Statistical features of rapidly rotating decaying turbulence: Enstrophy and energy spectra and coherent structures

Abstract

In this paper we investigate the properties of rapidly rotating decaying turbulence using numerical simulations and phenomenological modelling. We find that as the turbulent flow evolves in time, the Rossby number decreases to $\sim 10^{-3}$, and the flow becomes quasi-two-dimensional with strong coherent columnar structures arising due to the inverse cascade of energy. We establish that a major fraction of energy is confined in Fourier modes $(\pm1,0,0)$ and $(0,\pm1,0)$ that correspond to the largest columnar structure in the flow. For wavenumbers ($k$) greater than the enstrophy dissipation wavenumber ($k_d$), our phenomenological arguments and numerical study show that the enstrophy flux and spectrum of a horizontal cross-section perpendicular to the axis of rotation are given by $\epsilon_\omega\exp(-C(k/k_d)^2)$ and $C\epsilon_\omega^{2/3}k^{-1}\exp(-C(k/k_d)^2)$ respectively; for this 2D flow, $\epsilon_\omega$ is the enstrophy dissipation rate, and $C$ is a constant. Using these results, we propose a new form for the energy spectrum of rapidly rotating decaying turbulence: $E(k)=C\epsilon_\omega^{2/3}k^{-3}\exp(-C(k/k_d)^2)$. This model of the energy spectrum is based on wavenumber-dependent enstrophy flux, and it deviates significantly from power law energy spectrum reported earlier