Scale-Dependent and Self-Similar Rayleigh--Taylor and Richtmyer--Meshkov Dynamics Induced by Acceleration Varying with Length Scale

Rayleigh--Taylor (RT) and Richtmyer--Meshkov (RM) instabilities and RT/RM interfacial mixing are omnipresent in nature and technology and are often driven by variable acceleration. This work presents the detailed study of RT/RM dynamics induced by the acceleration varying as power-law with the length scale. We consider RT/RM dynamics within the framework of group theory and momentum model and find solutions for the scale-dependent dynamics and for the self-similar mixing. The effect of fluctuations on the self-similar mixing is also investigated by augmenting the momentum model with stochastic process. We find that the scale-dependent dynamics and the self-similar mixing can be RT type and RM type depending on the exponent of the acceleration power-law. For the scale-dependent dynamics the exponent value separating RT and RM subregimes approaches negative infinity, whereas for the self-similar mixing it is a finite negative value depending on the drag. Based on these results, we elaborate new theory benchmarks for future research.