SECT. 5] WIND WAVES 691 



height being the difference between the crest and the preceding trough. This is 

 called "the significant wave height". "The significant wave period" is the 

 mean time between the preceding and following troughs for each of these waves. 

 This apparently arbitrary method was adopted because the smallest waves in 

 a record often appear to be unimportant. For example, if a large swell is 

 present, a local wind may produce short low waves which break up the contour 

 of the swell and thus reduce the measured height if the mean of all crests is 

 taken, even though the total energy has obviously increased. Taking the mean 

 of the highest third of the waves reduces this kind of effect. 



Other measures have some advantage. The most fundamental measurement 

 of wave height is the root-mean-square deviation of the record, Hr.m.s., which 

 is proportional to the square-root of the wave energy. This is tedious to measure 

 directly from the record without special equipment, however, and is rarely 

 used. The height of the highest wave in a record, Hm&x, is a more reliable 

 measure of wave height than one would expect, is easy to measure, and is the 

 parameter which is most important to a civil engineer designing coast defence 

 works. 



The average period of the wave crests, Ti, and of the crossings of the mean 

 water-level line in an upward direction, To, are two other useful measures of 

 wave period. They are related by the formula 



(TilTo)^ = 1-62, (19) 



where e is a parameter which is a measure of the width of the power spectrum. 

 No adequate theory is available relating the values of Hy^ and ^max to 

 Hr.m.s. for records with large values of e, but when e is small (in practice less 

 than 0.3) the following relationships apply ^ 



Hy^ = 4.004^r.m.s. (20) 



^max = [2.82 (loge i\^)'/^ -f 0.82 (loge iV)-'/^]^r.m.s. (21) 



valid for N > 20. 



All these measurements are subject to random errors which become smaller 

 the longer the wave record. In practice, a record containing between 50 and 

 100 waves seems to have been accepted as a reasonable compromise between 

 accuracy and recording time, typically giving random errors of the order of 

 20% (r.m.s.) in wave height. 



Frequency spectra may be measured by analogue or digital methods. In 

 principle, all methods are equivalent to passing the wave signal through a 

 filter which passes components with frequencies in a certain range, and then 

 measuring the energy (mean square amplitude) of the output from the filter. 

 In practice, the pass-band of the filter does not have sharp limits, and the 



1 In referring to Chapter 15, section 6, note that N is the number of crests in the whole 

 record, Nq is the sum of the number of upward and downward zero crossings per second, 

 Ni is the sum of the number of crests a7id troughs per secotid. Thus, Tq = 2/Nq and Ti = 2/Ni. 

 Also, Hfrn.s. =Wio*'2. 



