Self-similar interfacial mixing with variable acceleration

Rayleigh-Taylor (RT) interfacial mixing has critical importance for a broad range of processes in nature and technology, from supernovas and planetary interiors to plasma fusion, oil recovery, and nano-fabrication. In most instances, RT flows are driven by variable acceleration, whereas the bulk of existing studies considered only constant and impulsive accelerations. By analyzing symmetries of RT dynamics for certain patterns of variable acceleration, we discover a special class of self-similar solutions and identify their scaling, correlations, and spectra. We find that dynamics of RT mixing can vary from superballistics to sub-diffusion depending on the acceleration and retain memory of deterministic and initial conditions for any acceleration. These rich dynamic properties considerably impact the understanding and control of Rayleigh-Taylor relevant processes in fluids, plasmas, and materials and reveal whether turbulence can be realized in RT interfacial mixing.