Barotropic tidal dynamics of the Bay of Biscay shelf: observations, numerical modelling and physical interpretation

Abstract

The first order dynamics of the Bay of Biscay shelf are mostly dominated by barotropic semidiurnal tides. The diurnal tides and currents are weak. Quarter-diurnal tides are strongly amplified on the shelf. In this paper, we investigate the two major superinertial tidal bands (semidiurnal and quarter-diurnal). A description in terms of data is given first (Section 2). Coastal sea level and original open sea data (bottom pressure and currents), harmonically analysed, are studied. A numerical model is then used to provide a coherent and dense picture of the tidal dynamics of M 2 and M 4 and their variability (Section 3). Care is taken to assess the validity of the model by comparison with bottom pressure and coastal sea level data. M 2 amplitudes are increasing crossshore by an order of 20% and M 2 phases are slowly propagating to the northwest. M 2 currents are maximum at the shelf break. M 4 amplitudes are increasing by a factor 10 between the shelf break and the coast: the shelf is actually close to resonance in its central part. M 4 phases are propagating to the north. An amphidromic point is apparent in the northern outer part of the shelf. Using the data, we then produce a shelf-scale momentum and continuity balance for M 2 (Section 4). The simple model described by Battisti and Clarke (1982a, Journal of Physical Oceanography, 12, 8–16) is applied successfully. The M 2 equilibrium may be interpreted as follows: the deepsea Kelvin wave induces on the shelf a Poincaréwave which is almost perfectly reflected. The energy fluxes are directed alongshore (southeastward) on the shelf and little dissipation is seen to occur. The alongshore variability may be explained partly by the alongshore variations of the cross-shore bathymetric profile. For the quarter-diurnal band (Section 5), the shelf is close to resonance in its central part [the Clarke and Battisti (1981, Deep-Sea Research, 28, 665–682) criterion is met: ga/(ω 2 − f 2) ∼ L, where a is an average cross-shore bottom slope, ω the frequency and L the shelf width]. A modified version of the Battisti and Clarke (1982a) theory is applied successfully to M 4. M 4 energy fluxes are directed onshore. Both onshore and alongshore phase propagation and partial reflection follow. Through resonance, M 4 is strongly amplified cross-shelf and dissipated in coastal areas. In addition to local generation, the M 4 tide is forced on the shelf from the shelf break. This is thought to result from an M 4 tide in the Bay of Biscay which is itself co-oscillating with an oceanic M 4 tide originating from the Celtic Sea and English Channel regions. The non-linear generation of M 4 at the shelf break is thought to be relatively unimportant.