Advanced spectral anisotropic modelling for shear flows

ABSTRACT

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 γ is independent of the large scales infrared slope σ, with $E(k\to 0)\sim k^{\sigma }$, unlike unstably stratified homogeneous turbulence where γ strongly depends on σ. 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 γ 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.

KEYWORDS:

• Homogeneous turbulence
• shear flows
• spectral modelling

Disclosure statement

No potential conflict of interest was reported by the authors.