Mixing efficiency of turbulent stratified flows

Small-scale mixing in the stratified interior of the ocean is a fundamental, but poorly characterized, controlling factor of the global Meridional Overturning Circulation (MOC). The mixing efficiency in the ocean has typically been assumed to be 20%, which is used as a basis to estimate the required turbulent dissipation to support the ocean diapycnal buoyancy flux. In this talk, we use DNS datasets to calculate the mixing efficiency in different classes of stratified turbulent flows. In particular, we compare flows forced thermodynamically by production of Available Potential Energy (APE) at a boundary, such as horizontal convection (a simple model for an ocean forced by differential surface heating) and flows that are forced mechanically by surface stresses. The mixing efficiency is calculated based on the irreversible diapycnal flux of buoyancy (Winters and D'Asaro, 1996; Scotti et al., 2006) instead of the more customary turbulent buoyancy flux, thereby isolating mixing from reversible processes (e.g., internal waves). For mechanically-driven flows, profiles of mixing efficiency vs. buoyancy Reynolds number are in agreement with accepted values for stratified turbulent shear flows. However, for flows in which mixing is driven in part or fully by thermodynamic forcing and an excess of APE, DNS results show much higher values of the mixing efficiency, approaching unity for horizontal convection. Implications of these results for the energy budget of the MOC are discussed. Note: The DNS data sets of turbulent stratified channel flow are provided courtesy of M. Garcia-Villalba and J. C. del Alamo.