The Deformation Radius with Bathymetry

The horizontal scale of ocean eddies is correlated with the first Rossby radius of deformation, which is proportional to the eigenvalue of the first baroclinic mode. The latter is usually derived assuming a flat ocean bottom. But taking bottom relief into account yields a set of baroclinic modes (the “surface modes”) which have zero horizontal flow at the bottom. The deformation radius associated with the first surface mode is larger than the flat bottom estimate, by 20-50%. We use a simplified model to show that the surface modes should prevail outside the tropical band, from roughly 3S to 3N, consistent with EOFs calculated from current meters. Thus ocean eddies should be larger than previously thought. The larger eddies in turn should propagate westward faster than over a flat bottom. We find that the long Rossby wave speed increases by a factor of 1.5-2 over the flat bottom estimate, in line with propagation estimates from satellite observations. In addition, we show that the larger deformation radius is somewhat easier to resolve in ocean models.