Mixing induced in a dense plume flowing down a sloping bottom in a rotating fluid: a new entrainment parameterization?

We will discuss laboratory experiments investigating mixing in a density driven current flowing down a sloping bottom in a rotating homogenous fluid. A systematic study spanning a wide range of Froude, Fr, and Reynolds, Re, numbers was conducted by varying four parameters: the rotation rate, the bottom slope, the flowrate, and the density of the dense fluid. Different flow regimes, i.e. laminar, wave, turbulent and eddy regimes, were observed either in different experiments, while changing the above parameters, or simultaneously in the same experiment, as the current descended the slope. Mixing in the density driven current was quantified within the observed different flow regimes and at different locations on the slope. The dependence of mixing on the relevant non-dimensional numbers, i.e. Fr and Re, will be discussed. Mixing increased with increasing Fr. For low Fr the magnitude of the mixing was comparable to mixing in the ocean. For large Fr and Re, mixing was comparable, or slightly lower, than in previous laboratory experiments that presented the classic turbulent entrainment behavior with larger Re. We will suggest a new empirical parameterization for entrainment in dense currents that presents two novelties when compared to the classical Ellison and Turner [1959] parameterization. First, it depends both on the Fr and Re of the flow and it accurately predicts both ocean and laboratory estimates of mixing. Second, it takes into account subcritical (Fr<1) mixing. The subcritical mixing observed in the present experiments could be of fundamental importance when determining the final water mass characteristics of a dense overflow current descending the continental slope. A weak but non zero entrainment can substantially change the final density and, consequently, the location of important water masses, such as the North Atlantic Deep Water, in the open ocean water column. Finally, a comparison of the laboratory results to those of a “stream tube” model will be presented. We will show that the model predictions are consistent with laboratory observations when the new entrainment parameterization is employed.