SECT. 5] SURGES 641 



or viscosity limits the magnitude of the currents and surface elevation. From 

 (52) it is seen that the influence of depth is to make the pressure terms relatively 

 more important in deep water, the wind-stress terms more important in shallow 

 water. Coastal areas adjacent to large shallow regions are particularly 

 susceptible to wind-generated surges. 



If a storm pattern moves over the water surface with speed approximately 

 that of a free wave, a large amplitude results. For example, if 



F = A cos (kx — at), 

 it is found from (51) that 



A cos {kx — at) 

 ^ ^ a'^-p-ghk^' 



If G and k have values corresponding to a free -wave solution, then the de- 

 nominator is zero and there is no solution. If a storm began to move in a 

 straight line with free-wave speed, it would be found from this theory that the 

 amplitude of the forced surface wave would increase with time without limit, 

 owing to the neglect of dissipation. Even though the conditions postulated 

 here are not fulfilled in nature, very large surges are sometimes generated in 

 this way. The free-wave velocity in the deep ocean is greater by orders of 

 magnitude than the speeds of storms, but in shallow water there is sometimes 

 a good "match". The destructive surge in Lake Michigan on June 26, 1954, 

 may have resulted from this effect (Harris, 1957). 



Attempts to take the earth's curvature into account have resulted in the 

 "beta-plane" theory. The effect of curvature is neglected in the equation of 

 continuity, but brought in by considering the Coriolis parameter as dependent 

 on y (distance northward), with dfldy = ^. Both ^ and/ (when not differentiated 

 with respect to y) are taken as constants. Cartesian coordinates are retained, 

 but the situation is now anisotropic, as the earth's rotation introduces a pre- 

 ferred direction. Essentially, the ocean surface is taken to be a parabolically- 

 curved plane, of small north-south extent, tangent to the surface of the 

 rotating earth and osculating along a meridian. The additional complication 

 makes it practical to consider only the simplest of cases. For free waves travel- 

 ling in the east-west direction, there are two classes of motion : the ordinary 

 inertio-gravitational waves and the planetary, or Rossby waves (Veronis and 

 Stommei, 1956). The former can move in either direction and their charac- 

 teristics are only slightly modified by the curvature. The planetary waves, on 

 the other hand, are propagated only westward, and are associated with water 

 motion largely geostrophically balanced. These waves are dispersive. There is 

 a wavelength of minimum period; waves longer or shorter than this wave- 

 length have longer periods. T5rpical periods and wavelengths may be of the 

 order of several days and several hundred kilometers, respectively. 



But surges are usually observed along coastlines, which greatly complicate 

 the theory. A whole new class of free-wave motions, called edge waves, is intro- 

 duced by a coast. The simplest mathematical way of introducing a coast is to 

 take an infinitely long vertical wall, in which case the edge waves can be 



