The phase speed of first mode baroclinic Rossby waves in a two-layer model is shown to be faster by a factor H/H_2 over a steep topography than over a flat bottom, H and H_2 being the total ocean depth and lower layer thickness, respectively. This arises from a dynamical decoupling of bottom pressure fluctuations. In order for H/H_2 to have a value of about two, as observed, a deep upper layer of the order of H/2 has to be assumed. Previous theoretical work on two-layer model calibration shows this is the correct choice if strong topographic interactions are to be modeled accurately. To make quantitative comparison with observations, we extend our two-layer theory to a continuously stratified fluid by projecting the equations of motion onto the standard flat-bottom vertical normal modes. We find that the amplification factor for the phase speed of the first baroclinic mode over a steep topography tends toward a value that depends only on the ratio of the deep Brunt-Vaisala frequency to that of its vertical average, with a convergence inversely proportional to the number of modes retained in a truncated series expansion. This amplification factor is estimated from the global Levitus dataset, and is found to lie on average between 2 and 3, with values generally increasing poleward, as observed. This suggests that topography is important in enhancing the propagation speed of actual baroclinic Rossby waves, in addition to the effect of mean flows previously proposed.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics