Analytical Derivation of Three Dimensional Vorticity Function for wave breaking in Surf Zone

TL;DR

This paper develops an analytical three-dimensional vorticity model for wave breaking in surf zones using nonlinear Boussinesq equations, aiding numerical simulations of wave dynamics.

Contribution

It introduces a novel analytical derivation of 3D vorticity equations incorporating rotational effects for wave breaking modeling.

Findings

Model reproduces key surf zone dynamics

Accurately predicts nonlinear wave heights near breaking

Provides foundational equations for numerical simulation

Abstract

In this report, Mathematical model for generalized nonlinear three dimensional wave breaking equations was de- veloped analytically using fully nonlinear extended Boussinesq equations to encompass rotational dynamics in wave breaking zone. The three dimensional equations for vorticity distributions are developed from Reynold based stress equations. Vorticity transport equations are also developed for wave breaking zone. This equations are basic model tools for numerical simulation of surf zone to explain wave breaking phenomena. The model reproduces most of the dynamics in the surf zone. Non linearity for wave height predictions is also shown close to the breaking both in shoaling as well as surf zone. Keyword Wave breaking, Boussinesq equation, shallow water, surf zone. PACS : 47.32-y