Estimating tidal current amplitudes outside estuaries and characterizing the zone of estuarine tidal influence

Abstract

Tidal currents within many estuaries are stronger than on the adjacent continental shelf. Estuarine tidal influence extends onto the shelf elevating tidal amplitudes above ambient shelf levels over a region outside the estuary. In this paper, a kinematic theory that describes tidal flow in these estuary–shelf tidal interaction zones is derived and tested. Using these results, tidal current amplitudes outside estuaries are estimated and the range and intensity of estuarine tidal influence is characterized. The estimates for the tidal current amplitudes ( u tide) of the dominant constituent are appropriate for linear or weakly nonlinear systems with predominantly barotropic tides; the ratio of tidal height to water depth is small ( η/ h≪1) in linear or weakly nonlinear regimes. Within tidal interaction zones, the tidal current amplitude is composed of an ambient shelf part ( u a) and an estuary-induced part ( u e). The characteristic shelf amplitude far from the estuary is used to set u a. Continuity arguments indicate that u e (averaged over a control volume arc centered on the mouth with radius r and a swath angle of γπ) approximately equals the ratio of the tidal volume flux through the mouth ( V m) and the cross-sectional area of any control volume arc ( u e ≈ V m / γ π r h ¯ ) . This approximation holds where the squared product of the tidal wave number and radial distance is small: ( kr) 2≪1. For a shelf with constant slope α and small coastal wall depth, the arc-averaged depth is h ¯ ≈ sr (where s=2 α/ pi for γ=1). For this shelf bathymetry, u e decays with squared radial distance from the estuary mouth. Theoretical predictions are consistent with observed tidal current amplitudes outside the Delaware Bay and Block Island Sound. In both test cases, the estimated and observed amplitudes exhibit an r −2 dependence and decay over a similar distance. The relative importance of estuarine tidal influence is assessed with the tidal interaction index ( T i= u e/ u a). The intensity of estuarine influence is characterized by the value of T i at the mouth ( T im). The extent of an estuary–shelf tidal interaction zone is measured by the interaction radius r i (where T i=1) and by r ∞ (where T i=0.1). These metrics are used to compare the tidal interaction zone characteristics for the Delaware Bay, Block Island Sound, several other major estuaries, and a small tidal inlet. The kinematic theory can be applied outside other estuaries where only limited tidal information is available or used to interpret observed patterns in tidal amplitudes and characterize the degree of estuarine influence.