The dynamic coupling of a third-generation wave model and a 3D hydrodynamic model through boundary layers

Abstract

Abstract A third-generation wind wave model based on the energy balance equation taking into account the effects of time-varying currents and coupled dynamically with a semi-implicit three-dimensional hydrodynamic model incorporating the influences of time- and space-varying vertical eddy viscosity, bottom topography and wave-current interactions is presented in this paper. The wave model is synchronously coupled with the three-dimensional hydrodynamic model through the surface atmospheric turbulent boundary layer and the bottom boundary layer. The theory of Janssen (1991) (in Journal of Physical Oceanography 21 , 1631–1642) is used to incorporate the effects of waves on the surface boundary layer, while the theory of Grant and Maddsen (1979) [in Journal of Geophysical Research (Oceans) 84 , 1797–1808], which was used by Signell et al. (1990) (in Journal of Geophysical Research 95 , 9671–9678) on the bottom boundary layer for constant waves, is modified for the inclusion of time-varying waves. The mutual influences between waves and currents are investigated through an idealized continental shelf case and hindcastings of storm events in the sea area adjacent to Hong Kong in the northern South China Sea. Calculations are compared with other computed results and observations. Calculations show that the wave-dependent surface stress incorporated in the three-dimensional hydrodynamic model has significant impact on water surface velocities and surface elevations (over 10% higher). The inclusion of wave-dependent bottom stress also shows some effects; however, in the presence of the wave-dependent surface stress, its effect on surge levels becomes negligible. The effect of currents on waves amounts to the reduction of the significant wave height by about 8% and less for wave mean periods. However, the inclusion of the wave-dependent bottom stress in the three-dimensional hydrodynamic model has little effect on wave characteristics whether or not the wave-dependent surface stress is considered although it does reduce the bottom flow velocities, especially in shallow water regions. © 1997 Elsevier Science Ltd