Jet formation in decaying two-dimensional turbulence on a rotating sphere

Abstract

Jet formation in decaying two-dimensional turbulence on a rotating sphere is reviewed from the view point of wave mean-flow interaction for both shallow-water case and non-divergent case as the limit of Fr (Froude number) going to zero. A series of computations have been performed by ourselves to confirm the behavior of zonal mean zonal flow generation on the parameter space of the nondimensional rotation rate Ω and Fr. When the flow is non-divergent and Ω is large, intense retrograde circumpolar jets tend to emerge in addition to a banded structure of mean zonal flows with alternating flow directions in middle and low latitudes. As Fr increases, the circumpolar jets disappear and a retrograde jet emerges in the equatorial region. The appearance of the intense retrograde jets can be understood by the angular momentum transport associated with the propagation and absorption of Rossby waves. When the flow is non-divergent, long Rossby waves tend to be absorbed around the poles. In contrast, when Fr is large, Rossby waves can hardly propagate poleward and tend to be absorbed near the equator. The direction of the equatorial jet, however, is not always retrograde. Our ensemble experiments showed the emergence of a prograde jet, though less likely. This result is contrasted with the previous studies that reported retrograde equatorial jets in most cases for shallow-water turbulence. Furthermore, a mean zonal flow induced by wave-wave interactions was examined using a weakly nonlinear model to clarify the acceleration mechanisms of the equatorial jet. The second-order acceleration is induced by the Rossby waves and mixed Rossby-gravity waves and the acceleration mechanism can be categorized into two types.