Modeling the Coastal Ocean over a Time Period of Several Weeks

TL;DR

This paper develops and analyzes nonlinear hyperbolic PDE models for coastal ocean hydrodynamics over several weeks, proving existence, convergence, and characterizing the limiting behavior as a small parameter approaches zero.

Contribution

It introduces a simplified hyperbolic PDE model for coastal ocean dynamics and proves existence, uniform time interval, and convergence results as the small parameter tends to zero.

Findings

Existence of classical solutions on uniform time intervals

Weak-* convergence of solutions as small parameter approaches zero

Characterization of the limit equation satisfied by the solutions

Abstract

From a scale analysis of hydrodynamic phenomena having a significant action on the drift of an object in coastal ocean waters, we deduce equations modeling the associated hydrodynamic fields over a time period of several weeks. These models are essentially non linear hyperbolic systems of PDE involving a small parameter. Then from the models we extract a simplified and nevertheless typical one for which we prove that its classical solution exists on a time interval which is independent of the small parameter. We then show that the solution weak-* converges as the small parameter goes to zero and we characterize the equation satisfied by the weak-* limit