Tides and storm surges in a long uniform gulf

Abstract

One of the most outstanding problems in the study of storm surges is that of the interaction with tides. Since the equations of motion are non-linear the surge cannot be adequately studied or forecast in relation to the meteorological situation until this problem of inter-­action is solved. The important subject of probability of the combined effects of surges and tides reaching or exceeding danger levels also necessitates the solution of the problem, for there is some evidence to show that the largest apparent surges (that is, the excess of actual levels over those of the purely tidal levels) do not occur at or about the times of the purely tidal high water. The problem has been investigated for a long uniform gulf about 100 miles long and about 21 fathoms deep. This has required the development of methods of calculation of tides in the channel, taking account of all non-linear terms in the equations of motion, a problem which in itself is mathematically intractable. The numerical methods have been applied also to cases where storm surges have been superposed upon the tides, with the maximum of the surge occurring near high water, or near low water, or near one of the two half-tide levels. These four cases reveal the character and magnitude of the interaction in this particular gulf. The mean of the four cases shows no obvious tidal interaction, but it is shown that the apparent surge is dependent upon the coefficient of friction and that the magnitude of this is greatly affected by the tides. The actual apparent surge at the mouth of the gulf is, of course, affected by the reflexion which takes place at the head of the gulf, and a method is given for computing the incident and reflected oscillations. It is remarked that it is the incident part which is directly due to the meteorological disturbances in the sea, so that correlations of apparent surges with meteorological data are complicated by the reflected oscillation.