Effects of topography on the cumulative mixing efficiency in exchange flows

Abstract

Buoyancy‐driven, hydraulically controlled two‐layer exchange flows were established in a laboratory flume with a lateral constriction and a bottom sill placed at its midpoint. The shear flow was unstable within the constriction, and the overall amount of turbulent mixing was determined from measurements of vertical density profiles after the exchange. The potential energy changes are used to evaluate the mixing efficiency (or flux Richardson number), defined as the fraction of the available potential energy released into kinetic energy that is converted to potential energy through irreversible mixing. Mixing efficiencies asymptote at large Reynolds numbers to values of 8% for a sill with sloping sides and 11% ± 1% for both a weir with vertical sides and the same constriction with no bottom topography. The latter is identical to the value previously reported for shorter, smoothly varying lateral constrictions. Thus, all controlled exchanges examined here undergo less mixing than implied by the commonly assumed maximum turbulent mixing efficiency of 20%, and the actual efficiency is insensitive to the form of the topography. This result implies that calculations of the global energy balance of the ocean may need to be reevaluated.