Expansion-compression motions in the single-mode Rayleigh-Taylor instability.

In order to study the influence of compressibility on Rayleigh-Taylor (RT) instability, we used a high-order central compact finite difference scheme to numerically simulate the late-time evolution of two-dimensional single-mode compressible Rayleigh-Taylor instability for isothermal background stratification. The simulations were presented for different stratification strengths, corresponding to different isothermal Mach numbers ($M)$ at Atwood numbers ($A_{t} )$ 0.1 and 0.5. We studied the solenoidal component and compressible component of the velocity field employing the Helmholtz decomposition. At low Mach number, the expansion-compression motion is very weak and flow field is close to the incompressible state. For the case of $A_{t} \mbox{=}0.1$ and $M\mbox{=}0.5$, the rising light fluid expands and the falling heavy fluid is compressed, but the expansion and compression motions are weak. The expansion-compression motion at $A_{t} \mbox{=}0.5$ is significantly stronger than that at $A_{t} \mbox{=}0.1$ for the same Mach number $M\mbox{=}0.5$ in the mixing zone. The fluid outside the mixing zone also has stronger expansion and compression at $A_{t} \mbox{=}0.5$. The expansion motion inside the bubble can promote the development of the bubble.