Interaction Between Tide and Surge in the Thames

Abstract

Observations of storm surges in the Thames reveal an interaction effect between tide and surge which is statistically significant, and takes the form of an amplification of surge height (whether positive or negative) on the rising tide. Representing the estuary by a channel of constant depth and exponentially varying breadth the distributions of elevation and current along the estuary have been computed for different combinations of input (at the seaward end) of tide and surge. The results agree remarkably well with the phenomenon as observed in nature; they provide the basis for a simple physical explanation of the interaction, in which it is argued that the principal mode of interaction is by the surge changing the phase of the tide, and vice-versa. This argument requires the tides in the Thames to be of progressive wave type; this is shown to be true, in general, for tides subject to friction in an exponential estuary of constant depth. The computations also reveal that maximum levels are propagated upstream so that a higher maximum is amplified less than a lower maximum. The paper confirms a number of Proudman's earlier theoretical results on interaction in estuaries.