Invariance of Two-Dimensional Rayleigh-Taylor Instability Species Profile on Atwood Number

The turbulent mixing induced by Rayleigh-Taylor instability exists widely in nature and engineering applications. When a light fluid is on a heavy fluid under gravity acceleration, the system is balanced but unstable. However, when there are perturbations at the interface, the heavy fluid penetrates into the light fluid (spikes) and the light fluid penetrates into the heavy fluid (bubbles). The system loses its balance. This process is called Rayleigh-Taylor instability. The species profile shows the composition of fluid at any time and at any height. With the computational fluid dynamics software CFD², the dependence of mass fraction profile of heavy fluid on Atwood number was studied by two-dimensional numerical simulations at different density ratios (i.e., Atwood number=0.1, 0.5, 0.9). The normalized mass fraction profiles with the height of bubbles and spikes show that the mass fraction profile of heavy fluid is independent on Atwood number. At different density ratios, the mass fraction profile follows the same law:f_m~\frac12\mathop\rm erf\nolimits \left( 4\left( \fracy-h_\rmsh_\rmb-h_\rms-\frac12 \right) \right) + \frac12.