Advanced spectral anisotropic modelling for shear flows

Antoine Briard (1, 2) , Benoît-Joseph Gréa (3) , Vincent Mons (4) , Claude Cambon (5) , Pierre Sagaut (2) , Thomas Gomez (6)

1 CMLA - Centre de Mathématiques et de Leurs Applications
2 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres
3 DAM/DIF - DAM Île-de-France
4 JHU - Johns Hopkins University
5 LMFA - Laboratoire de Mecanique des Fluides et d'Acoustique
6 LMFL - Laboratoire de Mécanique des Fluides de Lille - Kampé de Fériet

In this work, the spectral modelling developed in MCS [Mons, Cambon, Sagaut. A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically-averaged descriptors. J Fluid Mech. 2016;788:147-182] for shear-driven turbulence is further analysed and then improved. First, using self-similarity arguments, it is shown that the asymptotic kinetic energy exponential growth rate is independent of the large scales infrared slope sigma, with, unlike unstably stratified homogeneous turbulence where strongly depends on sigma. The MCS model relies on the truncation at the second order of the spectral two-point velocity correlation expansion into spherical harmonics. The expansion is here pursued at the next even order, the fourth one: the noteworthy consequence is that is decreased compared to MCS and is thus closer to values obtained in direct numerical simulations and experiments. Finally, some analytical considerations about odd-order contributions in the expansion of polarisation anisotropy are proposed.

Domaines: Mécanique [physics]; Physique [physics]; Physique des plasmas [physics.plasm-ph]

Antoine Briard, Benoît-Joseph Gréa, Vincent Mons, Claude Cambon, Pierre Sagaut, et al.. Advanced spectral anisotropic modelling for shear flows. Journal of Turbulence, 2018, 19 (7), pp.570-599. ⟨10.1080/14685248.2018.1478092⟩. ⟨hal-02112204⟩