Capturing Physical Dispersion Using a Nonlinear Shallow Water Model

An integrable shallow water equation with linear and nonlinear dispersion.

We use asymptotic analysis and a near-identity normal form transformation from water wave theory to derive a 1+1 unidirectional nonlinear wave equation that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation. This equation is one order more accurate in asymptotic approximation beyond KdV, yet it still pr...

A dispersion-relation-preserving algorithm for a nonlinear shallow-water wave equation

The paper presents an iterative algorithm for studying a nonlinear shallow-water wave equation. The equation is written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. We propose a two-step iterative method that first solves the evolution equation by the implicit midpoint rule and then solves the Helmholtz equation using a three-poi...

Nonlinear shallow - water solutions using the weak temperature gradient approximation

A form of the weak temperature gradient (WTG) approximation, in which the temperature tendency and advection terms are neglected in the temperature equation so that the equation reduces to a diagnostic balance between heating and vertical motion, is applied to a two-dimensional nonlinear shallow-water model with the heating (mass source) parameterized as a Newtonian relaxation on the temperatur...

Nonlinear edge waves and shallow-water theory

A Shallow Water Spectral Wave Model

A shallow water spectral wave prediction model based on a numerical solution of the radiative transfer equation is presented. The model is second generation and uses a simple yet effective representation for the nonlinear source term. In addition, the model pays particular attention to the shallow water processes of refraction, shoaling, bottom friction, and wave breaking. The flexibility of th...