The effects of wind on the generation of surface wave in the shallow water equation
Rifky Fauzi, L. Hari Wiryanto
Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung, 40132, Indonesia
Abstract
In this paper, the shallow water equation is modified so that it includes wind effect using Jeffreys sheltering theory. The modification allows this model to have a wave grow or decay mechanism under the action of wind gust above the surface. The wave generation or damping is investigated by calculating critical wind velocity to excite oscillatory waves on the surface. The result shows that critical wind is proportional to a numerical constant, namely the sheltering coefficient, which related to the capability of wave overcome the wind gust. Thus this model has the convenience that the critical wind speed may comparable to physical data for a suitable choice of this constant.
Keywords: shallow water equation; wave instability; wind effect; Jeffreys sheltering mechanism
Topic: Coastal and Ocean Dynamics