On the energy spectrum of rapidly rotating forced turbulence

Abstract

In this paper, we investigate the statistical features of a fully developed, forced, rapidly rotating, turbulent system using numerical simulations and model the energy spectrum that fits well with the numerical data. Among the wavenumbers (k) larger than the Kolmogorov dissipation wavenumber, the energy is distributed such that the suitably non-dimensionalized energy spectrum is Ē(k¯)≈exp(−0.05k¯), where the overbar denotes appropriate non-dimensionalization. For the wavenumbers smaller than that of forcing, the energy in a horizontal plane is much more than that along the vertical rotation-axis. For such wavenumbers, we find that the anisotropic energy spectrum, E(k⊥, k∥), follows the power law scaling, k⊥−5/2k∥−1/2, where “⊥” and “∥,” respectively, refer to the directions perpendicular and parallel to the rotation axis; this result is in line with the Kuznetsov–Zakharov–Kolmogorov spectrum predicted by the weak inertial-wave turbulence theory for the rotating fluids.