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

In this paper, we investigate the properties of rapidly rotating decaying turbulence using numerical simulations and phenomenological modeling. We find that as the turbulent flow evolves in time, the Rossby number decreases to ∼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 (±1, 0, 0) and (0, ±1, 0) that correspond to the largest columnar structure in the flow. For wavenumbers (k) greater than the enstrophy dissipation wavenumber (kd), 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 ϵω⁡exp(−C(k/kd)2) and Cϵω2/3k−1⁡exp(−C(k/kd)2), respectively; for this 2D flow, ϵω 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 turbulen...