Casimir preserving spectrum of two-dimensional turbulence

Abstract

The existence of two inertial ranges of forced homogeneous two-dimensional turbulence was conjectured about half a century ago. Given a forcing, confined to a typical wavenumber ${k}_{f}$, a direct cascade with ${k}^{\ensuremath{-}3}$ scaling for $k\ensuremath{\gg}{k}_{f}$ and an inverse cascade with ${k}^{\ensuremath{-}5/3}$ scaling for $k\ensuremath{\ll}{k}_{f}$ would be established. Using a geometric integrator on a unit sphere we are able to provide robust evidence for the double cascade spectrum at modest numerical resolution.

Topics & Concepts