20 



Table I. — Crest and trough depths of natural bars 



Locality and investigator 



Average 

 slope 



Factor 



Zone 



II 



III 



IV 



Pomeranian Coast (Otto) 



Pomeranian Coast (Lehmann) 



Pomeranian Coast (Otto) 



Pomeranian Coast (Hartnack) 

 Xiake Michigan (Evans) 



0.013 

 .013 

 .013 

 .017 

 .017 

 .017 

 .014 

 .014 

 .014 

 .017 

 .017 

 .017 

 .017 

 .017 

 .017 



HBliit.). 

 HcIHb.. 

 HtlHc... 

 Halift-)- 

 HIcHb- 

 HijHc... 

 Hb (ft). 

 HcIHb- 

 HtlHc— 

 Hb (ft.). 

 HcIHb- 

 HilHc... 

 Hb (ft.). 

 HcIHb- 

 H,IHc-.. 



3.12 

 .54 

 1.71 



2.22 

 .42 

 1.86 



3.8 



.46 

 1.79 

 5.74 



.55 

 1.50 

 7.02 



.46 

 1.87 

 6.56 



.49 

 1.77 

 7.12 



.55 

 1.45 



6.5 



.57 

 1.56 

 10.40 



.57 



1.66 



12.20 



.52 

 1.77 

 9.88 



.55 



13.37 

 .62 

 1.42 



14.8 

 .58 

 1.56 

 20.8 

 .52 

 1.81 

 13.1 

 .62 



20.6 

 .62 

 1.55 



The dimensions shown are average values derived from different 

 profiles for natural bars found in similar zones. The bar nearest the 

 shore is designated as being in the first zone, but at times it was 

 difl&cult to recognize that zone. Therefore, in some cases the zone 

 designation may not be correct. The data in table I, as would be 

 expected, indicate that the depth of the bar base increases with the 

 t>rder of zones. The ratio of the crest depth to the bar base depth 

 tends to increase as the distance the bars lie from the shore increases. 

 This may indicate that the bars that are farther away from the shore 

 liave lost material from their surface. It is possible, also, that the 

 larger waves do not operate long enough in this area for the complete 

 formation of bars. The mean value of HcIHb when computed from 

 the table is 0.54 which compares favorably with the corresponding 

 ratio, HcIHb of 0.58, obtained from the laboratory tests. For the 

 different determinations the ratio of trough depth to the bar crest 

 depth varies between 1.42 and 1.86. The average value HtHc of 1.66 

 compares well with the average of the laboratory determination; 

 HtlHc of 1.69. 



B. Lake Michigan bars and observed waves. — The profiles of the bars 

 of Sylvan Beach, near the White Lake piers on the eastern shore of 

 Lake Michigan, were measured by Evans in 1939 (reference 5) . Some 

 of these measurements are reproduced in figure 11. The essential 

 bars in a given profile are three in number, ignoring the indefinite 

 forms near the shore. An application of the results shown in figure 7A 

 might be to determine the magnitude of the waves necessary to pro- 

 duce those bars. The underlying supposition is, of course, that each 

 bar in a given profile is created under the action of a singular system 



