Propagation of axi-symmetric nonlinear shallow water waves over slowly varying depth

Propagation of Axi-Symmetric Nonlinear Shallow Water Waves over Slowly Varying Depth

A problem in nonlinear water-wave propagation on the surface of an inviscid, stationary fluid is presented. The primary surface wave, suitably initiated at some radius, is taken to be a slowly evolving nonlinear cylindrical wave (governed by an appropriate Korteweg-de Vries equation); the depth is assumed to be varying in a purely radial direction. We consider a sech profile at an initial radiu...

Nonlinear edge waves and shallow-water theory

Shallow Water Waves over Polygonal Bottoms

The traditional shallow water model for waves propagating over varying bathymetry depends for its derivation on the asymptotic analysis of a Dirichlet-Neumann operator. This analysis however is restricted to smoothly varying topographies. We propose an adaptation to one dimensional polygonal bottoms using the conformal mapping idea of Hamilton and Nachbin. The asymptotic analysis of the Dirichl...

On Slowly Varying Stokes Waves

ON SLOWLY VARYING STOKES WAVES by VINCENT HWA-HING CHU In this thesis investigations are made on the theory of a train of slowly modulated gravity waves propagating over uneven bottom topography. The primary object is to study the interplay of amplitude dispersion the frequency dispersion in waves on the surface of water where the depth is not too shallow compared to a typical wave length. The ...

Depth inversion in shallow water based on nonlinear properties of shoaling periodic waves 1

Two depth inversion algorithms applicable to coastal waters are developed, calibrated, and validated based on results of computations of periodic waves shoaling over mild slopes, in a two-dimensional numerical wave tank based on fully nonlinear potential flow theory. In actual field situations, these algorithms would be used to predict the cross-shore depth variation h based on sets of values o...