities. An analytical investigation has been carried out to investigate some of these effects. The two- dimensional nonlinear equations describing the Rayleigh--Taylor turbulence are analytically solved; a dipole vortex solution has been obtained and its stability to secondary perturbations examined. Results show that there is a significant growth of the secondary perturbation due to ellipticity of the vortex. copyright 1995 American Institute of Physics

[en] The stability of elliptical vortex flow to the excitation of low-frequency electrostatic drift waves is investigated. It is demonstrated that finite ellipticity of flow drives the secondary instability of drift/drift-acoustic waves. When flow ellipticity is small, certain matching conditions between the rotation frequency and secondary wave frequency are needed for instability to occur. The case of large eccentricity is solved by asymptotic methods and gives a growth rate for the instability that depends logarithmically on eccentricity. Such secondary instability mechanisms can act as a sink of vortex energy (limiting the vortex condensation at the long-wavelength end) and thereby help in our understanding of nonlinear saturation of low-frequency instabilities. copyright 1996 American Institute of Physics

[en] One of the puzzles of the nonlinear theory of low frequency instabilities in a fusion plasma (such as drift instabilities, Kelvin - Helmholtz instabilities etc.) is that the energy accumulates at the long wavelength end where there are no obvious sinks of energy. One is thus often left with large vortex flows which may also have significant ellopticity. In this paper we have analysed the stability of such flows to secondary perturbations with short parallel wavelength. We demonstrate that the flow ellipticity can drive secondary instabilities of shear Alfven waves provided certain resonance conditions between the rotation speed and the Doppler shifted secondary wave frequency are satisfied. Such secondary processes can act as major sinks of energy and thereby help in our understanding of the nonlinear saturation of low frequency instabilities. (author). 6 refs, 1 fig

[en] Numerical and analytical investigations of the two dimensional gravitation induced Rayleigh Taylor instability are carried out to understand some recent experimental observations on the BETA device. The primary emphasis is on the study of the fluctuation statistics and the possible mechanisms of intermittency in the turbulence. (authors)

[en] In this paper the stability of long scale vortex flows to secondary perturbations with short parallel wavelength is analyzed. It is demonstrated that flow ellipticity can drive secondary instabilities of ion-acoustic and shear Alfven waves provided certain resonance conditions between the rotation speed and the Doppler shifted secondary wave frequency are satisfied. Such secondary processes can act as a major sink of energy and may help in our understanding of nonlinear saturation of low frequency instabilities. copyright 1995 American Institute of Physics

[en] The properties of electrostatic transverse shear waves in a strongly coupled dusty plasma are examined using the nonlinear version of the generalized hydrodynamic equation. In the kinetic limit, it is shown that strongly coupled plasmas support localized dipolar vortexlike solutions with amplitude modulated periodically.

[en] The well known Jeans instability is studied for a viscoelastic gravitational fluid using generalized hydrodynamic equations of motions. It is found that the threshold for the onset of instability appears at higher wavelengths in a viscoelastic medium. Elastic effects playing a role similar to thermal pressure are found to lower the growth rate of the gravitational instability. Such features may manifest themselves in matter constituting dense astrophysical objects.

[en] The properties of electrostatic transverse shear waves propagating in a strongly coupled dusty plasma with an equilibrium density gradient are examined using the generalized hydrodynamic (GH) equation. In the usual kinetic limit, the resulting equation has similarity to zero energy Schrodinger's equation. This has helped in obtaining some exact eigenmode solutions in both Cartesian and cylindrical geometries for certain nontrivial density profiles. The corresponding velocity profiles and the discrete eigenfrequencies are obtained for several interesting situations and their physics discussed.