| An investigation is made on the effect of strong stratification, or horizontal divergence, on almost freely decaying geostrophic turbulence on a β-plane. In the periodic domain of a model ocean, the surface layer is assumed to be active above the quiet deep layer, so that barotropification was prohibited a priori to purify the effect of horizontal divergence. In other words the Charney-Hasegawa-Mima equation is adopted as the governing equation. 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/β < 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 β-effect induces a highly anisotropic field characterized by a band of zonal currents, which phenomenon is known as the Rhines effect. It is confirmed also that kinetic energy has a one-dimensional spectrum approximately proportional to k-5 at high wavenumbers k. A moderate value of UF/β slightly increases the preferred meridional scale of the zonal currents. Then, horizontal divergence is enlarged enough so that UF/β >> 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 β-effect though it takes a longer time for turbulence to transfer energy to longer scales; and (3) the one-dimensional spectrum of kinetic energy (not total energy) is proportional to k-3 at high wavenumbers. An argument based on the physics of long baroclinic Rossby waves is presented to explain why strong horizontal divergence suppresses the β-effect. Furthermore a transform of variables leads to a modified governing equation, which clearly shows that the β-effect should disappear for large horizontal divergence. This argument is confirmed by additional experiments based on those different forms of governing equations; the resulting spectra cannot be distinguished one from another, indicating the total suppression of the β-effect for strong horizontal divergence. |
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