Small-Peclet-number approximation for stellar turbulent mixing zones.

The purpose of this work is to derive a small turbulent Péclet-small turbulent Mach number approximation for hydroradiative turbulent mixing zones encountered in stellar interiors where the radiative conductivity can overwhelms the turbulent transport. To this end, we proceed to an asymptotic analysis and determine orders of magnitude for the fluctuating temperature and pressure, as well as closed expressions for the fluctuating conduction and velocity divergence. The latter is used to extend a Reynolds stress model to the small-Péclet regime. Three-dimensional direct numerical simulations of radiative Rayleigh-Taylor turbulent mixing zones are performed, first, to validate the asymptotic predictions and, second, to validate their use in the Reynolds stress model.

Pseudocompressible approximation and statistical turbulence modeling: application to shock tube flows.

In this work, a pseudocompressible approximation relevant for turbulent mixing flows encountered in shock tubes is derived. The asymptotic analysis used for this purpose puts forward the role played by four dimensionless numbers on the flow compressibility, namely, the turbulent, deformation, stratification, and buoyancy force Mach numbers. The existence of rapid distortion and diffusion-dissipation regimes is also accounted for in the analysis. Some consequences of the derived pseudocompressible approximation on statistical turbulence models are discussed. In particular, the evolutions of the density variance and flux are examined, as well as the turbulent transport of energy. The different aspects of this study are assessed by performing a direct numerical simulation of a shock tube flow configuration.