Evolution of Rayleigh-Taylor instability under interface discontinuous acceleration induced by radiation

Rayleigh-Taylor instability (RTI) under radiation background is commonly found in both engineering applications and natural phenomena. In the optically thin and incompressible limit, the corresponding problem can be simplified as an interface discontinuous acceleration (IDA) RTI problem, but to date has only been studied in the linear stage. In this paper, the entire IDA-RTI evolution was studied numerically and theoretically, particularly for the stages beyond the linear stage. The results show that the IDA-RTI problem is equivalent to the classical RTI with the effective acceleration $g_{\mathrm{eff}}^{*}$ that is introduced in this work. Moreover, our studies further show that IDA-RTI can occur if and only if $g_{\mathrm{eff}}^{*}>0$ (from heavy fluid to light fluid). This criterion means that IDA-RTI can occur when (i) heavy fluid supports (or accelerates) the light fluid or (ii) the two fluids have the same density, in contrast to the classical RTI problem. Moreover, the quasisteady bubble and spike velocities are theoretically predicted with quantitative accuracy, showing good agreement with the results of numerical simulations in a wide range of density ratios and acceleration configurations.

Figure 1

Evolution of the dimensionless (a) bubble velocity ${\mathrm{Fr}}_B\equiv u_B^{*}/\sqrt{{\frac{A}{1+A}{\overline{g}}^{*}{\lambda }^{*}}^{\phantom{\int }}}$ and (b) spike velocity ${\mathrm{Fr}}_S\equiv u_S^{*}/\sqrt{{\frac{A}{1-A}{\overline{g}}^{*}{\lambda }^{*}}^{\phantom{\int }}}$ with time $t\equiv t^{*}\sqrt{{\frac{A{\overline{g}}^{*}}{(1+A){\lambda }^{*}}}^{\phantom{{\int }^0}}}$ at different $A$ and $A_g$. Here 0.461, 0.326, and 0.230 are the quasisteady ${\mathrm{Fr}}_B$ and ${\mathrm{Fr}}_S$ calculated by Eq. (32) for $A_g=-0.5$, 0, and $A$, respectively.

Figure 2

Mass fraction $Y_1$ and dimensionless $y$-direction velocity $u_2\equiv u_2^{*}/\sqrt{{\frac{A}{1+A}{\overline{g}}^{*}{\lambda }^{*}}^{\phantom{\int }}}$ for $A=0.3$ and (a) $A_g=-0.15$, (b) $A_g=0$, and (c) $A_g=0.3$ at the same bubble height $H_B\approx 0.5$.

Figure 3

Evolution of dimensionless (a) bubble velocity ${\mathrm{Fr}}_B^{\prime }=u_B^{*}/\sqrt{{\frac{A}{1+A}{g}_{\mathrm{eff}}^{*}{\lambda }^{*}}^{\phantom{\int }}}$ and (b) spike velocity ${\mathrm{Fr}}_B^{\prime }=u_B^{*}/\sqrt{{\frac{A}{1+A}{g}_{\mathrm{eff}}^{*}{\lambda }^{*}}^{\phantom{\int }}}$ with time $t^{\prime }=t^{*}\sqrt{{\frac{A{g}_{\mathrm{eff}}^{*}}{(1+A){\lambda }^{*}}}^{\phantom{{\int }^0}}}$ and at different $A$ and $A_g$.

Figure 4

Evolution of dimensionless bubble velocity ${\mathrm{Fr}}_B^{\prime }=u_B^{*}/\sqrt{\frac{A+A_g}{1+A}{\overline{g}}^{*}{\lambda }^{*}}$ and spike velocity ${\mathrm{Fr}}_S^{\prime }=u_S^{*}/\sqrt{\frac{A+A_g}{1-A}{\overline{g}}^{*}{\lambda }^{*}}$ with time $t^{\prime }=t^{*}\sqrt{\frac{(A+A_g){\overline{g}}^{*}}{(1+A){\lambda }^{*}}}$ for (a) the $A=0.1$, $A_g=-0.3$, and ${\overline{g}}^{*}<0$ case and the classical RTI case with $A=0.1$ and (b) the $A=0$ and $A_g=0.3$ case and the classical RTI case with $A=0.1$.