Bathymetry Geometry Research Articles

Regions of estuarine convergence at high Rossby number: A solution in estuaries with elliptical cross sections

Generation of convergence regions in homogeneous rotating rectilinear estuaries is addressed. The mechanism investigated is the tilting of the planetary vorticity by the vertical shear of the along‐estuary flow, which can result in rapidly growing surface convergence regions aligned along the axis of the estuary. The complexity introduced by the bathymetry geometry and the nonlinearity of the equations has resulted in computationally intensive numerical solutions to this problem [Mied et al., 2000; Handler et al., 2001]. However, an analytical solution that will allow the study of varying parameters and the observation of general trends is possible with a judicious choice of bottom bathymetry and appropriate analytical simplifications. The equations for the along‐channel flow (V) and the cross‐channel stream function (ψ) become independent in the limit of vanishingly small rotation or large Rossby number. Consequently, we express them as an asymptotic series in the reciprocal of the Rossby number (1/Ro), and find that the choice of an elliptically shaped bottom profile allows us to solve for the leading order terms. The steady along‐channel flow is a Poiseuille flow on a nonrotating Earth, while the related cross‐channel response is a closed circulation cell with a clockwise rotation when looking in the direction of the along‐channel flow. A salient result is that the associated cross‐channel surface convergence is proportional to the Coriolis parameter (f), the maximum along‐channel velocity, and the aspect ratio (depth/width) of the channel.