Western Boundary Currents (WBC) are a dominant feature in the world oceans. The stability of an idealized barotropic WBC on an $f$-plane is studied in a domain periodic in the alongshore direction. The jet profile has been chosen based on observations of the Agulhas Current, south of South-Afrika, and is such that both the on- and offshore side of the jet are susceptible to instabilities. The nonlinear interaction of these unstable modes is investigated as a function of the lateral Ekman number and results in pulse-like modulations of the background flow.
A Galerkin method is used to obtain a low dimensional dynamical system governing the finite amplitude evolution of the perturbations on the jet. A basis for projection is constructed using the linearly unstable eigenvectors and their inverted nonlinear interactions. This expansion has a close relationship to the underlying physics of the system. The resulting low-dimensional model allows for a detailed analysis of the dynamics of the jet in the nonlinear regime. Use is made of numerical parameter continuation techniques. This encompasses the tracking of periodic orbits as a function of model parameters and determining their stability characteristics by means of Floquet theory. The resulting bifurcation diagram provides insight in the mechanisms involved in the generation of pulse-like behaviour in WBCs. The relevance of the results with respect to observed phenomena in WBCs, such as Natal Pulses in the Agulhas Current, will be discussed.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics