Nonlinear shallow water dynamics with odd viscosity

Spectral Viscosity for Shallow Water Equations in Spherical Geometry

A spherical spectral viscosity operator is proposed as an alternative to standard horizontal diffusion terms in global atmospheric models. Implementation in NCAR’s Spectral Transform Shallow Water Model and application to a suite of standard test cases demonstrates improvement in resolution and numerical conservation of invariants at no extra computational cost. The retention in the spectral vi...

Nonlinear edge waves and shallow-water theory

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...

Investigating vortex dynamics in shallow water with topography

Nonlinear Viscosity Algorithm with Perturbation for Nonexpansive Multi-Valued Mappings

In this paper, based on viscosity technique with perturbation, we introduce a new non-linear viscosity algorithm for finding a element of the set of fixed points of nonexpansivemulti-valued mappings in a Hilbert space. We derive a strong convergence theorem for thisnew algorithm under appropriate assumptions. Moreover, in support of our results, somenumerical examples (u...