Strongly Anisotropic Turbulence Using Statistical Theory: Still a Computationally Demanding Problem

Abstract

Strongly anisotropic turbulence is described by a minimal set of angle-dependent spectra, including in general both directional anisotropy — which includes dimensionality — and polarization anisotropy. The first kind of anisotropy is addressed in rotating turbulence, with various statistical approaches including wave-turbulence theory, and DNS. In addition to the long-term relevance of resonant triads, the role of anisotropic phase mixing is essential for explaining various, more or less transient, trends from the simplest properties of linear solutions for second-order statistics to the more complex dynamics of triads. A new approach to the asymmetry in terms of cyclonic and anticyclonic vertical vorticity distribution in rotating turbulence is discussed, with encouraging preliminary results. The case of stably stratified turbulence is touched upon at the end, in order to identify some analogies, as the relevance of gravity waves phase mixing for vertical — more generally poloidal — velocity, and differences with the rotating case. The main difference is that the horizontal layering can be described by an ‘anti-2D’ toroidal nonlinear energy drain, which is essentially disconnected from rapid gravity waves dynamics. In all cases, however, statistical theory, with strong anisotropy including dimensionality, appears as a useful complement to DNS/LES, and can offer alternative explanations with respect to oversimplified stability analysis.