236 Long Waves in Canals and Standing Waves in Closed Basins 



bottom (no bottom current) this factor becomes I and with an intermediate 

 coefficient of viscosity a value between these two extremes. If the friction 

 is proportional to the bottom velocity u h , viz. pqu h , then we have, as shown 

 by Nomitsu (1935), 



e= 1 



PQ{h + rj) 

 7.(i 



1 + 



PQJh + r j) 

 3/* 



If the depth varies irregularly the above-mentioned equation can be used 

 step by step to determine the variation in the piling-up effect, starting from 

 the points where -n is negligible up to the beach. If h is a simple function 

 of x (VI. 144) can be integrated directly. 



If h = const, at a point x calculated starting from the open ocean, where 

 y=0, 



r\ = h 



V 



l + 2e^x] 

 ggh 2 



(VI. 145) 



With a uniformly sloping sea bottom (see Fig. 100), h = h — xtanyt 

 = h (l — [x/L]) and with the condition 



we obtain 



n = »?<>+ Wog 



J rjdx = , 







Vho-(h + r] ) 



*]ho+(h + ri — xta.ny)) ' 



(VI. 146) 



in which rj means the elevation at x = and rj h0 = e[T/(ggh )]L the elevation 

 of the water level at the shore with a uniform depth h Q (according to (VI. 144), 



Fig. 100. Computation of the effect of piling up by wind on level shores. 



neglecting r\)\ 2rj is the elevation of the water piled up according to 

 (VI. 144) with rising bottom as shown in Fig. 100. If tj be small, we obtain 

 at the shore: 





+ log(^-l) =log(=^-l). (VI. 147) 



Who ! Who J 



