Classification of tidal response in estuaries from channel geometry

Abstract

Summary. By using exponential functions to approximate channel geometry, the tidal response in an estuary can be directly classified into one of three types. Thus, with the breadth represented in dimensionless form by boexp(αx) and the depth by exp(βx) (x is the dimensionless length along the estuary) the three types are delimited by: (1) α+ 2β < 10, (2) α+ 2β≪ 10 and (3) α+ 2β∼ 10. Using an analogy with the free vibrations of a damped simple‐harmonic oscillator, α+ 2β represents the ‘damping factor’. Estuaries of type (1) are under‐damped and the elevation amplitudes vary in an oscillatory manner along the x‐axis. Such estuaries exhibit a response peak at some ‘natural frequency’ roughly approximating quarter‐wavelength resonance. Estuaries of type (2) correspond to critical damping and produce maximum amplification of tidal elevations. Estuaries of type (3) are over‐damped and elevation amplitudes increase monotonically towards the head. In this category, the channel geometry expands at a rate such that quarter‐wavelength resonance does not occur. The above findings stem from a combination of analytical and numerical methods. Validation of the theory follows from a comparison of observed and calculated responses in 10 major estuaries. For the first time, the large tidal ranges experienced in the Bay of Fundy and Bristol Channel are shown to result more from their overall shapes (i.e. they have values of α+ 2β∼ 10) rather than from a specific resonant length. The construction of a tidal barrier at some distance x1 from the head of an estuary effectively increases both α and β by a factor exp(β1/2). Thus the impact of barriers on any estuary is readily apparent and the high sensitivity of type (2) estuaries such as Fundy and the Bristol Channel to barrier construction is explained. The variation of tidal response with differing tidal species is examined with particular emphasis on how the appropriate linearized friction coefficient varies for each constituent. The sensitivity of an estuary to variations in this linearized friction coefficient is shown to be strongly influenced by the dimensionless estuarine length xL. Copyright © 1985, Wiley Blackwell. All rights reserved