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If the deviation of mean flow from mean temperature contours is small, it is shown that a part of the eddy heat flux can be separated out which circulates around eddy potential energy contours, and has a component up/down the mean temperature gradient if there is flow advection of eddy potential energy into/out of the region. If the mean flow is strong, this rotational flux is large and results in regions of up- and downgradient flux. It is a prominent feature of maps of geostrophic eddy fluxes in the ocean and atmosphere.
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Marshall et al. (1981) studied this question.
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