Snezhana I. Abarzhi ^1,2*

• ¹ University of Western Australia, Perth, Australia
• ² California Institute of Technology, Pasadena, California, United States

Unstable interfaces govern many processes in fluids, plasmas, materials, in nature and technology. In distinct physical environments, the interface dynamics exhibit similar characteristics and couple micro to macro scales. Our work establishes the rigorous theory examining the classical problem of the dynamics of an interface with mass and energy fluxes under destabilizing accelerations. We consider thermally conducting fluids in the low Mach regime with weak compressibility prevailing over thermal transport. We find the attributes of perturbation waves, solve the boundary value problem, and identify the flow fields structure, the interface perturbations growth, and the interface velocity. The interface dynamics is stabilized primarily by the inertial mechanism and is unstable when the acceleration exceeds a threshold. The thermal heat flux provides extra stabilizations, seeds energy perturbations, creates the vortical field in the bulk, and rescales the interface velocity. Our results agree with experiments in plasmas and complex fluids and with contained turbulence experiments. We outline extensive benchmarks for experiments and simulations, and chart future research directions.