GREEN LAW REVISITED - TIDAL LONG-WAVE PROPAGATION IN CHANNELS WITH STRONG TOPOGRAPHY

Green's Law states that tidal long-wave elevation zeta and tidal transport Q vary with width b and depth h according to zeta congruent-to b-1/2h-1/4 and Q congruent-to b+1/2h+1/4. 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 lambda). 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 congruent-to 90-degrees phase difference between Q and zeta and a very large phase speed, without the presence of a reflected wave; (4) channels with strong friction and/or strong topography (L << lambda) show very large deviations from Green's Law; and (5) these deviations arise because both frictional damping and the direct dependence of [Q[ and [zeta[ on topography (topographic funnelling) must be considered.