Advanced spectral anisotropic modelling for shear flows

Abstract

0) ∼ k σ , 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. 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 →

Nonlinear spectral model for rotating sheared turbulence

“…(ii) On the contrary, models perform poorly when the linear dynamics yields algebraic growth, best illustrated with the plane shear flow without rotation: any model using a truncated expansion in terms of spherical harmonics wrongly gives an exponential growth. In spite of satisfactory results at short time, MC -even with further introduction of fourth-degree harmonics (Briard et al 2018)-is disqualified for a quantitative comparison with DNS. A similar comment applies to the other 'neutral case' (figure 6c), although to a lower extent.…”

Inertial range scaling of inhomogeneous turbulence

“…It contains two contributions: the production of turbulent kinetic energy and a linear transfer term (Cambon, Jeandel & Mathieu 1981; Briard et al. 2018). These terms are important mainly at large scales, and become zero at points in space where the velocity gradient vanishes.…”

Turbulence modeling and simulation advances in CFD during the past 50 years

“…Stimulated by the peculiar properties of rotating turbulence, two-point closures were further studied and developed by introducing two anisotropy tensors for the polarization anisotropy and for the directional anisotropy in wave vector space [129][130][131] in order to figure out the complex tensorial properties of the fluctuating turbulent field. A similar concept was also developed in physical space [132].…”