Long-period water surface fluctuations on a horizontal coastal shelf with a steep seaward face

Abstract

Steep slopes significantly influence the propagation of both short period waves and accompanying long-period waves with the same time scale as the wave groups. Therefore, conventional wave models are not directly appropriate for the computation of the wave field on such a slope. A numerical model is proposed for the simulation of long-period water surface fluctuations forced by short-period wave groups. This model is based on the generalized conservation equations of mass and momentum. The conventional closure relationship used for radiation stresses in most previous long-period wave models is upgraded for steep slopes and an explicit relationship is found for the dynamic component of the mean bottom pressure. The model is verified through some wave flume data collected on a steep slope. The model is then used to investigate long-period water surface fluctuations on horizontal shelves with steep seaward faces. It is found through numerical investigations that the long-period water surface fluctuations on a steeply faced coastal shelf greatly depend on the transmission of short-period waves. For short-period waves propagating without breaking, steeply faced shelves provide large long-period waves while opposite is true for breaking short-period waves.