33 



their experiments. Mitchim (1939) found that for 28 deep-water 

 runs his measured velocities were 1 percent too large according to 

 Gerstner's equation and 0.3 percent too small for the third approxi- 

 mation of Rayleigh. 



Wave profile. — Wave profiles have been studied both in nature and 

 in the wave tank. Gaillard's work contains four profiles photographed 

 in the Duluth Canal and compared to the theoretical shapes. Cornish 

 noted trochoid-like shapes in his observations. Kolilschutter and 

 Schumacher on the "Meteor" investigations (1928) and Weinblum, 

 Schnadel, and Block on the '*San Francisco" expedition photographed 

 waves corresponding closely to trochoids. 



In wave tanks, Meyer-Peter, Larras, Waters, and others, have 

 checked their wave shapes against the theory with good agreement. 

 R. D. Meyer noted that in shallow water the wave front was steeper 

 and the back slope flatter than the trochoid. 



Dimensionless ratios.— The height-length ratio of waves has re- 

 ceived considerable attention. Paris found that the ratio in deep 



L 



water T=39 corresponded to a light sea, 21 to a rough sea, and 19 to 



a heavy sea. Schott's observations verified these findings. Gaillard 



L 



found that the y ratio varied from 9.1 to 15.0 for 235 observations in 

 fi 



shallow water; Cornish observed ratios as low as 13 during storms. 



Larras used the length-height ratio as a check on his work on 

 vertical jetties, keeping the ratio between 20 and 11 for shallow-water 

 conditions. Mitchim noted this ratio in applying the third approxi- 

 mation of Rayleigh to his results, using the limits of 12 and 26 for his 

 studies in deep water. 



The depth-length ratio has been generally accepted as the criterion 

 of deep- and shallow-water waves. Almost all investigators have used 

 this check in determining the applicable formula. 



The percentage of wave height above still water level is of particular 

 significance in studies of wave pressure against structures. Gaillard 

 made a total of 834 observations at St. Augustine and Duluth (1890- 

 1902), and the Beach Erosion Board made 365 observations at Long 

 Branch, N. J., in 1929-30. 



In laboratories, the following studies are known to this office: 

 Larras, France, 1937; K. C. Reynolds, Massachusetts Institute of 

 Technology, 1937; F. K. lOauck, Massachusetts Institute of Tech- 

 nology, 1937; C. H. Waters, University of California, 1938; and the 

 Beach Erosion Board, 1939, made observations on the percentage of 

 wave height above still water level in conjunction with other studies. 

 All these observations, both in nature and in the wave tank, made 

 in shallow water under a variety of bottom conditions, showed close 

 general agreement with the Laplace-Airy theory. 



