Oscillating Barotropic Currents along Short Channels

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Abstract
Intuitively, the transport of an oscillating flow in a short channel should be constrained to be approximately the same at all cross sections; that is, the transport is nondivergent. This intuitive constraint is quantified by developing a generalized definition of “shortness” given by the smallness of a nondimensional parameter ε. This parameter assesses the shortness of channels of variable cross-sectional area, with linear or nonlinear dynamical balances and, thus, is applicable to a wide range of channels, from tidal flow through the entrance to an estuary to subinertial flow through a strait. This analysis leads to a general result for a barotropic oscillating flow, which states that the variation in the amplitude of the transport along the channel is of order 2ε of the mean transport and the variation in the transport’s phase is of order 2 tan−1ε. A diagnostic model for tidal flow within a “short” narrow channel of variable depth is developed. The model shows that the phase of the cross-sectional average velocity is dependent only on the relative amplitude and phase of the surface oscillation at the ends of the channel. Tidal measurements presented in a companion paper provide observational support for both the general result and diagnostic model.

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