North Sea pole tide dynamics

Abstract

S U M M A R Y Laplace tide equations (LTEs) augmented to include linear bottom friction and Chandler wobble forcing have been solved numerically for the pole tide in the North Sea employing realistic bottom topography and geometrical boundaries. The motivation for our study is the need to explain observations of enhanced pole tide amplitudes and eastward intensification along the southern boundary of the Sea. Following Wunsch (1974), the tidal dynamics are considered to depend on non-equilibrium pole tide behaviour at the open northern boundary of the Sea. With reasonably small bottom friction and open boundary forcing, the amplitude of the pole tide in the North Sea is found to be close to equilibrium, i.e. the coastal amplitudes do not match the observations. However, the phase lag obtained is close to those inferred from tide gauge analyses. Under these conditions, the North Sea has the potential to dissipate a considerable fraction (-25 per cent) of Chandler wobble energy. If much larger bottom friction is considered, the resulting pole tide amplitudes are more highly variable within the Sea, and-if the open-boundary forcing is also much larger-the tidal amplitudes match many of the observations; in this case, however, the tidal currents dissipate an unacceptably huge amount of wobble energy. An earlier version of this problem-proposed by Wunsch (1974) and reconsidered by Dickman & Preisig (1986), in which time-independent LTEs are postulated in a North Sea modelled with analytical bottom topography and a rectangular domainis also fully solved, via the method of weighted residuals. The solutions include one in which the non-equilibrium portion of the tide height is nearly constant all over the domain. The corresponding tidal currents are negligibly slow. Our work points to the importance of realistic bottom topography and coastline geometry in affecting the tidal dynamics; such factors to date have not been considered in theoretical analyses of the North Sea pole tide. The realistic bathymetry and geometry produce a large variability in bottom friction, which is inversely proportional to the water depth, and thereby generate substantial dynamic behaviour-despite the long period of the pole tide. We find that these factors significantly enhance the tidal currents and promote an eastward intensification of the non-equilibrium tide height near the southern coast.