Two-dimensional turbulence on the surface of a sphere

Abstract

Large-scale atmospheric flow shares certain attributes with two-dimensional turbulence. In this paper, we study the effect of spherical geometry on two-dimensional turbulence.Energy transfer is multi-component in spherical geometry in contrast to energy transfer among triads of wave vectors in Cartesian geometry. It follows that energy transfer is more local in spherical than in Cartesian geometry. Enstrophy transfer to higher wavenumbers in spherical geometry is less than enstrophy transfer to higher wavenumbers in Cartesian geometry. Since both energy and enstrophy are inviscid constants of motion, the back transfer of energy is also less in spherical than in Cartesian geometry. Therefore, with a finite viscosity, enstrophy decays more slowly in spherical geometry than in Cartesian geometry. Here these conjectures are tested numerically by spectral methods. The numerical results agree well with the conjectures.