Self-similar regimes of turbulence in weakly coupled plasmas under compression

Abstract

Turbulence in weakly coupled plasmas under compression can experience a sudden dissipation of kinetic energy due to the abrupt growth of the viscosity coefficient governed by the temperature increase. We investigate in detail this phenomenon by considering a turbulent velocity field obeying the incompressible Navier-Stokes equations with a source term resulting from the mean velocity. The system can be simplified by a nonlinear change of variable, and then solved using both highly resolved direct numerical simulations and a spectral model based on the eddy-damped quasinormal Markovian closure. The model allows us to explore a wide range of initial Reynolds and compression numbers, beyond the reach of simulations, and thus permits us to evidence the presence of a nonlinear cascade phase. We find self-similarity of intermediate regimes as well as of the final decay of turbulence, and we demonstrate the importance of initial distribution of energy at large scales. This effect can explain the global sensitivity of the flow dynamics to initial conditions, which we also illustrate with simulations of compressed homogeneous isotropic turbulence and of imploding spherical turbulent layers relevant to inertial confinement fusion.

Sudden diffusion of turbulent mixing layers in weakly coupled plasmas under compression

“…To describe a turbulent plasma under compression, we consider a hydrodynamic formulation similar to that used in Refs. [4,6] assuming small Knudsen numbers with the mean free path of charged particles smaller than gradients length scales. (Although the fluid approach is not always valid for some ICF targets especially at the end of the compression requiring kinetic approaches).…”

“…In the simulations of inhomogeneous turbulent kinetic energy layers of ICF capsule size under compression, an increased transport of turbulence toward the center of the capsule have also been measured during the implosion [6]. These observations, although not accounting for plasma molecular diffusion, suggest that this mechanism, producing mixing of the heavy elements from the ablator into the DT fuel, may occur in ICF.…”

“…The concept proposed by Davidovits and Fisch [4] would indeed require supersonic turbulence. The different regimes and scaling laws characteristic of compressed turbulent plasmas have been explored theoretically and using a spectral Eddy Damped Quasi-normal Markovian mode (EDQNM) model in Viciconte et al [6]. This unveils an important sensitivity to initial conditions related to the distribution of energy fluctuations between length scales during the sudden viscous dissipation phase.…”

Self-consistent feedback mechanism for the sudden viscous dissipation of finite-Mach-number compressing turbulence

“…The model was then used to estimate the partition of energy between the turbulence and heat, as the compression proceeds in time. A two-point spectral model based on the EDQNM formulation was used by [15], along with direct numerical simulations, to reproduce the sudden viscous dissipation mechanism. The lower computational cost of the EDQNM model allowed for the analysis of high-Reynolds-number effects and thus the identification of three distinct regimes: turbulent production, non-linear energy transfer, and viscous dissipation.…”

Bulk hydrodynamic stability and turbulent saturation in compressing hot spots

“…As a step towards these ends, a model (ordinary differential equation) that predicts the (turbulent) non-radial hydrodynamic motion (hydromotion) for plasma undergoing 3D, constant velocity, compression has recently been developed 15 . Other modeling efforts provide more detail on the influence of initial conditions 16 . As a separate, parallel approach, the present work develops a stability criterion for hot-spot hydromotion that gives intuition and predictions as to which trajectories (in ρR vs T space) are more or less likely to have substantial hydromotion.…”