A barotropic model of the linear semidiurnal tide over a continental slope

Semidiurnal tides, and especially the lunar tide M-2, are dominant dynamics in the Bay of Biscay. Strong tidal currents are associated with the presen ce of a significant continental slope. By combining Newton's gravitation la ws and Euler's equations, Laplace's equations contain the astronomical forc ing responsible for the observed semidiurnal tides. In shallow waters, this direct forcing is often neglected. We study here its influence on the tida l dynamics over the continental slope through the development of a simple m odel describing the barotropic semidiurnal dynamics on a transect perpendic ular to the slope. This new model results from the combination of two diffe rent models, i.e. the one developed by Rosenfeld and Beardsley (1987), whic h takes into account the tide-generating force, and that of Battisti and Cl arke (1982), which neglects it. A first model is developed by neglecting th e direct astronomical forcing in equations: it consists in solving a second -order homogeneous propagation equation for the barotropic semidiurnal tide and needs only coastal conditions as well as the knowledge of the along-sl ope wave number of the solution. For a mean slope typical of the South Brit tany area, this non-forced model provides results in accordance with those of Battisti and Clarke and Le Cann (1990). in particular, in the upper part of the slope, it shows a polarization inversion of tidal ellipses characte ristic of the tidal dynamics observed in this area. Then, the direct astron omical forcing is kept in equations. The simple model developed without thi s forcing is fitted in order to solve the resulting forced propagation equa tion for the barotropic tide. The solution of this second model is the sum of a forced wave responding to the direct astronomical forcing and of a fre e wave generated at the coastal boundary. Under the same boundary condition s, the results obtained with the influence of the tide-generating force are then compared with those obtained without it. This comparison allows one t o apprehend the importance of the direct astronomical forcing on tidal dyna mics across the slope: in particular, the main difference appears in deep w aters where this forcing induces a phase-lag between the plain and the shel f for the sea-surface slope. (C) 2001 Elsevier Science Ltd. All rights rese rved.