INFLUENCE FUNCTIONS FOR EDGE WAVE-PROPAGATION OVER A NONPLANAR BOTTOMBATHYMETRY

The problem of edge waves propagating over a nonplanar bottom bathymet ry is examined. Assuming that the variation from the planar case is sm all, we examine the problem using a perturbation expansion. This assum ption allows an analytical estimate of how nonplanar features change t he frequency and spatial structure of an edge wave with a given wavenu mber. We find that these changes can be conveniently expressed in term s of ''influence functions.'' For example, the change in frequency, si gma(1,n), of a given edge-wave mode, n, can be expressed as sigma(1,n) /sigma(0,n) = integral(0)(infinity)h(1)I(sigma)dx where x is the cross -shore coordinate, h(1)(x) is the deviation from the planar topography , sigma(0,n) is the frequency of the edge wave on a plane beach, and I -sigma is the influence function. Similar results are also derived for the spatial structure of the edge wave. The results show that 1) in g eneral, the spatial structure of the edge wave is more sensitive to bo ttom perturbations than the frequency, and 2) at a given wavenumber, t he higher modes are more sensitive to shoreline features than the lowe r modes. (C) 1998 American Institute of Physics.