On the Efficiency of Baroclinic Eddy Heat Transport across Narrow Fronts*
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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 hear is transported primarily by baroclinic eddy pairs, an analytical expression for the cross-front eddy hear flux is derived as <(u’rho’)over bar> = c(e)V(m)Delta rho, where u’ and rho’ are deviations from the temporal or spatial mean cross-front velocity and density, Delta rho is the density change across the front, V-m is a scale for the alongfront velocity (which may be interpreted as the maximum alongfront velocity for a front with density change Delta rho over a horizontal scale of the deformation radius, assuming a deep level of no motion), and c(e) 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 c(e) 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 c(e) approximate to 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 hear transport is carried primarily by heton-like eddy pairs with values of c(e) between 0.02 and 0.04, in general agreement with the theory. These values of c(e) are also consistent with numerous previously published laboratory and numerical studies.