On Critical Regimes and Horizontal Concentration of Momentum in Ocean Currents with Two-Layered System

The principles of minimum momentum transport and minimum energy which are commonly used in hydraulics of an open channel are applied to the current in a two-layered ocean, in which the geostrophic relation holds. For a flow of a finite width over the motionless lower layer these principles with the constancy of total volume transport predict the critical values of current width and upper layer thickness which will be attained by the flow after losing momentum or energy by friction. The two principles lead to critical regimes with almost similar order of magnitude. The critical width thus determined is less than 100 km and the upper layer disappears at the left edge of the flow in the critical regime, being in good agreement with the Gulf Stream and the Kuroshio. The analysis is also applied to a model of vertically continuous density stratification. Further the momentum transport of double jets often observed in actual currents is shown to be the minimum among multiple jets, next to a single jet corresponding to the critical regime.