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Growth rate of a shocked mixing layer with known initial perturbations

Published online by Cambridge University Press:  14 May 2013

Christopher R. Weber ,
Andrew W. Cook  and
Riccardo Bonazza
Christopher R. Weber*
Affiliation:
University of Wisconsin, Madison, WI 53706, USA Lawrence Livermore National Laboratory, Livermore, CA 94551, USA
Andrew W. Cook
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA 94551, USA
Riccardo Bonazza
Affiliation:
University of Wisconsin, Madison, WI 53706, USA
*
†Email address for correspondence: [email protected]
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Abstract

We derive a growth-rate model for the Richtmyer–Meshkov mixing layer, given arbitrary but known initial conditions. The initial growth rate is determined by the net mass flux through the centre plane of the perturbed interface immediately after shock passage. The net mass flux is determined by the correlation between the post-shock density and streamwise velocity. The post-shock density field is computed from the known initial perturbations and the shock jump conditions. The streamwise velocity is computed via Biot–Savart integration of the vorticity field. The vorticity deposited by the shock is obtained from the baroclinic torque with an impulsive acceleration. Using the initial growth rate and characteristic perturbation wavelength as scaling factors, the model collapses the growth-rate curves and, in most cases, predicts the peak growth rate over a range of Mach numbers ($1. 1\leq {M}_{i} \leq 1. 9$), Atwood numbers ($- 0. 73\leq A\leq - 0. 35$ and $0. 22\leq A\leq 0. 73$), adiabatic indices ($1. 40/ 1. 67\leq {\gamma }_{1} / {\gamma }_{2} \leq 1. 67/ 1. 09$) and narrow-band perturbation spectra. The mixing layer at late times exhibits a power-law growth with an average exponent of $\theta = 0. 24$.

JFM classification

Mixing: Mixing Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 725 , 25 June 2013 , pp. 372 - 401
Copyright
©2013 Cambridge University Press 

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