Schmidt, Gavin Anthony; (1994) The calculation, scattering and stability of topographic rossby waves. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis discusses the calculation and properties of topographic Rossby waves in homogeneous and continuously stratified rotating flow. These waves exist due to variations in the background potential vorticity arising from changes in topography or rotation. The first part considers the calculation of the frequency and wavenumber of trapped topographic Rossby waves over various types of topography - along a coastal shelf (giving coastally trapped waves), over a submerged ridge and around an axisymmetric sea mount. A new direct method of calculation in the low frequency continuously stratified case is introduced. This uses a Green's function to reduce the problem to a one dimensional integral across the shelf. Asymptotic expansions in the stratification parameter B = ND/fL, where N is the buoyancy frequency, D a typical depth, L a typical length and f the Coriolis parameter are presented. Both strong stratification (B > 1) and weak stratification (B < 1) are treated in this fashion and approximations that are accurate for all B are constructed for certain simple topographies. The circumstances that can lead to singularities appearing in the solution are investigated and the consequences for general circulation models discussed. The numerical method is applied to the solution of scattering problems as the topography changes and to determining the wind-forced response. An isobath tracing result is used to calculate the distribution of energy among the transmitted waves. Examples are given using various geometries including straits and ridges abutting a coastal shelf. The stability of horizontal shear flow to small disturbances is considered. These disturbances have the form of topographic Rossby waves. Unstable modes can occur over ridges. Detailed examples are worked out in the barotropic case and in the continuously stratified long-wave case. In both cases the instabilities are centred at points where the shear flow brings two opposing waves relatively to rest.

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