Three-Dimensional Tidal Flow in an Elongated, Rotating Basin

The three-dimensional tidal circulation in an elongated basin of arbitrary depth is described with a linear, constant-density model on the f plane. Rotation fundamentally alters the lateral flow, introducing a lateral recirculation comparable in magnitude to the axial flow, as long as friction is not too large. This circulation is due to the imbalance between the cross-channel sea level gradient, which is in near-geostrophic balance with the Coriolis acceleration associated with the vertically averaged axial flow, and the Coriolis acceleration associated with the vertically sheared axial flow. During flood condition, for example, the lateral Coriolis acceleration near the surface exceeds the pressure gradient, tending to accelerate the lateral flow, while the converse is true near the bottom. As a result, with rotation, fluid parcels tend to corkscrew into and out of the basin in a tidal period. The axial flow is only weakly modified by rotation. When friction is small, the axial velocity is uniform in each section, except in a narrow bottom boundary layer where it decreases to zero. The boundary layer thickness increases with friction, so that with moderate or large friction, axial velocities are sheared from bottom to surface. When friction is large, the local and Coriolis accelerations are both small and the dynamics are governed by a balance between friction and the pressure gradient.