SECT. 5] WIND WAVES 671 



will have to take account of both these mechanisms. Possibly Phillips's theory" 

 can account for the initial generation of waves, whereas a theory such as that 

 of Miles can account for the subsequent growth. i 



Even if a satisfactory theory for the energy transfer from the wind to waves 

 can be produced, it will be necessary to know much more about how waves 

 dissipate energy before satisfactory predictions of real wave patterns can be 

 made. In Jeffrey's energy balance quoted above (6), for example, the kinematic 

 viscosity appears, which in practice will represent a turbulent viscosity and 

 will almost certainly be dependent on wavelength and wind speed (Groen, 

 1954). In any case, it seems unlikely that a simple conception of turbulent 

 viscosity will suffice, since steep waves probably lose most of their energy in 

 "white horses", the foaming crests seen on the sea during strong winds. 



4. Wave Prediction 



The fundamental theory of the generation of waves by wind has not yet 

 reached the stage where it can usefully be applied to practical wave prediction, 

 so that this at present relies on formulae which are to a large extent empirical, 

 though some theory may also be involved. The first empirical formula was a 

 very simple one published by Thomas Stevenson (the father of Robert Louis 

 Stevenson) in 1864, and another, based on visual observations, was given by 

 Vaughan Cornish in 1934. These formulae were not satisfactory, however, and 

 the military necessity of the 1939-45 war started considerable research aimed 

 at improving methods of wave prediction. The growing military and civilian 

 importance of this subject has ensured continued effort. 



The systems for wave prediction developed during the war are due to Suthons 

 (1945) and Sverdrup and Munk (1947). Both methods are still in limited use, 

 that due to Sverdrup and Munk having been modified by Bretschneider (1959). 

 At the time these were developed, frequency analysis had not been applied to 

 sea waves, and it was necessary to use some suitably defined mean wave- 

 height H and period T, and to find relationships between these and the wind 

 speed V, duration (the time for which the wind has been blowing), fetch (the 

 distance over which the wind is blowing), etc. Systems of this type have also 

 been developed in Russia (for example, Krilov, 1958; Shuleikin, 1959). 



With the development of frequency analysis of sea waves, and the realization 

 of the theoretical and practical importance of frequency spectra, these methods 

 have been to a large extent superseded in the Western World by methods 

 which predict the wave spectrum, from which the other parameters may be 

 derived. 



All methods begin by considering waves on deep water, and in this case 

 Sverdrup and Munk were able to argue that one might expect a relationship 



1 Since this account was written, more theoretical and experimental work has been done 

 on this theory, though the basic principles remain unchanged. Readers are referred to 

 Cartwright (1961) for a summary of this work. In this paper he also summarizes other 

 recent work on the wave spectrum. 



