A Saturation Paradigm of Kelvin-Helmholtz Turbulence

Abstract

While shear flows in laboratory and geo- and astrophysical fluids abound, are often unstable, and have been studied both experimentally and numerically, a reliable understanding of the nonlinear saturation of the instability remains elusive. The common assumption of instability-saturation is that the unstable-mode energy, in its entirety, is cascaded to small scales where it is dissipated. Though the cascade exists, I will show, using novel eigenmode-coupled energy transfer analyses, that in both two- and three-dimensional driven shear-flow turbulence almost all the unstable-mode energy is transferred to large-scale linearly stable modes at the instability scale itself. These stable modes then return the turbulent energy to the background gradient. This finding is consequential also to magnetized turbulence where removing the stable modes of Kelvin-Helmholtz-instability in numerical simulations enhances, by an order of magnitude, both the small-scale cascade and dissipation, including that of magnetic fluctuations. Detailed examination shows that the flow composed of the unstable modes, in stable modes’ absentia, rapidly distorts and folds the magnetic field lines [1]. In the shear layer, up-gradient momentum transport by the stable modes cancels 70%-90% of down-gradient momentum transport by the unstable modes [2]. A model based on only a few unstable and stable modes accurately reproduces the transport rates from full-scale turbulence simulations. With this new instability-saturation paradigm, inroads to old and important problems of shear-driven dynamos and reconnection-driven outflows may be possible.