School of Mechanical Engineering Yuval Yevnin

School of Mechanical Engineering Seminar
Monday, April 26, 2017 at 14:00
Wolfson Building of Mechanical Engineering, Room 206

A bottom reflection source term for wave forecasting models

Yuval Yevnin

MSc student under supervision of Dr. Yaron Toledo

The Wave Action conservation Equation (WAE) is a commonly used governing equation in numerical ocean wave models today. The WAE is based on the conservation of wave action flux – a frequency normalized wave energy, to generate a wave propagation forecast in these numerical models. During the derivation of the WAE, wave reflection from the sea bottom is neglected. The neglected wave reflection occurs when waves propagate in the nearshore environment over a sloping sea bottom and a part of the incident wave energy is transferred to a wave propagating in the opposite direction. Wave reflection can have a significant effect on the nearshore wave regime. It can alter the wave height in as much as 20% and generate waves that penetrate harbors or get trapped in the nearshore environment (edge waves). Nevertheless,   wave forecasting models use either a limited empirical source term for taking into account the bottom reflection, or neglect it entirely.

In the presented work, the mathematical basis for a new bottom reflection source term fitting for the entire spectral regime is described and discussed. The Mild-Slope Equation (MSE), a simplification of the Laplace equation with the assumptions of free-surface and impermeable mildly-sloping bottom boundary conditions, is written in form of two coupled terms – one for the incident wave, and the other for the reflected component. Assuming small reflection, a perturbation approach is applied resulting in the decoupling of the equations to two separate wave-action equations in the leading order. The solution of the second order equation results in a source term accounting for wave reflection. With this development, a fully analytical solution to the wave reflection of a sloping sea bottom is provided for use in numerical wave prediction models. The approximation shows good results in comparison to the MSE.