A steady state cross‐shelf density gradient of a wind‐free coastal ocean undergoing winter time cooling is found for cooling and geometries which do not vary in the along‐shelf direction. The steady state cross‐shelf density gradient exists even when the average density of the water continues to increase. The steady state density gradient can be attained in less than a winter for parameters appropriate to the mid‐Atlantic Bight. The cross‐shelf eddy‐driven buoyancy fluxes which cause this steady state gradient are found to depend critically on bottom friction and bottom slope, and the coastal polyna solutions of Chapman and Gawarkiewicz [1997] are significantly modified by this dependence in the limit of polynas with a large alongshore extent. Bottom friction retards the cross‐shelf propagation of eddies, so that the buoyancy transport is no longer carried by self‐advecting eddy pairs but mixed across the shelf by interacting eddies. The eddy interaction changes the length scale of the eddies until it is the lesser of the Rhines arrest scale or an analogous frictional arrest scale. The estimates of the steady state cross‐shelf density gradient are found to compare well with numerical model results.
