Alongslope mean flow and an associated upslope bolus flux of tracer in a parameterization of mesoscale turbulence

Abstract

We explore a parameterization for mesoscale turbulence, closely related to that of Gent and McWilliams, in which forcing terms proportional to the isopycnal flux of potential vorticity appear in the averaged momentum equations. We show that in the presence of variable bottom topography, the parameterization predicts alongslope mean flow and a corresponding upslope bolus (eddy) flux of tracer that is associated with an alongslope-directed bottom eddy stress. The upslope bolus flux is in qualitative agreement with observations of a cold dome over seamounts. The predicted alongslope flow corresponds to flow fields found in geostrophic turbulence experiments and has some similarity (although conceptually very different, as discussed in the text) to Holloway's prediction based on statistical mechanics. By considering continuous stratification as a limiting case of a multilayer model, we show how to treat the surface and bottom boundaries. Practical application of the parameterization is illustrated using a three-dimensional z -coordinate ocean circulation model that is very similar to the Bryan–Cox–Semtner model. The model-computed flow is consistent with observations of anticyclonic flow around a seamount. We show that the bottom eddy stress associated with the parameterization can be large, even compared to the annual mean surface wind stress, and hence could have important implications for the biology and water mass distribution of the coastal ocean as well as for the large-scale ocean circulation. From the climate modelling perspective, the approach adopted here provides a single formalism that combines the advantages of the Gent and McWilliams parameterization with alongslope mean flow similar to that suggested by Holloway.