The downstream effect of closing a barrier across an estuary with particular reference to the Thames

Abstract

The theory given in this paper considers the reflected surge experienced downstream due to closing a tidal barrier across an estuary during a rising tide or storm surge. The estuary considered is exponential in width and of constant depth, and the discussion is based on linear shallow-water theory with friction taken proportional to the velocity in accord with Lorentz’s linearization of Chezy’s law. In the calculation of the surge, the initial non-steadiness of the motion of the water in the estuary, due to the original tidal action, is neglected. The theory finds the surge initiated when a steady velocity is brought impulsively or otherwise to rest at the barrier. Shortly after closure the resultant water level is obtained by adding the transient surge, obtained in this way, to the tidal curve for the unobstructed estuary. Expressions are obtained for the reflected surge which occurs seawards of the barrier for the three cases, namely, complete instantaneous closure, a state approximating partial instantaneous closure and gradual closure. For example, in the case of instantaneous closure, the surge at any point downstream of the barrier begins with a bore followed by a more gradual change of the water surface level. The height of the bore is shown to fall off seawards as (width of estuary) -1/2 x (an exponential damping factor dependent on the friction). The theory is applied to the proposed Thames Tidal Barrier and the results are in reasonable agreement with model tests.