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Article
Green's Law Revisited: Tidal Long-Wave Propagation in Channels with Strong Topography
Journal of Geophysical Research
  • David A. Jay, Portland State University
Document Type
Article
Publication Date
11-1-1991
Subjects
  • Tides -- Influence of topography on,
  • Tides -- Mathematical models,
  • Perturbation (Mathematics)
Abstract

Green's Law states that tidal long-wave elevation ζ and tidal transport Q vary with width b and depth h according to ζ ≌ b−1/2h−1/4 and Qb+1/2h+/4. This solution is of limited utility because it is restricted to inviscid, infinitesimal waves in channels with no mean flow and weak topography (those with topographic scale L ≫ wavelength λ). An analytical perturbation model including finite-amplitude effects, river flow, and tidal flats has been used to show that (1) wave behavior to lowest order is a function of only two nondimensional parameters representing, respectively, the strength of friction at the bed and the rate of topographic convergence/divergence; (2) two different wave equations with nearly constant coefficients can be derived that together cover most physically relevant values of these parameters, even very strong topography; (3) a single, incident wave in a strongly convergent or divergent geometry may mimic a standing wave by having a ≡ 90° phase difference between Q and ζ and a very large phase speed, without the presence of a reflected wave; (4) channels with strong friction and/or strong topography (L ≪ λ) show very large deviations from Green/s Law; and (5) these deviations arise because both frictional damping and the direct dependence of |Q| and |ζ| on topography (topographic funnelling) must be considered.

Description

Copyright 1991 American Geophysical Union

Persistent Identifier
http://archives.pdx.edu/ds/psu/8053
Citation Information
Jay, D. A. (1991), Green's law revisited: Tidal long-wave propagation in channels with strong topography, J. Geophys. Res., 96(C11), 20585–20598, doi:10.1029/91JC01633.