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Modelling Surface Driven Flows in the Ocean

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Buoyancy driven flows at the top of the ocean or bottom of the atmosphere are inherently different from their interior dynamics. Oneidealized model that has recently become very popular to idealizethese surface flows with strong rotation is Surface Quasi-Geostrophic (SQG) dynamics. This model is appropriate for large-scale dynamics and assumes the motion is in near geostrophic and hydrostatic balance. Many of the numerical simulations of SQG have shown thatvortices are frequently generated at very small scales scales thatare well beyond the SQG limits.In this talk we examine the dynamics of a rotating three-dimensionalelliptic vortex in both the SQG model and a more general and muchmore complicated primitive equation model. In order to compute highresolution solutions to the three dimensional primitive equations we make use of Sharcnet resources. We find that in the case of strongrotation (small Rossby number) we confirm the predictions from SQG.With weaker rotation (moderate Rossby number) we see the non-SQG effects that arise and find that the regime where SQG can beappropriate can be very limited. We conclude that some of thepredictions that arise from the SQG model might not be very accuratein idealizing geophysical flows at the surface.