Finite-thickness effect of the fluids on bubbles and spikes in Richtmyer–Meshkov instability for arbitrary Atwood numbers

This paper investigates the finite-thickness effect of two superimposed fluids on bubbles and spikes in Richtmyer–Meshkov instability(RMI) for arbitrary Atwood numbers by using the method of the small parameter expansion up to the second order. When the thickness of the two fluids tends to be infinity, our results can reproduce the classical results where RMI happens at the interface separating two semi-infinity-thickness fluids of different densities. It is found that the thickness has a large influence on the amplitude evolution of bubbles and spikes compared with those in classical RMI. Based on the thickness relationship of the two fluids, the thickness effect on bubbles and spikes for four cases is discussed. The thickness encourages(or reduces)the growth of bubbles or spikes, depending on not only Atwood number, but also the relationship of the thickness ratio of the heavy and light fluids, which is explicitly determined in this paper.

Magnetohydrodynamic Kelvin-Helmholtz instability for finite-thickness fluid layers

We have derived the analytical formulas for the Kelvin-Helmholtz instability(KHI)of two superposed finite-thickness fluid layers with the magnetic field effect into consideration.The linear growth rate of KHI will be reduced when the thickness of the fluid with large density is decreased or the thickness of fluid with small density is increased.When the thickness and the magnetic field act together on the KHI,the effect of thickness is more obvious when the magnetic field intensity is weak.The magnetic field transition layer destabilizes(enforces)the KHI,especially in the case of small thickness of the magnetic field transition layer.When considering the effect of magnetic field,the linear growth rate of KHI always decreases after reaching the maximum with the increase of total thickness.The stronger the magnetic field intensity is,the more obvious the growth rate decreases with the total thickness.Thus,it should be included in applications where the effect of fluid thickness on the KHI cannot be ignored,such as in double-cone ignition scheme for inertial confinement fusion.

Linear Growth of Rayleigh-Taylor Instability of Two Finite-Thickness Fluid Layers

The linear growth of Ftayleigh-Taylor instability （FtTI） of two superimposed finite-thickness fluids in a gravita- tional field is investigated analytically. Coupling evolution equations for perturbation on the upper, middle and lower interfaces of the two stratified fluids are derived. The growth rate of the RTI and the evolution of the amplitudes of perturbation on the three interfaces are obtained by solving the coupling equations. It is found that the finite-thickness fluids reduce the growth rate of perturbation on the middle interface. However, the finite-thickness effect plays an important role in perturbation growth even for the thin layers which will cause more severe RTI growth. Finally, the dependence of the interface position under different initial conditions are discussed in some detail.