SEAWAY 



31 



I I u 



5 5.4 G 



S.67 7.5 8.57 10 12 15 20 



8.57 10 12 15 



5cale of Wave Period (sec.) 



30 



Fig. 26 Typical wave record and spectrum (from Darbyshire, 19 52) 



20 



o o 12 



g 



E 

 E 



b^ 





s 1.2 lA 3.e 4.8 e.O 7.2 8.4 9.6 



Square Root of the Sum of the Squares 

 of all Peaks in Wave Pressure Analysis 



Fig. 2 7 Comparison between maximum wave 

 height and equivalent wave height (from Darby- 

 shire, 1952) 



«th peak in the spectrum. If H is the hei,u;ht of a hj'pd- 

 thetie;il single sine-wa\'e train which has the same 

 energy per unit area as the complicated wave pattern, 

 then gpHVS = </pS//„-/8 and H can be defined as the 

 equivalent height of waves. To compare such eciui\'a- 

 lent height with the maximum heights measured on wa\-e 

 records, corresptjiiding \'alues of H and maximum height 

 -f^max are plotted in Fig. 27. The graph shows that 



^max = 2H. 



"The idea of an eciuivalent height can be extended to 

 parts of a wave spectrum as well as the whole. The 

 energy E.j. in a unit wa^'e-period interval T — (1/2) to 

 T + '(1/2) is given by 



X T+l/2 J 



-£V = o f/P E ^«' = o ^fP ^^T- (59) 



O T-1/2 o 



"The information available consists mostly of synoptic 

 meteorological charts and records of wave motion usually 

 in the form of records of the pressure fluctuations pro- 

 duced by the wa\'es on the sea bed at a depth of about 50 

 feet at one point on the coast, . . ." "There are not 

 usually sufficient observations of wind strength in the 

 wave generating area to allow detailed comparisons be- 

 tween the wave and wind characteristics, and it was made 

 a general practice to compute the wind from isobaric 

 charts. Six hourly charts provided by the Naval 

 Weather Service were fouiul most convenient, and gra- 



100 



5 80 



,e-6o 



40 



20 







4 8 12 IG 20 



Maximum Wave Period (sec.) 



24 



Fig. 28 Correlation of maximum wave period with 

 maximum wind strength for all storms (from Darbyshire, 

 1952) 



dient wind speeds were calculated according to the instruc- 

 tions in the Admiralty Weather Manual. The relation 

 between surface wind and gratlient wind \'aries with the 

 atmo.sphcric stability and other factors, but Gordon 

 (1950), using (jl)ser\-atioiis over the sea, found that the 

 ratio between the two \'aried between 0.t)0 and O.SO, the 

 mean value being 0.66. The best that can be done 

 at present is to assume a constant ratio of 0.66 and to 

 compare wave characteristics with the gradient wind 

 speeds. There is some advantage in doing this since in 

 any application of this work it is more likely that weather 

 charts will be a\'ailal)le than wind ob.servations." 



l''rom examination of the wave record, Darbyshire 

 came to the conclusion that wave characteristics become 

 practically independent of fetch after 200 to 300 miles.-' 

 As the characteristic information to he abstracted from 

 the records, Darbyshire chose maximum wind speed vs. 

 maximum component wave period (see Fig. 28) and 

 mean wind speed \ersus the wave component period cor- 



^' Very much longer fetches are needed to attain steady wave 

 conditions according to Sverdrup and Munk (1947) and Neumann 

 (1952, 1953). The n,se of the chart in Fig. 20 indicates that in 

 the gradient wind of 60 knots, corresjionding to anemometer 

 height wind of 40 knots, a fetch of abont 700 nautical miles is 

 req\iired. 



