Note on the Dynamics of Storm-Surges

In this note a treatment is given of the fundamental differential equations relating to storm-surges, and then solutions of these equations are obtained for a channel of uniform width and depth in the absence of wind and variable atmospheric pressure. Friction and geostrophic effects are taken into account, but product-terms are neglected so that the equations are linear. The chief feature of the treatment is that approximate equations for the elevation of the sea-surface are obtained which depend on the depth-mean values of the current but not on the vertical distribution of the current. The solutions obtained represent damped Kelvin-waves and damped Poincaré-waves.