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Quasi-geostrophic instabilities of planetary geostrophic circulation

Quasi-geostrophic instabilities of planetary geostrophic circulation

Institute for Mathematics and Its Applications

**Roger Samelson **,COAS Oregon State University

Instabilities of the large-scale mean flow are one likely source of mesoscale ocean variability. In general, however, the coupling of the fluctuating, mesoscale flow to the large-scale circulation remains poorly understood. One approach to this problem is through a multiple scale technique that explicitly recognizes the existence of two different types of geostrophic motion. In this picture, the large-scale flow is described by planetary geostrophic equations, and the mesocale flow by quasi-geostrophic equations. The quasi-geostrophic instabilities of solutions of an idealized planetary geostrophic model circulation may then be examined directly. In the present study, linear plane-wave quasi-geostrophic normal-mode instabilities are calculated numerically for vertical profiles of density and horizontal velocity extracted from the subtropical gyre of a planetary geostrophic circulation model. All of the profiles support growing modes. The most rapidly growing modes have e-folding times less than 1 month and horizontal wavelengths less than 10 km. These modes have vertical scales of 500 m and are centered at a shallow thermostad that may be identified as subtropical mode water. They may be interpreted in terms of a baroclinic `defect' instability, in which a linear vertical shear of horizontal geostrophic velocity is destabilized by an arbitrarily small but sufficiently sharp local decrease in buoyancy frequency. An analytic dispersion relationship may be obtained asymptotically for the defect instabilities. Instabilities with larger vertical scales and horizontal wavelengths of 30-300 km have smaller growth rates, similar to previous estimates for mid-ocean baroclinic instability.