Continental Shelf Waves 



the neighborhood of the east coast {I - -i^), therefore, this wave travels north- 

 ward with a speed Cj = 200 cm/sec, which is half the observed speed of 400 cm/ 

 sec. In the neighborhood of the west coast (-& = l^), the wave travels southward 

 with a speed Cj = 310 cm/sec, which just lies within the error bounds for the 

 observed speed, viz., 300 to 600 cm/sec. 



EFFECT OF BOTTOM FRICTION ON SEA LEVEL BEHAVIOR 



If we vertically integrate the horizontal momentum equations, retain only 

 linear terms, and neglect lateral eddy viscosity, we obtain 



^-™,..H|S.i(K.-F,). (20) 



where 



Fg.Gg = r,i// components of the wind stress on the sea surface, 



Fg,GB = r.i// components of the frictional stress of water on the ocean floor, 



Ur'U^ = r,i/' components of transport. 



Upon combining (20) and (21) with the continuity equation, it can be shown that 

 for typical values of the parameters, the forcing terms due to F^ and G^ are an 

 order of magnitude smaller than the term due to the atmospheric pressure fluc- 

 tuations; henceforth we take f^ = G^ = 0. We assume (8) 



Fg = K U ^^ 

 ^ ' (22) 



where K is a small positive constant of dimensions sec ' ^. For our problem we 

 take K to lie in the range 10"^ to 10'^ sec"^, which is obtained by equating the 

 bottom stress as given by Eq. (22) to the well-known expression for the bottom- 

 layer Ekman stress in which the vertical eddy viscosity (for the shelf region) is 

 taken to lie in the range 1 to 10" ^ cm Vsec (see page 482 of Ref. 9). The same 

 estimate for K is also obtained if we equate Fg, Gg (with velocities u^ = o(10"-^ 

 cm/sec), and u^ = o (1 cm/sec)) to the well-known bottom-frictional force ex- 

 pression kpu^, where k is a drag coefficient usually taken to have the value 

 2.5 xlO-3 (see page 136 of Ref. 10). From Eq. (20), Eq. (21), and the continuity 

 equation, we obtain, for h = h(r), the following equation for f): 



hLV^Ti + h'(L^, ^+ fr-if;,^) + (L^ + f ^ ) g- i 77, ^ = (L^ + f 2) g" ^ cp, ^ , (23) 



where L - B/3t + K. 



In the unforced case we anticipate a solution of the form 



487 



