| Abstract: | Recently, a growing interest has been devoted to the investigation of solution techniques of shelf waves in a stratified fluid using so-called ''Resonance Iterative" methods, e.g., Brink and Chapman's model (1987) and Wilkin's model (1988). A new numerical technique for finding eigenvalues and flow fields for this coupled shelf wave problem is presented here which seems to be simple to apply, of fast convergence and accurate. The new method employs a representation of vertical structure using dynamic basis functions which depend on the stratification; however unlike the Wilkin (1988) model, it reduces the problem to a set of ordinary differential equations whose solution employs an iterative shooting algorithm. In order to show the accuracy and usefulness of the present method, the results of our computation have been compared with those obtained by exact solutions in a few cases, by Brink and Chapman's model (1987) and by Wilkin's model (1988). A major result of the present study is the discovery of spurious and abnormal resonances which can occur by the resonance iteration method; several examples of these anomalous modes have been demonstrated. The proposed new algorithm avoids the potentially serious problems associated with spurious modes generated by the resonance iteration method, provided that the number of vertical basis functions employed in the representation of flow fields is restricted to a value dependent on the degree of stratification. |
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