Tidal flow around an island with a regularly sloping bottom topography

Abstract

A numerical model of the tides in the neighbourhood of Portland Bill (Pingree & Maddock, 1977; Maddock & Pingree, 1978) indicated that there was some asymmetry in the flood and ebb tidal patterns due to the effects of the Earth's rotation. Thus, in addition to the generation of vorticity due to the bottom frictional torque which becomes large in the high-velocity shoaling region near the promontory, vorticity is generated as columns of water with planetary vorticity are stretched or squashed as they move across water depth contours.In order to examine the Portland Bill situation in more detail, a model was developed in plane polar coordinates (Pingree & Maddock, 1979). This model allowed the flow to be taken around the promontory without the numerical difficulties associated with corners in rectangular grid meshes and gives increased resolution near the headland where the major changes in tidal structure occur. The regular geometry of the polar model also allows the use of an idealized submarine topography and therefore changes in tidal flow due to imposed beach gradients can readily be examined.The polar model has now been developed to derive the tidal flow around an idealised circular island surrounded by a uniformly sloping beach gradient. In the absence of effects due to the Earth's rotation the derived tidal structure and the associated patterns of residual flow possess twofold symmetry. In a rotating reference frame, however, some asymmetry in these flow patterns can be detected. In this paper some numerical results showing the hourly tidal streams around an island are derived.