Effect of horizontal divergence on the geostrophic turbulence on a beta-plane: Suppression of the Rhines effect

An investigation is made on the effect of strong stratification, or horizontal divergence, on almost freely decaying geostrophic turbulence on a beta-plane. In a model ocean, the surface layer is assumed to be active above the quiet deep layer, so that barotropification is prohibited a priori to purify the effect of horizontal divergence. Spectral evolution is accelerated numerically by an adjustment to keep kinetic energy constant against the retarding effect of horizontal divergence. First, numerical experiment is carried out for small or moderate horizontal divergence as control runs for comparison; UF/beta<O(1), where U is the characteristic velocity of turbulence and F the squared inverse of the radius of deformation. As has been reported repeatedly, the beta-effect induces a highly anisotropic field characterized by a band of zonal currents. It is confirmed also that kinetic energy has a one-dimensional spectrum approximately proportional to k(-5) at high wave numbers k. Then, horizontal divergence is enlarged enough so that UF/beta>>1, for which geostrophic turbulence turns out to behave just as on an f plane: (1) the field becomes isotropic with no significant zonal currents; (2) the inverse cascade of energy is not hindered by the beta effect though it takes a longer time for turbulence to transfer energy to longer scales; and (3) the spectrum of kinetic energy (not total energy) is proportional to k(-3) at high wave numbers. An argument based on the physics of long baroclinic Rossby waves is presented to explain why strong horizontal divergence suppresses the beta effect. Furthermore a transform of variables leads to a modified governing equation, which clearly shows that the b effect should disappear for large horizontal divergence. (C) 2003 American Institute of Physics.