Bubble

Incompressible flow

Compressibility

Turbulence

Rayleigh–Taylor instability

Biology

Shock (circulatory)

Dormancy

Mach number

Operating system

Seed dormancy

Computer science

Botany

Classical mechanics

Thermodynamics

Physics

Stratification (seeds)

Instability

Optics

Rayleigh scattering

Internal medicine

Medicine

Stratified flow

Richtmyer–Meshkov instability

Mechanics

Mode (computer interface)

Germination

Number density

Physics of Fluids

In order to study the effect of compressibility on Rayleigh-Taylor (RT) instability, we numerically simulated the late-time evolution of two-dimensional single-mode RT instability for isothermal background stratification with different isothermal Mach numbers and Atwood numbers (At) using a high-order central compact finite difference scheme. It is found that the initial density stratification caused by compressibility plays a stabilizing role, while the expansion-compression effect of flow plays a destabilizing role. For the case of small Atwood number, the density difference between the two sides of the interface is small, and the density distribution of the upper and lower layers is nearly symmetrical. The initial density stratification plays a dominant role, and the expansion-compression effect has little influence. With the increase in the Atwood number, the stabilization effect of initial density stratification decreases, and the instability caused by the expansion-compression effect becomes more significant. The flow structures of bubbles and spikes are quite different at medium Atwood number. The effect of compressibility on the bubble velocity is strong at large At. The bubble height is approximately a quadratic function of time at potential flow growth stage. The average bubble acceleration is nearly proportional to the square of Mach number at At = 0.9.

Effects of compressibility and Atwood number on the single-mode Rayleigh-Taylor instability