The development of hydrodynamic instabilities may be significantly affected by the presence of suprathermal high-energy particles (HEPs). These effects are particularly pronounced in high-energy-density plasmas. We develop a single-equation diffusion-type turbulence model that describes the turbulent mixing arising from the growth of instability at the interface of a material that strongly emits HEPs. We derive a basic governing equation of this model and its self-similar solutions, which allow us to constrain the growth rate of the mixing zone width $h_{\text{turb}}$. We show that key turbulence characteristics, including the spectrum and the mixing zone dynamics, depend primarily on the ratio of HEP free paths in the active and passive materials. In particular, the model predicts an asymptotic behavior $h_{\text{turb}}\sim t^{1/3}$ when the HEP free path in the active material exceeds that in the passive material, and $h_{\text{turb}}\sim t^{2/5}$ in the opposite case. We compare the predictions of the derived model with three-dimensional simulations of instability development and find good agreement between the simulated evolution of the mixing zone width and that obtained by numerical integration of the model equation. The asymptotic growth rates inferred from the self-similar solutions are also observed in the simulations.

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• Fluid-particle interactions
• Hydrodynamic instabilities
• Turbulence