Energy transfer in the Richtmyer-Meshkov instability

Abstract

The variable-density spectral kinetic energy budget for the Richtmyer-Meshkov-induced turbulent mixing layer is presented using results from a 512{3} implicit large eddy simulation. The budget is presented at several time instants and as a function of the inhomogeneous direction as the layer transitions from the initial impulse through to self-similarity. There are clear parallels in the development of the mixing layer with a previous analysis for the Rayleigh-Taylor instability. In the core of the layer, the quadratic terms are largely negative in the energy-containing scales. The transfer spectra are clearly asymmetric, where the majority of the activity occurrs on the spike side. The quadratic and pressure components are of opposite sign and almost cancel each other out in the spikes. The dilatational terms are negligible in comparison to the difference between the quadratic and pressure transfer. A notable result is that vortex rings are identified as the key source of alternating fields of negative and positive energy transfer within the mixing layer. This helps explain similar observations noted in direct numerical simulations of Rayleigh-Taylor instability. Finally, the spectral numerical dissipation for this scheme is computed for the self-similar layer. This demonstrated that the effects of numerical dissipation are small compared to the other terms at low wave numbers, whereas at higher wave numbers where modes become significantly underresolved the numerical dissipation is approximately twice the nonlinear transfer term and behaves in approximate analogy to an effective spectral eddy viscosity.