Generation, Growth and Propagation of Waves 95 



shown in which way these two variables have to be considered in the growth 

 of waves. In order to test the theory we need complete observations, consist- 

 ing of at least the following five variables: 



(a) Significant wave height H. 



(b) Significant wave period T, or velocity c or length X. 



(c) Wind velocity U. 



(d) Wind fetch x. 



(e) Wind duration t. 



It must, furthermore, be borne in mind that the waves in any one region 

 are the result, not only of local winds but also of winds in other areas, and 

 that the relation between wind and waves during the periods of growth or 

 of decay (sea or swell) should be considered separately. 



The observations which have been entered as points in Fig. 43 have been 

 collected from different series of older and newer observations, where it was 

 possible to determine the non-dimensional parameter through special ob- 

 servations. However, generally it is not possible to have such complete series 

 of observations available. 



From earlier days we have empirical relations between the wave height, 

 the distance and the duration of the fetch, and also between the wave height, 

 the wave velocity and the force of the wind. However, these relations are only 

 approximate, e.g. Stevenson (1851, p. 189, 1852, p. 358) has established an 

 empirical formula giving the "greatest" wave height //as function of the fetch 

 (both in cm), according to which H = 0105 \/x. The formula was established 

 by means of data from lakes, where the value of x ranged from a few kilo- 

 metres up to 250 km. For the Mediterranean Cornish has verified the relation 

 for fetches up to 830 km, and it is generally assumed that the relationship 

 holds for values of x up to 1000 km. The formula is incomplete, since it does 

 not take the wind velocity into account, but it is intended to apply at the 

 highest wind velocity which can be expected to occur. Figure 43 gives the 

 dimensionless relationship between //, x and U, and Stevenson's formula 

 fits this relation only when there is a definite connection between the wind 

 force and the fetch. 



Boergen (1890, p. 1) has given an empirical formula for the relation 

 between wave height and duration of the wind; it is a linear formula, in 

 which H = HJ{\ +a/t). H is the wave height to be determined and H m the 

 maximum wave height for any given wind velocity and t the duration of 

 the wind action ; for / = 0, H = 0, and for t = oo, H = H m . The coefficient a 

 must be determined from observations. Although a comparision of this 

 formula with theory is not possible, its chief features seem to be in agreement. 

 Boergen has attempted to combine the three factors: wind, velocity, duration 

 of the wind action and active length of the fetch, and devised the formula 



