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 o ften 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 t he same result holds if the bottom pressure fluctuations are uncorrelated f rom 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 ava ilable evidence supporting this scenario is reviewed and a method that exte nds the idea to a continuously stratified fluid is developed. It is establi shed that the resulting amplification factor is at leading order captured b y the formula, [GRAPHICS] where C-fast is the enhanced phase speed, C-standard the standard phase spe ed, Phi (1)'(z) is the standard first mode for the velocity and pressure, a nd 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 C-fast/C-standard = 1 + 2N(b)/(N) over bar, where N-b is the deep Brunt-Vaisala frequency and (N) over bar its vertical average. 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. an d others. The link between the faster mode and the surface-intensified mode s occurring over steep topography previously discussed in the literature is also established.