b. Selection of Linear Scale . 



(1) Short-Period Waves . Coastal harbor models in which the 

 problem involves the protection of mooring basins from the attack of 

 short-period wind waves are designed in accordance with Froude's law 

 and are constructed geometrically similar to the prototype harbor. The 

 linear scale is selected so that internal friction and surface tension 

 forces are negligible, compared with gravity forces. The linear scale 

 should also be selected so that the reduction of model wave heights by 

 bottom friction in the viscous boundary layer is negligible, or is such 

 that the lack of similarity of the friction forces, model-to-prototype, 

 can be corrected by analytical and experimental methods. The harbor 

 wave action model must usually reproduce the complete prototype harbor, 

 with enough upcoast and downcoast distances to allow the littoral current 

 to generate, and with enough ocean area to allow the waves to generate in 

 depths of water so that the refraction of waves, between the wave gener- 

 ator and the harbor, will reproduce correctly. Thus, in most instances, 

 a prototype area of considerable size must be reproduced in the model; 

 since economical considerations require the selection of a linear scale 

 so that the model will be as small as possible consistent with the need 

 for accurate test results, a trade-off situation between cost of model 

 construction and the magnitude of scale effects is usually encountered. 

 The linear scale must also be selected so that model wave heights obtained 

 in the problem areas are of sufficient magnitude for accurate measurement. 

 Experience has shown that, considering the size of harbors, the depths of 

 water, the wave dimensions encountered, and the type of wave gages and 

 model shelter area usually available (and considering other factors men- 

 tioned above), the linear scales selected for harbor wave action models 

 where short -period waves are the cause of the problem are usually within 

 the range of about 1:75 to 1:150, model-to-prototype. 



(2) Intermediate- and Long-Period Waves . The intermediate- and 

 long-period waves of primary interest to harbor wave action conditions 

 are the relatively long-period, small -amplitude waves with periods rang- 

 ing from about 20 or 25 seconds to 2 to 3 minutes. For ordinary commer- 

 cial vessels, the critical range of wave periods for vessels moored with 

 the-commonly-used elastic mooring-line assemblies is between about 25 

 seconds and 2 minutes. During the last decade, vessels of about 250,000- 

 ton displacement or more have been constructed and placed in operation. 

 When harbors become available that have sufficient navigable depths to 

 accommodate these large vessels, the range of critical wave periods will 

 increase unless more sophisticated mooring assemblies are devised. How- 

 ever, the problems of selecting linear scales and designing hydraulic 

 models for study of mooring problems should not be affected appreciably. 

 The selection of linear scales and the design of harbor models for 

 intermediate- and long-period waves are more difficult than the problems 

 encountered when the model study involves only short-period wind waves. 

 There are several reasons for this situation. One reason is that the 

 ocean area that should be reproduced in the model increases with wave- 

 length, and wavelength increases as the square of the wave period for 

 deepwater waves and for intermediate-depth waves at equal relative 



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