Generation, Growth and Propagation of Waves 89 



It has been pointed out (p. 36 ff.) that the new instructions for wave 

 observations aim at obtaining the characteristics of wave trains. Experience 

 shows that a careful observer will always note wave values fitting the defined 

 values of significant waves. The significant waves behave differently than 

 do the classical waves composing a single wave train. The individual waves 

 of such a train are conservative and as its wave length remains unchanged, 

 in the neighborhood of a geometrical point which travels with a group 

 velocity C (see p. 14) we obtain 



dX dX dX 8c ccc 



dt dt dx dt 2 dx 



We can see from this relation that a steady state (dc/dt = 0) cannot exist 

 simultaneously with an increase of the wave velocity (or period) with distance 

 in fetch. Nor can there exist a transient state during which the wave velocity 

 (or period) increases with time, while it remains uniform over the area under 

 consideration (dc/dx = 0). 



These conclusions are in contrast with experience as to the behaviour 

 of the significant waves. When a wind of constant velocity blows for a long 

 time over a limited stretch of water (a lake), a steady state will soon be 

 established. At any fixed locality the characteristics of significant waves do 

 not change with time, but on the downward side of the lake the waves are 

 higher and longer than on the upwind side. If, on the other hand, a uniform 

 wind blows over a wide ocean, the waves grow just as fast in one region 

 as in any other region and the significant waves change with time, but they 

 show no alteration in a horizontal direction. 



The discrepancy between the behaviour of significant waves and individual 

 waves lies in the fact that the crests of significant waves do not maintain 

 their identity, i. e. significant waves are not conservative in the storm area. 

 This follows from the wave picture resulting from the superposition of several 

 simple conservative wave trains, as shown in Fig. 7. In all events, in order 

 to agree with the observations, the relations between waves and wind, fetch, 

 duration, must be based upon a study of significant waves. Such a study 

 represents a radical departure from the study of the conservative waves of 

 the classical theory. 



To deduct the fundamental relations between waves and wind, Sverdrup 

 and Munk (1947) determine the energy budget of conservative and significant 

 waves, giving particular consideration to the manner in which the energy 

 progresses with the wave. We will first discuss the transient or unsteady 

 state. 



The total energy per unit crest width of a wave equals EX, where E is the 

 mean energy per unit surface area. The energy added each second by the 

 normal pressures of the wind is ±R N X (IV. 25) and that which is added by 

 tangential stress equals R T X (IV. 31). Only half the energy, the potential 



