M. S. Janaki

Viscosity gradient-driven instability of 'shear mode' in a strongly coupled plasma

The influence of the viscosity gradient (due to shear flow) on low-frequency collective modes in a strongly coupled dusty plasma is analyzed. It is shown that for a well-known viscoelastic plasma model, the velocity shear-dependent viscosity leads to instability of the shear mode. The inhomogeneous viscous force and velocity shear coupling supply the free energy for the instability. The combined strength of the shear flow and viscosity gradient dominates over any stabilizing force and makes the shear mode unstable. The implications of this novel instability and its applications are briefly described.

Jeans instability in a viscoelastic fluid

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.

Relaxation in electron-positron plasma: a possibility

Abstract For a non-relativistic electron–positron plasma the possibility of obtaining a relaxed state is explored. The Euler–Lagrange equations are obtained by minimizing the hyper-resistivity with generalized helicities and magnetofluid energy as the constraints. The relaxed state is shown to be morphologically similar to the steady-state equilibria of the electron–positron plasma system.

Nonlinear evolution of ion-acoustic waves in unmagnetized plasma

In a fluid description large amplitude electrostatic ion-acoustic waves have been studied in an unmagnetized plasma using Lagrangian variables. We obtained solutions for ion-acoustic waves with nontrivial space and time dependence. The non-dispersive solutions demonstrate that under well defined initial and boundary conditions the amplitude of the solutions decreases indicating a new class of nonlinear solutions that lead to short lived structures.

Shear wave vortex solution in a strongly coupled dusty plasma

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.

Dissipative relaxed states in two-fluid plasma with external drive

In this work the principle of minimum dissipation rate is applied to an externally driven two-fluid plasma. The definition of generalized helicity has been modified to a gauge invariant form to incorporate open systems. The relaxed state is represented by a double-curl equation and supports nonzero flow. In the limit of vanishingly small dissipation, the equation is shown to retain the double-curl form that represents a steady state configuration supported by a two-fluid plasma.

Field-reversed configuration (FRC) as a minimum-dissipative relaxed state

Abstract The field-reversed configuration (FRC) with a completely null toroidal field and finite plasma beta is shown to result from a relaxation mechanism based on the principle of minimum dissipation of energy.

Tokamak, reversed field pinch and intermediate structures as minimum-dissipative relaxed states

The principle of minimum energy dissipation rate is utilized to develop a unified model for relaxation in toroidal discharges. The Euler–Lagrange equation for such relaxed states is solved in toroidal coordinates for an axisymmetric torus by expressing the solutions in terms of Chandrasekhar–Kendall (C–K) eigenfunctions analytically continued in the complex domain. The C–K eigenfunctions are hypergeometric functions that are solutions of the scalar Helmholtz equation in toroidal coordinates in the large-aspect-ratio approximation. Equilibria are constructed by assuming the total current J=0 at the edge. This yields the eigenvalues for a given aspect-ratio. The most novel feature of the present model is that solutions allow for tokamak, low-q as well as reversed field pinch-like behavior with a change in the eigenvalue characterizing the relaxed state.

Nonlinear shear wave in a non Newtonian visco-elastic medium

An analysis of nonlinear transverse shear wave has been carried out on non-Newtonian viscoelastic liquid using generalized hydrodynamic model. The nonlinear viscoelastic behavior is introduced through velocity shear dependence of viscosity coefficient by well known Carreau-Bird model. The dynamical feature of this shear wave leads to the celebrated Fermi-Pasta-Ulam problem. Numerical solution has been obtained which shows that initial periodic solutions reoccur after passing through several patterns of periodic waves. A possible explanation for this periodic solution is given by constructing modified Korteweg de Vries equation. This model has application from laboratory to astrophysical plasmas as well as in biological systems.

Shear flow instability in a strongly coupled dusty plasma.

Linear stability analysis of strongly coupled incompressible dusty plasma in presence of shear flow has been carried out using the generalized hydrodynamical (GH) model. With the proper Galilean invariant GH model, a nonlocal eigenvalue analysis has been done using different velocity profiles. It is shown that the effect of elasticity enhances the growth rate of shear flow driven Kelvin- Helmholtz (KH) instability. The interplay between viscosity and elasticity not only enhances the growth rate but the spatial domain of the instability is also widened. The growth rate in various parameter space and the corresponding eigenfunctions are presented.