Wave-anisotropy principle in near-resonant energy transfer in shear-flow turbulence*

Global symmetry-breaking factors like three-dimensional (3D) shear flow, magnetic field, etc. introduce anisotropic linear physics, which renders turbulent structures anisotropic, a phenomenon called the wave-anisotropy principle. The principle is found to apply to the Kelvin-Helmholtz (KH) and the Goldreich-Schubert-Fricke (GSF) instabilities.

                                                                                                           

The KH instability grows in 3D chiefly via 2D fluctuations; however, the system quickly becomes fully 3D by nonlinearly exciting fluctuations that vary only in the direction orthogonal to the 2D shear-flow plane. Such fluctuations, akin to the zonal flows of fusion plasmas, have near-zero frequencies. Thus, they near-resonantly transfer energy from KH-unstable to stable modes, endowing nonlinear transfer with anisotropy.

 

The GSF instability occurs in stars with gradients of destabilizing angular momentum and stabilizing density. When the buoyancy force is eliminated by fast thermal diffusion relative to viscous momentum diffusion the instability dominates. With KH-like anisotropic growth rate spectrum, the GSF instability saturates via a resonance provided by a near-zero-frequency mode, which couples to unstable modes. A thus-informed statistical closure model predicts turbulent transport rates, with which numerical simulations agree.