Atwood-number dependence of the instability evolution at a shock-accelerated heavy fluid layer

Numerical simulations and theoretical analysis are conducted to investigate the Atwood-number dependence of perturbation evolution in a shocked heavy fluid layer. For layers without reverberating waves, a higher Atwood number of one interface significantly enhances its coupling effect on the perturbation growth at the opposite interface. A theoretical model incorporating the startup, linear and nonlinear stages is developed to predict the interface mixing width. Dimensionless formulae are derived, identifying eight distinct modulation regimes of multi-interface instability. When reverberating waves are present, the individual effects of the upstream ( $A_1$ ) and downstream ( $A_2$ ) Atwood numbers are examined. The model is further modified to account for additional reverberating waves required at higher $A_2$ values for accurate amplitude prediction. Both theory and simulations demonstrate that perturbation growth at one interface can be actively controlled by adjusting the Atwood number of the opposite interface. These findings provide insights for mitigating instabilities in applications such as inertial confinement fusion through appropriate material selection.