Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies

It is shown that the available potential energy in the large-scale mean ocean circulation, excluding the boundary layers, is of order (Ba)2 times the kinetic energy, where B is the basin dimension and a = cf is the internal radius of deformation (c is the speed of long internal waves and f the Coriolis parameter). This ratio is of order 1000. The Sverdrup solution for a two-layer ocean is examined, and the rate of input of energy by the wind estimated. In the steady-state model, this energy is lost to the western boundary layer. It is then shown that potential energy available in the mean circulation can be converted into eddy energy by baroclinic instability. The stability properties depend only on the mean density field, and calculations are made for a number of cases. Maximum growth rates are obtained for eddies with wavelength of about 200 km, typical e-folding times being about 80 days. These eddies have significant velocities only in the surface layers. Secondary maxima in the growth rate curves are found for eddies with wavelengths of 300–500 km, e-folding times being 120 days or more. These eddies have significant velocities in deep water, their structure being something like that of the first baroclinic mode. In the models examined, the conversion of available potential energy took place in the upper 400 m, and the rate of conversion can be related to the maximum eddy velocity. If it is supposed that eddies grow to such a size that mean energy is lost to eddies as fast as it is supplied by the large-scale wind field, then the larger eddies would have maximum velocities of about 0·08 m s−1 and the smaller surface trapped eddies would have maximum velocities of about 0·14 m s−1. Observations indicate the existence of eddies of this strength, and with wavelength and periods of the same order as given by the baroclinic instability calculations.