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Richtmyer-Meshkov instability (RMI) plays an important role in many areas ofscience and engineering, from supernovae and fusion to scramjets andnano-fabrication. Classical Richtmyer-Meshkov instability is induced by asteady shock and impulsive acceleration, whereas in realistic environments theacceleration is usually variable. We focus on RMI induced by acceleration withpower-law time-dependence and apply group theory to solve the long-standingproblem. For early-time dynamics, we find the dependence of the growth-rate onthe initial conditions and show that it is independent of the accelerationparameters. For late-time dynamics, we find a continuous family of regularasymptotic solutions, including their curvature, velocity, Fourier amplitudes,and interfacial shear, and we study their stability. For each solution, theinterface dynamics is directly linked to the interfacial shear, thenon-equilibrium velocity field has intense fluid motion near the interface andeffectively no motion in the bulk. The quasi-invariance of the fastest stablesolution suggests that nonlinear coherent dynamics in RMI is characterized bytwo macroscopic length-scales -- the wavelength and the amplitude, in agreementwith observations. The properties of a number of special solutions areoutlined, these being respectively, the Atwood, Taylor, convergence,minimum-shear, and critical bubbles, among others. We also elaborate new theorybenchmarks for future experiments and simulations.

On Richtmyer-Meshkov unstable dynamics of three-dimensional interfacial coherent structures with time-dependent acceleration