On Wavenumber Estimates for Forced Continental Shelf Waves

Abstract

We derive expressions that predict the variations of Cartesian, rotaryand elliptical properties of free and forced barotropic continentalshelf waves as functions of alongshore and cross-shore location.Bottom friction is shown to significantly complicate these expressions.Particular attention is given to the spatial variability in the phasesof forced waves as functions of the wavenumber of the forcing andthe corresponding free wave mode. Consideration of the alongshoreand across-shelf structure predicted by the theory indicates that,for a given frequency, the relative merits of Cartesian or rotaryFourier analysis of data depends on the location of the observationstations in the across shelf direction and on the geometry of thecontinental shelf and slope. The specific case of observed, diurnalperiod (K1) continental shelf waves off Vancouver Island is usedto illustrate how the free and forced shelf wave models lead to differentinterpretations for the wavelengths of the free wave component. Theresults demonstrate the nontrivial nature of the forced problem andemphasize the need for accurate resolution of the wavenumber of thedriving mechanism.