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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 99, NO. C2, PAGES 3321-3336, FEBRUARY 15, 1994 Tidal propagation in strongly convergent channels Carl T. Friedrichs 1 and David G. Aubrey Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts Abstract. Simple first- and second-order analytic solutions, which diverge markedly from classical views of cooscillating tides, are derived for tidal propagation in strongly convergent channels. Theoretical predictions compare well with observations from typical examples of shallow, "funnel-shaped" tidal estuaries. A scaling of the governing equations appropriate to these channels indicates that at first order, gradients in cross- sectional area dominate velocity gradients in the continuity equation and the friction term dominates acceleration in the momentum equation. Finite amplitude effects, velocity gradients due to wave propagation, and local acceleration enter the equations at second order. Applying this scaling, the first-order governing equation becomes a first-order wave equation, which is inconsistent with the presence of a reflected wave. The solution is of constant amplitude and has a phase speed near the frictionless wave speed, like a classical progressive wave, yet velocity leads elevation by 90 ø, like a classical standing wave. The second-order solution at the dominant frequency is also a unidirectional wave; however, its amplitude is exponentially modulated. If inertia is finite and convergence is strong, amplitude increases along channel, whereas if inertia is weak and convergence is limited, amplitude decays. Compact solutions for second-order tidal harmonics quantify the partially canceling effects of (1) time variations in channel depth, which slow the propagation of low water, and (2) time variations in channel width, which slow the propagation of high water. Finally, it is suggested that phase speed, along-channel amplitude growth, and tidal harmonics in strongly convergent channels are all linked by morphodynamic feedback. 1. Introduction 1.1. Classical Tidal Cooscillation In this paper a new asymptotic solution is presented for the barotropic tidal wave in strongly convergent channels. The type of wave described here, which paradoxically exhibits properties of both standing and progressive waves simultaneously, occurs in real tidal estuaries such as the Thames and the Tamar in the United Kingdom and the Delaware in the United States (Figure 1). Like a classical progressive wave, this wave does not appreciabl'y grow or decay along channel, and its phase speed is nearly equal to the frictionless wave speed. Like a classical standing wave, it produces currents which are slack near high and low water. Unlike either wave, however, the dynamic balance which produces this asymptotic solution is strongly frictional. This new solution and its governing equation are markedly different from the classical view of damped tidal cooscillation, yet some of its properties may be confused
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This note was uploaded on 01/21/2011 for the course ADFA 1082 taught by Professor Dr.xiaohuawang during the Three '10 term at University of New South Wales.

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