We thank Paul O’Gorman, Alan Plumb, Isaac Held, and John Marshall for helpful comments and discussions. We would also like to thank Tapio Schneider and Eli Tziperman for very constructive reviews. This work was supported through NFS award OCE-0849233.
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Notice that we here use the PV definition used by Koh and Plumb (2004) or “convention II” discussed by Schneider (2005). However, if it is assumed that the isentropic slope varies little over the depth of the SL, “convention I” of Schneider (2005) yields a result very similar to Eq. (9) except for an additional factor of
Isentropes tend to flatten out in the Ekman layer in our simulations (an effect arising from a combination of Ekman drag and convective adjustment). Hence we use the model temperature above this Ekman layer, at a height of about 300 m, as the “surface” temperature.
Because of the use of no-slip boundary conditions in the simulations discussed here, the actual eddy flux vanishes at the surface. We therefore evaluated the flux–gradient relationship to calculate the eddy diffusivity above the surface Ekman layer at 300-m height. Note that the theoretical predictions derived in section 3 assume a downgradient flux for the geostrophic eddy flux of surface buoyancy