The Rhines effect is an interaction of Rossby waves and two-dimensional turbulence that induces alternating zonal flows, thereby deforming and eventually destroying coherent vortices that might exist. Large-scale geophysical flows are not strictly two-dimensional. To be applicable to these flows the Rhines effect is therefore generalized. A novel aspect of the generalized Rhines effect is its possible suppression. On Jupiter, it is suppressed in the polar regions and at specific lower latitudes. It is remarkable that exactly there storms (vortices) have been observed, suggesting that storms can exist only where Rossby waves cannot interact with them. Thus the Rhines effect plays not only a role in the formation of the alternating zonal winds on Jupiter, as previously suggested, but in its generalized form also dictates the latitudes at which storms can exist.