92 



Generation, Growth and Propagation of Waves 



when we have c < U and c > U respectively. The solution of the equa- 

 tion (IV. 40) gives the height and velocity as function of fetch after a steady 

 state has been reached, i.e. for t > ? min . It will be shown that ? min depends 

 upon fetch and wind velocity. The value of t min determines whether the 

 equation (IV. 38) (the duration equation) or the equation (IV. 40) (the fetch 

 equation) is to be used for determining the characteristics of the significant 

 waves. 



Each of these relations contains two unknowns, the energy and the wave 

 velocity. As the energy depends only on the wave height, we can consider 

 this latter and the wave velocity as the unknowns. A third relation is necessary 

 for the solution of these equations. Sverdrup and Munk form this relation 

 from empirical data derived from observations, and therefore their theory 

 is based only partly on purely theoretical deductions. 



In the past many fruitless attempts have been made to relate wave steepness 

 to wind velocity or other variables, but it has not been attempted to relate 

 steepness, 3 = H/A to wave age = c/U. Such a relationship is suggested 

 by dimensional considerations and, if existing, has the advantage of being 



$--<(#) 



Observations. 

 • Sverdup-Munk 



° Neumann 



M S. "Heidberg" 



» Roll (I95D 



77 

 10 



6 



20 



25 

 30 



40 



50 



100 



2 4 0-6 0-8 10 1-2 14 



/9--8/v 



1-8 



20 



Fig. 42a. Wave height d as a function of (5 = c/U. 



independent of fetch and duration. The question can be examined by sets 

 of more recently collected observations. The corresponding values of the two 

 non-dimensional parameters d and /? are plotted in Fig. 42a, which clearly 

 demonstrates that the two variables are related (Sverdrup and Munk, 

 1947; Neumann, 1952). The data were collected from observations at many 

 different localities and, although these values are scattered, there is nevertheless 

 a marked relation between the values. The heavy drawn curve has been fitted 



