Cosine effect on shallow water equations and mathematical properties

Cosine Effect on Shallow Water Equations and Mathematical Properties

This paper presents a viscous Shallow Water type model with new Coriolis terms, and some limits according to the values of the Rossby and Froude numbers. We prove that the extension to the bidimensional case of the unidimensional results given by [J.–F. Gerbeau, B. Perthame. Discrete Continuous Dynamical Systems, (2001)] including the Coriolis force has to add new terms, omitted up to now, depe...

New Developments and Cosine Effect in the Viscous Shallow Water and Quasi-geostrophic Equations

The viscous Shallow Water Equations and Quasi-Geostrophic Equations are considered in this paper. Some new terms, related to the Coriolis force, are revealed thanks to a rigorous asymptotic analysis. After providing well-posedness arguments for the new models, the authors perform some numerical computations that confirm the role played by the cosine effect in various physical configurations. Ke...

Shallow Water Equations

where an denotes a vertical acceleration of the fluid, e.g., due to gravity. This formulation can be derived from the NS equations by, most importantly, assuming a hydrostatic pressure along the direction of gravity. Interested readers can find a detailed derivation of these euqations in Section A. In the following sections we will first explain how to solve these equations with a basic solver,...

Shallow Water Equations Implemented on GPUs

On asymptotically equivalent shallow water wave equations

The integrable 3rd-order Korteweg-de Vries (KdV) equation emerges uniquely at linear order in the asymptotic expansion for unidirectional shallow water waves. However, at quadratic order, this asymptotic expansion produces an entire family of shallow water wave equations that are asymptotically equivalent to each other, under a group of nonlinear, nonlocal, normal-form transformations introduce...