P. K. Bhatia

Larmor radius effects on the instability of a rotating layer of a self-gravitating plasma

abstractThe instability of a stratified layer of a self-gravitating plasma has been studied to include jointly the effects of viscosity, Coriolis forces and the finite Larmor radius (FLR). For a plasma permeated by a uniform horizontal magnetic field, the stability analysis has been carried out for a transverse mode of wave propagation. The solution has been obtained through variational methods for the case when the direction of axis of rotation is along the magnetic field. The analysis for the case when the direction of rotation is transverse to the magnetic field has also been considered and the solutions for this case have been obtained through integral approach. The dispersion relations have been derived in both the cases and solved numerically. It is found that both the viscous and FLR effects have a stabilizing influence on the growth rate of the unstable mode of disturbance. Coriolis forces are found to have stabilizing influence for small wave numbers and destabilizing for large wave numbers.

Rayleigh-Taylor instability of two viscous superposed rotating and conducting fluids

The instability of the plane interface separating two viscous fluids superposed one over the other has been investigated to include simultaneously the effects of Coriolis forces and the finiteness of the ion Larmor radius. The relevant linearized perturbation equations have been solved by employing the normal mode technique and the solutions have been obtained when the fluids are assumed to be permeated by a uniform horizontal magnetic field. For the case of two highly viscous fluids, the dispersion relation has been derived and is numerically solved. It is found that the Coriolis forces have a destabilizing influence on the potentially unstable arrangement of the fluids while the effects of viscosity and the finiteness of the Larmor radius have a stabilizing influence on the system.

Rayleigh-Taylor instability of a viscous compressible plasma of variable density

A study has been made of the problem of the Rayleigh-Taylor instability of a hydromagnetic plasma of varying density to investigate the influence of the simultaneous presence of the effects of compressibility and viscosity. The solution is shown to be characterized by a variational principle. Based on the variational principle proper solutions have been obtained for a semi-infinite plasma, in which the density has a one-dimensional gradient along the direction of a uniform vertical magnetic field, confined between two planes. Both the viscosity and magnetic field are found to have a stabilizing influence. The effect of compressibility is found to be destabilizing.

Rayleigh-Taylor instability of a stratified hall plasma in two-dimensional horizontal magnetic field

The effects of Hall currents and viscosity have been investigated on the Rayleigh-Taylor instability of an incompressible infinitely conducting stratified plasma permeated by a two-dimensional horizontal magnetic field. A variational principle is shown to characterize the problem. Making use of existence of the variational principle, proper solutions have been obtained for a semi-infinite plasma in which density varies exponentially along the vertical. The dispersion relation has been derived and solved numerically. It is found that Hall currents have destabilizing influence while viscosity has stabilizing influence on the growth rate of unstable modes of disturbance.

Magnetic resistivity and Hall currents effects on the stability of a self-gravitating plasma of varying density in variable magnetic field

The effect of Hall currents have been studied on the instability of a stratified layer of a self-gravitating finitely conducting plasma of varying density. It is assumed that the plasma is permeated by a variable horizontal magnetic field stratified vertically. The stability analysis has been carried out for longitudinal mode of wave propagation. The solution has been obtained through integral equation approach. The dispersion relation has been derived and solved numerically. It is found that both the Hall currents and finite conductivity have a destabilizing influence on the growth rate of the unstable mode of disturbance.

Kelvin-Helmholtz instability of two viscous superposed rotating and conducting fluids

Kelvin-Helmholtz instability of the interface separating two viscous rotating-conducting fluids has been studied in the presence of finite ion-Larmor radius (FLR) effects. Emloying the normal mode technique, the solutions have been obtained when the fluids are assumed to be permeated by a uniform horizontal magnetic field. For the case of two highly viscous fluids, the dispersion relation has been derived and solved numerically. It is found that the streaming velocity has a stabilizing influence on the potentially unstable arrangement of the fluids. The viscosity and FLR effects are also found to have a stabilizing influence while the Coriolis forces have a destabilizing influence on the system.

The rayleigh-taylor instability of a stratified rotating fluid through a porous medium in a two-dimensional magnetic field

The effect of finite conductivity on the Rayleigh-Taylor instability of an incompressible, viscous rotating fluid through a porous medium has been studied in the presence of a two-dimensional horizontal magnetic field. It has been shown that the solution is characterized by a variational principle. By making use of the existence of the variational principle, proper solutions have been obtained for a semi-infinite fluid in which density has a one-dimensional (exponential) vertical stratification. The dispersion relation has been derived and solved numerically. It is found that finite resistivity and porosity have a destabilizing effect on the Rayleigh-Taylor instability while rotation has a stabilizing effect.

Instability of a gravitating partially-ionized plasma

The effect of Hall currents and collision with neutrals on the instability of a horizontal layer of a self-gravitating partially-ionized plasma of varying density have been studied. It is assumed that the plasma is permeated by a variable horizontal magnetic field stratified vertically. A variational principle is shown to characterize the problem. By making use of the existence of the variational principle, proper solutions have been obtained for a semi-infinite plasma in which density has a one-dimensional (exponential) vertical stratification. The dispersion relation has been derived and solved numerically. It is found that the collisions with neutrals have a stabilizing influence while Hall currents have a destabilizing influence.

Oscillatory convection in a viscoelastic fluid layer in hydromagnetics.

A study is made of the overstable mode of convection in an infinite horizontal layer of a viscoelastic fluid, heated from below, in the presence of a magnetic field. It is shown first that the problem is characterized by a variational principle. Proper solutions are then obtained for the case of two rigid boundaries using the variational method. It is found that the magnetic field has a stabilizing effect on the thermally induced overstability in a viscoelastic fluid, as in the case of an ordinary viscous fluid. The thermodynamic significance of the variational principle is also considered.

Instability of partially-ionized superposed plasmas

The stability of the plane interface separating two viscous superposed partially-ionized plasmas of uniform densities has been studied. The whole system is assumed to be immersed in a uniform two-dimensional horizontal magnetic field and the stability analysis has been carried out through the normal mode technique. The dispersion relation has been derived for the case of two superposed plasmas of equal kinematic viscosities. The dispersion relation has been solved numerically for different values of the physical parameters involved. It is found that viscosity and collision frequency of ionized plasmas both have stabilizing influence on the growth rate of the unstable mode of disturbance.