On the Efficiency of Baroclinic Eddy Heat Transport across Narrow Fronts*

Abstract

A simple theory is developed that relates the amplitude of eddy heat (or density) flux across a narrow front to the basic frontal parameters. By assuming that heat is transported primarily by baroclinic eddy pairs, an analytical expression for the cross-front eddy heat flux is derived as u9r9 5 ceVmDr, where u9 and r9 are deviations from the temporal or spatial mean cross-front velocity and density, Dr is the density change across the front, Vm is a scale for the alongfront velocity (which may be interpreted as the maximum alongfront velocity for a front with density change Dr over a horizontal scale of the deformation radius, assuming a deep level of no motion), and ce is an efficiency constant. Similar expressions for the eddy heat flux have been proposed previously, based on scaling or energetics arguments, but neither an a priori estimate for the value of the efficiency constant ce nor a clear dynamical understanding of what determines its value has been forthcoming. The theory presented here provides a dynamically based means of estimating the efficiency constant, which may be approximately interpreted as the ratio of the speed at which eddies propagate away from the front to the alongfront velocity, resulting in ce 0.045. Eddy-resolving numerical models are used to test this theoretical estimate for both unforced and forced frontal problems. For a wide range of parameters the cross-frontal heat transport is carried primarily by heton-like eddy pairs with values of ce between 0.02 and 0.04, in general agreement with the theory. These values of ce are also consistent with numerous previously published laboratory and numerical studies.