The Effect of Bottom Pressure Decoupling on the Speed of Extratropical, Baroclinic Rossby Waves

In layered models of the ocean, the assumption of a deep resting layer is often made, motivated by the surface intensification of many phenomena. The propagation speed of first-mode, baroclinic Rossby waves in such models is always faster than in models with all the layers active. The assumption of a deep-resting layer is not crucial for the phase-speed enhancement since the same result holds if the bottom pressure fluctuations are uncorrelated from the overlying wave dynamics. In this paper the authors explore the relevance of this behavior to recent observational estimates of "too-fast" waves by Chelton and Schlax. The available evidence supporting this scenario is reviewed and a method that extends the idea to a continuously stratified fluid is developed. It is established that the resulting amplification factor is at leading order captured by the formula, 2 F9 (2H ) 10 C /C 5 1 1.1, fast standard 0 1 2 F9 (z) dz E 1 H 0 2H 0 where C fast is the enhanced phase speed, C standard the standard phase speed, is the standard first mode for F9(z) 1 the velocity and pressure, and H 0 is the reference depth serving to define it. In the case WKB theory is applicable in the vertical direction, the above formula reduces to 2N b C /C 5 1 1 , fast standard N where N b is the deep Brunt--Vaisala frequency and its vertical average. N The amplification factor is computed from a global hydrographic climatology. The comparison with observational estimates shows a reasonable degree of consistency, although with appreciable scatter. The theory appears to do as well as the previously published mean-flow theories of Killworth et al. and others. The link between the faster mode and the surface-intensified modes occurring over steep topography previously discussed...