This simplified theory must be modified for most actual basins, because of 

 the variation in width and depth along the basin axes. 



Defant (1961) outlines a method to determine the possible periods for one- 

 dimensional free oscillations in long narrow lakes of variable width and 

 depth. Defant 's method is useful in engineering work, because it permits 

 computation of periods of oscillation, relative magnitudes of the vertical 

 displacements along chosen axes, and the positions of nodal and antinodal 

 lines. This method, applicable only to free oscillations, can be used to 

 determine the modes of oscillation of multinodal and uninodal seiches. The 

 theory for a particular forced oscillation was also derived by Defant and is 

 dj-scussed by Sverdrup, Johnson, and Fleming (1942). Hunt (1959) discusses 

 some complexities involved in the hydraulic problems of Lake Erie and offers 

 an interim solution to the problem of vertical displacement of water at the 

 eastern end of the lake. More recently, work has been done by Platzman and 

 Rao (1963), Simpson and Anderson (1964), Mortimer (1965), and Chen and Mei 

 (1974). Rockwell (1966) computed the first five modes of oscillation for each 

 of the Great Lakes by a procedure based on the work of Platzman and Rao 

 (1965). Platzman (1972) has developed a method for evaluating natural periods 

 for basins of general two-dimensional configuration. 



Field observations indicate that part of the variation in mean nearshore 

 water level is a function of the incoming wave field. However, these 

 observations are insufficient to provide quantitative trends (Savage, 1957; 

 Fairchild, 1958; Dorrestein, 1962; Galvin and Eagleson, 1965). A laboratory 

 study by Saville (1961) indicated that for waves breaking on a slope there is 

 a decrease in the mean water level relative to the Stillwater level just prior 

 to breaking, with a maximum depression or set-down at about the breaking 

 point. This study also indicated that what is called wave setup occurs: from 

 the breaking point the mean water surface slopes upward to the point of 

 intersection with the shore. Wave setup is defined as that superelevation of 

 the mean water level caused by wave action alone. This phenomenon is related 

 to a conversion of kinetic energy of wave motion to a quasi-steady potential 

 energy. 



Two conditions that could produce wave setup should be examined. The 

 simplest case is illustrated in Figure 3-49a in which the dashline represents 

 the normal Stillwater level; i.e., the water level that would exist if no wave 

 action were present. The solid line represents the mean water level when wave 

 shoaling and breaking occur. Also shown is a series of waves at an instant in 

 time, illustrating the actual wave breaking and the resultant runup. As the 

 waves approach the shore, the mean water level decreases to the minimum 

 point di where the waves break. The difference in elevation between the 

 mean water level and the normal Stillwater level at this point is called the 

 wave setdown, Sj,. Beyond this point d-^ , the mean water level rises until 

 it intersects the shoreline. The total rise AS between these points is the 

 wave setup between the breaking zone and the shore. The net wave setup S 

 is the difference between AS and S-l and is the rise in the water surface 

 at the shore above the normal Stillwater level. In this case, the wave 

 runup R is equal to the greatest height above normal Stillwater level which 

 is reached by the uprush of the waves breaking on the shore. For this type of 

 problem the runup R includes the setup component and a separate computation 



3-99 



