Abstract
A new general theory has been developed to determine both the tidal response of estuaries and the effects of cross-channel tidal barriers on this response. The theory is shown to be widely applicable and provides a connecting framework against which the response of different estuaries can be compared.
Assuming a breadth variation BL(X/λ)mM and a depth variation HL(X/λ)nM where X is the distance from the head of the estuary, general solutions are obtained for the, shallow-water wave equations expressed in a linearized one-dimensional form. These solutions introduce an important new parameter. v=(n+1)/(2−m), referred to as the estuarine shape number. For any estuary, tidal elevations and velocities are expressed as a function of position along the estuary and the appropriate v, value. By introducing a further dimensionless parameter y to represent position along the estuary, the expression for tidal elevation (or velocity) can be illustrated in a single diagram with v and y as orthogonal axes. For a particular location, the parameter y has the additional property of being directly proportional to tidal frequency. Hence the single diagram shows the tidal response at all points along any estuary for all tidal constituents. Alternatively, the same diagram may be used to show the frequency response at any particular location.
An extension of this theory examines the influence of tidal barriers. It is shown how the effect on both elevations and velocities varies according to 1) the position of the barrier, 2) the location along the estuary; 3) the location of the mouth, i.e., the position at which conditions are assumed unchanged; 4) the tidal constituent considered; and 5) the relevant friction coefficient. Thus, in modeling studies involving tidal barriers, the present theory provides a means of estimating how far downstream the open sea boundary must be located. Where the theory suggests a downstream boundary outside of the estuarial region, however, alternate approaches may be necessary. As examples of the application of this theory, tidal responses are examined in the following estuaries: Fraser, Rotterdam Waterway, Hudson, Potomac, Delaware, Miramichi, Bay of Fundy, Thames, Bristol Channel and St. Lawrence.
