Long-time asymptotic states of forced two-dimensional barotropic incompressible flows on a rotating sphere

This study re-examines a long-time asymptotic state of a two-dimensional barotropic incompressible flow with a small-scale, Markovian random forcing on a rotating sphere. Numerical simulations with different rotation rates of the sphere and different wavenumbers of the forcing are performed from zero initial condition. The integration time is extended to around 100-500 times that of the previous study by Nozawa and Yoden [Phys. Fluids9, 2081 (1997)]. At an early stage of the time integration, a multiple zonal-band structure or a structure with westward circumpolar jets emerges. However, in the course of time development, a multiple zonal-band structure is found to appear in all cases. The multiple zonal-band structure then enters quasisteady state, showing little energy increase with nearly steady energy spectrum. This is followed by a sudden merger/disappearance of the jets, accompanying an energy increase, and at the final stage of the time integration, a zonal-band structure with only two or three jets is realized in all cases. The characteristic total wavenumber of this asymptotic state is far lower than the Rhines wavenumber of the zonal flow, which suggests that the inverse energy cascade is not totally stopped by the β effect.