depths, and with the product d^'^T for long waves. The wave steep- 

 nesses of intermediate- and long-period waves are also small, and this 

 results in nearly perfect reflection of these waves from beach slopes 

 as flat as about 1:100. This causes problems of scale selection in two 

 ways: (a) Since longer period waves easily reflect from the beach and 

 harbor areas of the model, and because it is infeasible to reproduce a 

 sufficiently large ocean area to allow complete tests before the reflec- 

 ted waves reach the wave generator (located along the boundary of the 

 ocean area of the model), and because waves of long period and small 

 steepness are difficult to absorb without appreciable reflection from 

 the face of the absorber, a large part of the ocean area reproduced in 

 the model (including the area in front of the wave generator) must be 

 filled with wave-absorber material; and (b) the periods of long waves 

 and the resulting high reflection coefficients even on flat beach slopes 

 result in the phenomena of bay and shelf resonance which, in turn, if 

 the harbor is located on a continental shelf or in a bay, or both, can 

 make it necessary to include the bay and shelf in the modeled area. If 

 the shelf is comparatively narrow, long-period oscillations of the shelf 

 waters may occur within the range of critical wave periods of the moored 

 ships. Biesel and Le Mehaute (1955) have stated that when the shapes of 

 both the coast and the shelf are complex, the use of a small preliminary 

 model may be necessary to reproduce a large part of the coast and shelf 

 together with a considerable part of the adjacent ocean area seaward of 

 the shelf. 



Because of the situation discussed above, and the ever-present eco- 

 nomical and practical considerations, the use of distorted-scale models 

 is necessary in most instances. In such models the vertical and hori- 

 zontal linear scales are unequal, and 



SK V-p/h 



A few harbor models with the problem of intermediate-period waves have 

 been conducted using undistorted scales of about 1:100; however, most 

 of these studies are conducted using distorted scales. The vertical 

 scales for such models usually range from about 1:50 to 1:100, and the 

 distortion factor is usually from about 3 to 5; e.g., the Los Angeles- 

 Long Beach Harbor model designed and constructed in 1972 had a vertical 

 scale of 1:100 and a horizontal scale of 1:400. For preliminary models 

 where the modes of oscillation are of primary interest, and where the 

 waves and water depths are such that the long-wave velocity relation, 

 V = (gd)^/^, is applicable, the horizontal-scale ratio can be decreased 

 and the distortion factor increased. The degree to which the model can 

 be reduced in size and depth is dependent on the accuracy desired. For 

 waves and water depths where the long-wave velocity relation is not 

 applicable, and where the wave velocity is a function of both water 

 depth and wavelength, the error in wave refraction increases as the wave 

 period decreases for a given distortion factor. 



216 



