A new parameterization for entrainment in overflows

Dense overflows entrain surrounding waters at specific locations, for example, sills and constrictions, but also along the descent over the continental slope. The amount of entrainment dictates the final properties of these overflows, and thus is of fundamental importance to the understanding of the formation of deep water masses. Even when resolving the overflows, coarse resolution global circulation and climate models cannot resolve the entrainment processes that are often parameterized. A new empirical parameterization is suggested, obtained using an oceanic and laboratory dataset, which includes two novel aspects. First, the parameterization depends on both the Froude number (Fr) and Reynolds number of the flow. Second, it takes into account subcritical (Fr < 1) entrainment. A weak, but nonzero, entrainment can change the final density and, consequently, the depth and location of important water masses in the open ocean. This is especially true when the dense current follows a long path over the slope in a subcritical regime, as observed in the southern Greenland Deep Western Boundary Current. A streamtube model employing this new parameterization gives results that are more consistent with previous laboratory and oceanographic observations than when a classical parameterization is used. Finally, the new parameterization predictions compare favorably to recent oceanographic measurements of entrainment and turbulent diapycnal mixing rates, using scaling arguments to relate the entrainment ratio to diapycnal diffusivities.