[show abstract][hide abstract] ABSTRACT: Oceanic Rossby waves have been widely invoked as a mechanism for large-scale variability of chlorophyll (CHL) observed from satellites. High-resolution satellite altimeter measurements have recently revealed that sea-surface height (SSH) features previously interpreted as linear Rossby waves are nonlinear mesoscale coherent structures (referred to here as eddies). We analyze 10 years of measurements of these SSH fields and concurrent satellite measurements of upper-ocean CHL to show that these eddies exert a strong influence on the CHL field, thus requiring reassessment of the mechanism for the observed covariability of SSH and CHL. On time scales longer than 2 to 3 weeks, the dominant mechanism is shown to be eddy-induced horizontal advection of CHL by the rotational velocities of the eddies.
[show abstract][hide abstract] ABSTRACT: Oceanographic flows exhibit a subset of the fluid motions described by the primitive equations and can therefore often be simplified while retaining most the important physics. Starting from the spherical shallow water equations and assuming geostrophic dominance, we derive a potential vorticity conservation law in terms of all four non-dimensional parameters inherent in the equations while retaining the spherical geometry. The analysis is motivated by the desire to find appropriate equations to model altimeter-tracked mesoscale eddies. The resulting equation reduces to other existing geostrophic theories, such as quasi- geostrophy, hypo-geostrophy, and the Flierl-Petviashvili equation, by assuming a precise relationship between the non-dimensional parameters. However, by retaining freedom in the parameters we can determine at what scales the various theories remain valid. Further, it is now easily seen when and what new geostrophic theories arise from different parameter regimes, as well as their valid range of scales.