On the Resonance Effect in a Storm Surge (Part I)

Abstract

More or less varied estimations seem to be asserted concerning the sudden growth of high water as observed when a pressure disturbance passes through the resonance point defined with respect to the depth of water. Computations are performed in this paper with a view to studying the theoretical phase of the problem. Confining ourselves to the case of one-dimensional expanse of water surface, the equations of motion are reduced to the forms of the so-called 'shallow water theory'. In this simplification, the non-linear terms of the equations are preserved, while, on the other hand, effects of viscosity are altogether left out of consideration, because, as pointed out in the second report, they possibly do not modify the situation drastically. In the first place, the steady swell accompanying a disturbance of invariable intensity which advances with a constant velocity upon the surface of water of a uniform depth is formulated analytically without difficulty, and when the state is of near resonance results of the linear approximation generally used in the past are shown to need large corrections. In the next place, the swell of water taking place when a disturbance, climbing up an inclined bed and approaching a shore, goes through the resonance point is calculated numerically by the aid of an electronic computer. It is found that the smaller the slope of the bottom the higher is the tidal level, and that even an inclination usually experienced is still sufficient to produce an ascent of level up to several tens percent. It is concluded, therefore, that the resonance phenomenon could not possibly be neglected, except when it is canceled out by chance owing to some three-dimensional influences.