Free Surface Motions: Tides, Seiches, and Subtidal Variations

Document Type

Article

Publication Date

3-6-2012

Abstract

General governing equations for estuaries and coastal regions are given as a special case of those of Newtonian fluids under the influence of turbulence, density gradient, atmospheric pressure gradient, and tide-generating force. The equations are then simplified for barotropic motion, particularly tidal, seiche, and tidally-driven motions. The linearized equations are used to discuss frictional tidal propagation in an elongated straight channel. The importance of the Earth's rotation is then discussed with the Kelvin wave solutions in a long channel. For barotropic tidal or seiche problems, the Earth's rotation is shown to be quite small in general when there is no stratification. Two-dimensional (2D) and three-dimensional (3D) models are then discussed for the effect of variable bathymetry. The bottom friction and cross-channel depth variations are shown to have significant effect on the tidal phase and tidal ellipses of the current velocity. The sub-tidal (or residual) flow is then discussed for variable depth problems. Some relevant observations of sub-tidal flows are then analyzed. A technique to separate barotropic from baroclinic motions is discussed and the effect of channel curvature examined using both analytic model and observations. It is demonstrated that the advective nonlinearity is a dominant term when channel curvature and bathymetry variations are significant.

Publication Source (Journal or Book title)

Treatise on Estuarine and Coastal Science

First Page

91

Last Page

122

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