Water exchange in fjords induced by tidally generated internal lee waves

Abstract

Tidal processes are examined that control the water exchange between two basins of the Trondheimsfjord through a narrow channel with sills. For this purpose, a non-hydrostatic numerical model based on the laterally averaged Reynolds equations in the Boussinesq approximation was developed. The model takes into account the real vertical fluid stratification, variable bottom topography and variable cross-section of the fjord. Numerical experiments were performed to investigate tidally generated internal waves and their influence on the water exchange. The model produces both baroclinic tides and tidally generated lee waves. It was found that, for the Skarnsund strait which connects the Middle Fjord and the Beitstadfjord, the internal tides generated over the Skarnsund sills are very weak. Their amplitudes do not exceed 1 m. The intense short internal waves, which are identified as unsteady lee waves, comprise the basic input of the total internal wave field. These waves are generated by tidal currents at sill breaks, are trapped by topography in the generation area and grow by continuing feedback into large-amplitude waves. As the tidal flow slackens, they move upstream as freely propagating waves. As essentially nonlinear responses, the lee waves cause a nonlinear water transport. The detailed analysis of the residual currents produced by unsteady lee waves (which are propagating in both directions from the Scarnsund sills) has shown, in particular, that the residual currents can reach values as high as 0.27 m s−1. It was also found that such currents exert a considerable effect on the water exchange through the Skarnsund strait between the adjacent basins. This mechanism can play an important role in water renewal and formation of the Beitasdfjord waters.