The effect of magnetic field on the nonlinear growth rate of Rayleigh -Taylor instability induced two fluid interfacial structures has been investigated. The magnetic field is assumed to be parallel to the plane of the two fluid interface and acts in a direction perpendicular to the wave vector. If magnetic field is restricted only to either side of the interface the growth rate may be depressed (may almost disappear) or be enhanced depending on whether the magnetic pressure on the interface opposes the instability driving pressure difference g(ρ h − ρ l )y or acts in the same direction. If magnetic field is present on both sides of the two fluid interface, stabilization * e-mail: mrgupta − cps@yahoo.co.in † e-mail: laba.kanta@yahoo.com ‡ e-mail: phy.sou82@gmail.com § e-mail: mkhan − ju@yahoo.com 1 may also take place in the sense that the surface of separation undulates periodically when the force due to magnetic pressure on two sides are such as to act in opposite direction. This result differs from the classical linear theory result which predicts that the magnetic field parallel to the surface has no influence on the growth rate when the wave vector is perpendicular to its direction.2

The combined effect of viscosity and vorticity on the growth rate of the bubble associated with single mode Rayleigh -Taylor instability is investigated. It is shown that the effect of viscosity on the motion of the lighter fluid associated with vorticity accumulated inside the bubble due to mass ablation may be such as to reduce the net viscous drag on the bubble exerted by the upper heavier fluid as the former rises through it. *

A nonlinear formulation is presented to deal with the combined action of Rayleigh-Taylor and Kelvin-Helmholtz instabilities as well as combined Ricthmyer-Meshkov and Kelvin-Helmholtz instabilities at the two fluid interface under the influence of viscosity and consequent shear flow. Using Layzer's model, the development of the interfacial structures like bubbles is investigated analytically and numerically. It is found that the growth and normal velocity of the structures are dependent on the relative velocity shear and the kinematic coefficient of viscosity of both the fluids. Both the bubble growth and growth rate are reduced significantly for fluids of higher viscosity coefficient with small velocity shear difference. It is also observed that, for viscous fluids, the transverse velocity of the perturbed interface becomes slower under certain conditions.

Shock induced symmetric compression has been studied in a spherical target. The shock induced interfacial radius will shrink and would reach a minimum point during implosion situation. However, after implosion the plasma tries to expand in blow off/explosion situation and as a result the interfacial radius will increase. Effects of plasma parameters like density and temperature have been studied numerically. It is seen that the density increases many times due to the mass conservation in imploding situation of a compressible shell like ICF. However, temperature will change rapidly due to change of inner density and so would be the pressure of compressible fluid following adiabatic law. Our analytical results agree qualitatively with those of simulation results in spherical geometry and also experimental observations conducted in cylindrical container.

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