The fundamental and maximum period (T^ for n = 1) becomes 



If 

 T =— ^ (3-43) 



Equation 3-43 is called Merian's formula. (Sverdrup, Johnson and Fleming, 

 1942.) 



In an open rectangular basin of length %' and constant depth d, 

 the simplest form of a one-dimensional, non-resonant, standing longitudi- 

 nal wave is one with a node at the opening, antinode at the opposite end, 

 and n' nodes in between. (See Figure 3-40(C).) The free oscillation 

 period T^/ in this case is 



4V 



For the fundamental mode (n' = 0), T^ becomes 



T' =^1mL (3-45) 



The basin's total length is occupied by one-fourth of a wave length. 



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 nodes of oscillation of multinodal and uninodal seiches. 

 The theory for a particular forced oscillation was also derived by Defant 

 and is discussed by Sverdrup et al (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 Simpson 

 and Anderson (1964), Platzman and Rao (1963), and Mortimer (1965). 

 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. 



3.85 WAVE SETUP 



Field observations indicate that part of the variation in mean water 

 level near shore is a function of the incoming wave field. However these 



3-80 



