Interface dynamics in ideal and realistic fluids

Interface and mixing and their non-equilibrium kinetics and dynamics couple micro to macro scales. They are ubiquitous to occur in fluids, plasmas and materials, over scales of celestial to atoms. The understanding of interfaces and mixing has crucial importance for science, mathematics and technology. Stellar evolution, plasma fusion, reactive fluids, purification of water, and nano-fabrication are a few examples of many processes to which dynamics of interfaces is directly relevant. This talk yields the theory of interface stability to rigorously solve a singular boundary value problem at a freely evolving unstable discontinuity – a task even more challenging than the Millennium problem on the Navier-Stokes equation. We directly link the structure of macroscopic flow fields with microscopic interfacial transport, quantify the contributions of macro and micro stabilization mechanisms to interface stability, and discover fluid instabilities never previously discussed. In ideal and realistic fluids, the interface stability is set primarily by the interplay of the macroscopic inertial mechanism balancing the destabilizing acceleration, whereas microscopic thermodynamics create vortical fields in the bulk. By linking micro to macro scales, the interface is the place where balances are achieved. Scale-invariant dynamics of unstable interfacial mixing belongs to a special self-similar class.