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Startup process in the Richtmyer–Meshkov instability

Startup process in the Richtmyer–Meshkov instability An analytical model for the initial growth period of the planar Richtmyer–Meshkov instability is presented for the case of a reflected shock, which corresponds in general to light-to-heavy interactions. The model captures the main features of the interfacial perturbation growth before the regime with linear growth in time is attained. The analysis provides a characteristic time scale τ τ for the startup phase of the instability, expressed explicitly as a function of the perturbation wavenumber k k , the algebraic transmitted and reflected shock speeds U S 1 <0 U S 1 < 0 and U S 2 >0 U S 2 > 0 (defined in the frame of the accelerated interface), and the postshock Atwood number A + A + : τ = (1− A + )/ U S 2 +(1+ A + )/(− U S 1 )/(2 k ) τ = ( 1 − A + ) ∕ U S 2 + ( 1 + A + ) ∕ ( − U S 1 ) ∕ ( 2 k ) . Results are compared with computations obtained from two-dimensional highly resolved numerical simulations over a wide range of incident shock strengths S S and preshock Atwood ratios A A . An interesting observation shows that, within this model, the amplitude of small perturbations across a light-to-heavy interface evolves quadratically in time (and not linearly) in the limit A →1 − A → 1 − . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physics of Fluids American Institute of Physics
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