showing the distribution of energy in the waves 

 after each of the first five strokes. As shown in 

 the last line of the table a definite pattern has 

 already developed after five strokes ; the waves 

 which have traveled the greatest distance have 

 very little energy, the wave which has traveled 

 half way has an energy E/1, and each of the 

 waves closest to the machine has an energy 

 which approaches the full amount E. When a 

 large number of strokes has been completed 

 these gradations are much clearer and the dis- 

 tribution of energy can be represented sche- 

 matically by the curve in figure I.IO which 

 shows that the energy advances with a definite 

 front. At the front the wave height increases 

 from nearly zero to nearly its full value in a 

 distance corresponding to a small number of 

 wave lengths, and this front advances with half 

 the wave speed. 



Table 1.3. — Advance of waves from a wave machine 

 into still water 



When applying the above reasoning to the 

 behavior of wind waves which advance into 

 regions of calm it is necessary to consider also 

 the following facts: (1) The wave loses energy 

 because of the air resistance against the wave 

 form, and (2) the wave speed (period) in- 

 creases continuously. 



When the problem is treated analytically it 

 is not necessary to introduce any new constants. 

 The decrease in wave height and the period at 

 the end of the calm area can be obtained as spe- 

 cial solutions of the fundamental equation 



"FRONT "OF ADVANCING ENERGY 



Figure 1.10. — Advance of wave energy in time t from 

 a source into still water. A very small amount of 

 the energy has advanced Ct. The region of rapid 

 increase, the front, has advanced the distance Ct/2. 



which was discussed in the section on the 

 growth of waves. 



The travel time is computed from the group 

 velocity of the swell at the end of the calm ac- 

 cording to the relationship 



to = 



D 



VtCn 



or 



to =- 



J- D Id 



(1.13) 



(1.14) 



where to is given in hours, D in nautical miles, 

 and To in seconds. 



The graphical results of these equations are 

 presented in plate VI. The coordinates are the 

 wave period Tp at the end of the fetch F, and 

 the distance of decay D, that is, the distance 

 which the waves travel through areas of calm. 

 The main part of the graph contains three sets 

 of curves. One set gives the factor by which 

 the wave height at the end of the fetch Hp must 

 be multiplied in order to find the height of the 

 swell Hj) at the end of the distance of decay. 

 The second set gives the wave period at the end 

 of the distance of decay To- The third gives 

 the travel time to in hours for the distance D. 

 An inset shows wave speed and length cor- 

 responding to different periods. 



Effect of Following or Opposing Winds 



When a forecast of the weather situation or 

 a subsequent weather map shows that the 

 waves, instead of traveling through a calm, are 

 traveling through a region where the wind has 

 a component (greater than 10 knots) parallel 

 to the direction of progress, the forecast must 

 be modified by taking into account the effect of 

 the following or opposing wind. The decay dia- 

 gram (pi. VI) gives decrease in wave height 

 and increase in wave period as a function of 

 initial period and distance from the generating 

 area. The only factor, aside from characteris- 

 tics of the wave itself, which affects these 

 changes is the opposition of the air to the move- 

 ment of the wave. The decay diagram may be 

 thought of as giving the changes in height and 

 period as a function of the initial period and 

 the amount of air with which the wave comes 

 in contact, where the distances plotted along 

 the horizontal axis represent values for still 

 air. If the air is in motion, the actual distance 

 the wave moves during the time it comes into 

 contact with a given amount of air must be 



12 



