### Use of the semi-geostrophic model in understanding large-scale atmosphere and ocean flows

**Cullen, M ***(Met Office)*

Thursday 05 December 2013, 09:15-10:15

Seminar Room 1, Newton Institute

#### Abstract

The semi-geostrophic model is an accurate approximation to the Navier-Stokes equations when the Lagrangian Rossby number is small and the aspect ratio is less than f/N (where f is the Coriolis parameter and N the Brunt-Vaisala frequency). In practice this leads to a horizontal scale of around 1000km in the atmosphere and 100km in the ocean. The approximation is second order accurate in the limit epsilon tends to zero where the Rossby number is O(epsilon) and the Froude number O(sqrt(epsilon)). This approximation has a big advantage over the quasi-geostrophic approximation because it allow O(1) variations of the static stability, Coriolis parameter and orographic height. These features are essential in describing large-scale flows. The stability of the solutions of this system is consistent with the observed persistence of large-scale anomalies in the atmosphere and ocean. The failure of the approximation on smaller scales is associated with the lack of such structures on smal ler scales in the observed system. The talk will demonstrate how the semi-geostrophic model can be used to validate numerical methods, and how it can be extended to include a realistic model of the atmospheric boundary layer.

#### Presentation

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