Spectral anisotropy in forced two-dimensional turbulence on a rotating sphere

Abstract

The datasets on the forced two-dimensional turbulence on a rotating sphere obtained in our recent direct numerical simulations were analyzed to study the spectral anisotropy due to the rotation of the sphere. The results were also compared with those previously obtained in some β-plane experiments to assess the β-plane approximation of the rotating sphere. Owing to the effect of rotation the upward energy cascade ceases around a characteristic total wavenumber nβ at which the linear “β-term” is comparable to the nonlinear Jacobian term. The energy density of zonal components (m=0) is dominant in the range of n≲nβ while the energy is very small in an airfoil-shaped region at the lower edge in the wavenumber space (m,n). Anisotropic distribution of the energy is also found in the high wavenumber region n≳nβ; the energy density decreases as the zonal wavenumber m increases. The flow field in the spherical geometry is projected on some tangential planes from the equator to the poles to compare the spherical results directory with previous β-plane experiments. The energy distribution becomes anisotropic to have dominant zonal components as the local “β-effect” increases (or the tangential plane is put closer to the equator). In the case on equatorial tangential planes, the region in which the energy density is very small shows a dumbbell shape indicating strong anisotropy; this is the first confirmation of the recent finding by Vallis and Maltrud in full spherical geometry.