IRREGULAR WAVES ON A CURRENT

Abstract

In coastal areas interacting currents and waves are quite frequent. The currents are generated by the tides or the discharge of a river; the waves are irregular short crested, generated by the wind. A suitable numerical wave model for this situation is presented in this paper. It is based on the Boussinesq-Wave-Equations (BWE) which were extended to simulate the influence of a current on a wave as well as the effects of nonlinear wave-wave interaction in a propagating wave spectrum. An analytical approach to describe wave-current interaction was given by Longuet-Higgins/Steward (1960) [3]. They investigated linear small amplitude waves in a moving medium and introduced the concept of radiation stress to determine the change of wavelength and wave amplitude as a function of the current and the direction of wave propagation. Their fundamental work was the basis for the development of various numerical models, which were reviewed recently by Jonsson (1989) [2]. Most of these models are restricted to linear (small amplitude) wave theory. The wave climate in shallow water is generated by the influence of bottom topography as well as by nonlinear wave-wave interaction in a propagating wave spectrum, which cannot be described by linear wave theory. Instead, such weakly nonlinear waves are frequently modeled using the BWE. The development of models based on these equations first began in the late 70's. Since then, a number of studies have been carried out to verify their capabilities. It has been shown that they are able to simulate accurately combined refraction, diffraction, reflection and shoaling (see for example Madsen/Warren (1984)[4] as well as the nonlinear wave-wave interaction in a wave spectrum propagating over an uneven bed (see for example Priiser/Schaper/Zielke (1986)[7]). Boussinesq wave models have now become a practical tool for engineering applications.