checked to see if they are really fetch limited. If the formulas are used 

 rather than the nomograms, wave conditions should also be checked to see if 

 they exceed the fully developed condition. 



Wave growth with duration is not as well understood as wave growth with 

 fetch length. Equation (3-36) ensures that the growth of H and T with 



time reaches the fetch-limited value at about the same duration specified by 

 equation (3-39). The approximation works well except for long dimensionless 

 fetches (relatively long-fetch, low-windspeed cases). 



Inevitably, estimating wave height and period requires that checks be made 

 between fetch, duration, and fully developed limitations. Many design 

 situations require iteration between these approaches and the appropriate 

 averaged durations. The wave growth formulas must use the wind-stress factor 

 and not windspeed. The proper averaging times for the winds (as related to 

 the duration and fetch) must be used. This approach is approximate, and the 

 number of iterations and adjustments used should reflect this limited 

 accuracy. 



4. Narrow Fetch Conditions. 



When early users of the SMB curves applied them to reservoirs and small 

 lakes, calculated wave heights were much larger than observed wave heights, 

 it was thus assumed that the narrowness of the fetch was affecting wave 

 growth. The concept of an effective fetch was introduced which reduced fetch 

 length to account for the narrowness of the fetch. The adjustment provided 

 improved wave estimates. When the growth curves presented here were applied 

 to similar situations (Resio and Vincent, 1979) the effective fetch calcu- 

 lation resulted in wave heights that were too low, while a straight-line fetch 

 provided wave heights closer to observed values (Fig. 3-25). Data from inland 

 reservoirs were checked by computing H based on an effective fetch and on 

 straight-line fetch (Fig. 3-26). The straight-line fetch shows reasonable 

 agreement with the growth curves. 



The reason an effective fetch adjustment is required for the SMB curves is 

 that these curves overpredict wave heights for small values of F more than 

 do recent data. The effective fetch method implicitly assumes a cosine 

 directional spread for wind input to the sea. More recent data suggest that a 

 cosine to the 10th power describes the directional distribution near the peak 

 frequency of the spectrum. This is a much narrower spread. Effective fetch 

 should not he used with the growth curves presented herein. There may be a 

 critical fetch width where width becomes important, but this is not known at 

 this time. 



*************** EXAMPLE PROBLEM 4*************** 



GIVEN: Eight consecutive hourly observations of fastest mile windspeed U^ = 

 20 meters per second are observed at an elevation of Z, = 6 meters, 

 approximately 5 kilometers inland from shore. The observation site is at an 

 airport weather station. The air-sea temperature difference was estimated 

 to be -6°C. 



3-51 



