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We develop and test a method to observationally estimate lateral intrusive heat flux across a front. The model combines that of Joyce (1977), in which lateral cross-frontal advection by intrusions creates vertical temperature gradients, and Osborn and Cox (1972) in which vertical mixing of those gradients creates thermal microstructure that is dissipated by molecular conduction of heat. Observations of thermal microstructure dissipation T are then used to estimate the production by intrusions, and hence the lateral heat flux and diffusivity. This method does not depend on the precise mechanism(s) of mixing, or on the dynamical mechanisms driving the frontal intrusions. It relies on several assumptions: (1) lateral cross-frontal advection produces diapycnal temperature gradients that are mixed locally, (2) thermal variance is dissipated locally and not exported, (3) intrusion scales are larger than turbulence scales, and (4) isotropy of temperature microstructure is assumed in order to estimate T. The method is tested using microstructure observations in Meddy "Sharon," where the erosion rate and associated lateral heat flux are known from successive mesoscale hydrographic observations (Hebert et al., 1990). An expression is developed for the production (lateral heat flux times lateral temperature gradient, expected to equal T) in a front of steady shape that is eroding (detraining) at a steady rate; the production is proportional to the erosion speed and the square of the cross-frontal temperature contrast, both of which are well-known from observations. The qualitative structure and integrated value of the dissipation agree well with model assumptions and predictions: thermal variance produced by lateral intrusive heat flux is dissipated locally, dissipation in intrusive regions dominates total dissipation, and the total dissipation agrees with the observed erosion rate, all of which suggests that microstructure observations can be used to estimate intrusive heat flux. A direct comparison was made between lateral heat flux estimated from mesoscale Meddy structure plus the known rate of erosion, and lateral flux based on microscale temperature dissipation, with excellent agreement in the frontal zone and poorer agreement where lateral temperature gradient is too small to accurately measure.
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