0.66(2) (3.14) (0.67) (1.86) 10^ , -7o ^ /r ^q ^ ^^ a 



\ = 669 (12.4) (3.600) = ^'^^ ""'""^ ^^'^^ '^"'^ P" ^"'^^"^ 



Since a /a = 0.78 , a, = 0.78 (0.67) = 0.52 meter (1.72 feet) 

 h s h 



and the bay tidal range is 0.52 (2) or 1.05 meters (3.44 feet). 

 The tidal prism is 



2a A = 2 (0.52 (1.86) (10^) = 6.37 x 10^ (6.86 x 10^ cubic feet) 



h b 



If the average depth of the bay is 6.1 meters and the distance to the 

 farthest point in the bay is 6.4 kilometers, the time t^ it will take for 

 the tide vvave to propagate to that point is 



t. = , — ,- = ,. rt . ^ . . = 827 seconds, or 0.23 hour 

 * VgH: V9.8 (6.1) 

 D 



Since this time is significantly less than 12.4 hours, the assumption that 

 the bay surface remains horizontal is quite satisfactory. 



A************************************** 



b. Long Wave Currents in Inlets . When an inlet is sufficiently wide and 

 deep to allow propagation of the tidal vave through the inlet, the inlet 

 currents must be calculated using long wave theory. The propagation of long 

 waves through the inlet typically occurs in the case where the inlet is more 

 appropriately termed an estuary and the estuary has a large tidal prism. 



The water velocity at the entrance for a long vave propagating through an 

 inlet (or estuary) for the case of an "infinitely" long channel with no 

 frictional damping is 



a 



u = fp C cos ^ (4-70) 



where 



u = maximum vater velocity at the entrance to the channel 



a = tidal amplitude 



C =Vgh = celerity of long wave 



h = mean water depth of channel 



In the case of frictional damping, an additional reduction factor (<1) 

 must be applied to the velocity above, and a phase lag occurs betv«en the 

 maximum water level and the maximum velocity (Ippen, 1966). 



c. Effects of Salinity Currents . Velocities at inlets discussed thus far 

 pertain to inlets in which vertical mixing prevents vertical density stratifi- 

 cation. In inlets with tributary inflow or estuaries which terminate into 

 rivers, vertical stratification may take place and alter the current strengths 

 significantly from those discussed in Sections IX, 3, a and IX, 3, b. In the 



4-166 



