Transition to turbulence in shock-driven mixing: a Mach number study

Large-eddy simulations of single-shock-driven mixing suggest that, for sufficiently high incident Mach numbers, a two-gas mixing layer ultimately evolves to a late-time, fully developed turbulent flow, with Kolmogorov-like inertial subrange following a -5/3 power law. After estimating the kinetic energy injected into the diffuse density layer during the initial shock interface interaction, we propose a semi-empirical characterization of fully developed turbulence in such flows, based on scale separation, as a function of the initial parameter space, as (eta(0)+Delta u/nu) (eta(0)+L-rho)A(+)/root 1-A(+2) greater than or similar to 1.53 x 10(4)/l(2), which corresponds to late-time Taylor-scale Reynolds numbers greater than or similar to 250. In this expression, eta(0+) represents the post-shock perturbation amplitude, Delta u the change in interface velocity induced by the shock refraction, nu the characteristic kinematic viscosity of the mixture, L-rho the inner diffuse thickness of the initial density profile, A(+) the post-shock Atwood ratio, and W(A(+), eta(0)+lambda(0)) approximate to 0.3 for the gas combination and post-shock perturbation amplitude considered. The initially perturbed interface separating air and SF6 (pre-shock Atwood ratio A approximate to 0.67) was impacted in a heavy light configuration by a shock wave of Mach number M-1 = 1.05, 1.25, 1.56, 3.0 or 5.0, for which eta(0+) is fixed at about 25% of the dominant wavelength lambda(0) of an initial, Gaussian perturbation spectrum. Only partial isotropization of the flow (in the sense of turbulent kinetic energy and dissipation) is observed during the late-time evolution of the mixing zone. For all Mach numbers considered, the late-time flow resembles homogeneous decaying turbulence of Batchelor type, with a turbulent kinetic energy decay exponent n approximate to 1.4 and large-scale (k -> 0) energy spectrum similar to k(4), and a molecular mixing fraction parameter, Theta approximate to 0.85. An appropriate time scale characterizing the Taylor-scale Reynolds number decay, as well as the evolution of mixing parameters such as Theta and the effective Atwood ratio A(e), seem to indicate the existence of low- and high-Mach-number regimes.