In Inertial Confinement Fusion (ICF) capsules, hydrodynamics instabilities driven by compression lead eventually to a turbulent state. Simultaneously, the mixture between materials experiences a tremendous increase of temperature until
becoming a plasma. As a consequence, the viscosity coefficient grows implying a sudden dissipation of turbulent kinetic energy (TKE) as shown by [2, 3]. The modelling of turbulence subjected to this phenomenon is rather difficult, for instance classical one-point models are hardly applicable and refined models are required to account for the different scales of the turbulence dynamics.
In this work, we investigate this using both DNS and a statistical model based on isotropic Eddy Damped Quasi Normal Markovian (EDQNM) closures (see [4]). While the mean flow leading to a compressed state is inhomogeneous, turbulent quantities can be considered as homogeneous and isotropic in the moving reference frame as shown by [1]. In addition to time-varying viscosity effects due to temperature increase discussed in [3], we also introduce a more realistic contrast of viscosity due to the mixture inducing a non-uniform relaminarization process. Careful comparisons between DNS and model will be proposed for one point turbulent quantities such as TKE and two-point spectra.

References
[1] C. Cambon, Y. Mao, and D. Jeandel. On the application of time dependent scaling to the modelling of turbulence undergoing compression. Euro.J. Mech. B/Fluids, 683(11), 1992.
[2] Seth Davidovits and Nathaniel J. Fisch. Compressing turbulence and sudden viscous dissipation with compression-dependent ionization state.Phys. Rev. E, 94:053206, Nov 2016.
[3] Seth Davidovits and Nathaniel J. Fisch. Sudden viscous dissipation of compressing turbulence. Phys. Rev. Lett., 116:105004, Mar 2016.
[4] B.-J. Gréa, J. Griffond, and A. Burlot. The effects of variable viscosity on the decay of homogeneous isotropic turbulence. Phys. Fluids (1994-present), 26(3):–, 2014.