Barotropic current rectification by topographic irregularities is treated for a case with bottom friction and fluctuating forcing. Geometries both with underlying shelf-slope topography and with no mean topographic slope are considered. In common with many previous studies of this sort, the resulting time-mean flow roughly follows isobaths in the direction that long topographic Rossby waves travel, but the mean flow often deviates locally from this rule. Further, as might be expected, there is an area-averaged correlation of pressure and bottom slope in the sense that would propel the mean flow. If the topographic irregularities have a length scale shorter than roughly a particle fluctuation excursion, then the typical along-isobath mean flow is proportional to the bottom slope, the irregularity length scale, the amplitude of the cross-isobath velocity fluctuations, and the inverse of the water depth. If the spatial scale of the irregularities is greater than roughly a particle excursion, then the resulting mean flow does not depend on irregularity length scale, but does depend on the Coriolis parameter, the bottom slope, cross-isobath velocity squared, the inverse depth and the inverse frequency squared. For large amplitude fluctuations, eddy momentum transport leads to a further inverse proportionality of mean flow to the strength of bottom friction. The overall mean flow parameterization holds only in a statistical sense (as opposed to point-by-point) because of the spatial complexity of typical flows. In a forced, dissipative system, the mean flow generation is often just tidal rectification (e.g., Loder, 1980) if the particle excursion is short relative to topographic scales. However, as the irregularity scale decreases, mean flow becomes weaker.
Brink, K. H.. 2010. "Topographic rectification in a forced, dissipative, barotropic ocean." Journal of Marine Research 68, (3). https://elischolar.library.yale.edu/journal_of_marine_research/270