Journal of Conference Abstracts

The Rossby-wave Hydraulics of Coastal Flows

E R (Ted) Johnson (erj@math.ucl.ac.uk) & Simon Clarke (clarke@math.ucl.ac.uk)

Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, U.K.

This talk considers the role of long finite-amplitude Rossby-waves in determining the evolution of flow along a rapidly rotating channel with an uneven floor. The Rossby waves are forced on a potential vorticity interface in a channel with a cross-channel step change in depth where step position varies slowly along the channel. A nonlinear wave equation is derived describing the evolution of the potential vorticity interface. To leading order this is the hydraulic equation derived by Haynes, Johnson & Hurst (1993). Dispersion appears at the next order. Various solution regimes are identified. As well as slowly varying hydraulic solutions, two further types of steady solutions appear. These solutions are characterised by rapid transitions between supercritical branches of the hydraulic function. To fully resolve these solutions dispersive effects must be included. In the limit of very long obstacles these rapid supercritical transitions correspond to kink soliton solutions of the steady unforced problem allowing a criterion to be derived determining the position of the transitions. Steady and unsteady solutions of the dispersive hydraulic equation are presented which demonstrate that, apart from controlling the shape and position of the rapid supercritical transitions, the inclusion of dispersive effects generally results in an asymptotic solution in reasonable agreement with the hydraulic solution. However, in some cases dispersion can change the whole character of the flow.