400 MISCELLANEOUS STUDIES 



where a velocity directed away from the coast is regarded as positive. 

 That is, 



Yc="P e~ OI 'jcosAcosQ ay J-f sin Ash:Q -ay\ ( 



= V e- a cos(^ -ay A) (176) 



Let z equal the distance perpendicular to the coast, then V c from 

 equation (176) is the limiting value of the velocity perpendicular to 

 the coast as z increases. Also, adjacent to the coast where z equals 

 zero, the velocity perpendicular to the coast must be zero. Let the 

 velocity perpendicular to the coast at the distance z be given by 

 the equation 



V=V c f(z) (177) 



where /(0)=0 and f(z) =1 as z increases. The removal of 

 water at and near the surface due to a flow away from the coast 

 decreases the pressure at the lower levels, and gives rise to a com- 

 pensating flow of deep water toward the coast. Therefore in a coastal 

 region where the surface water flows away from the coast there is a 

 compensating upward flow of deep water. 



Denoting the vertical velocity by W, the equation of continuity is 



dz dy 



neglecting the variation of the component parallel to the coast. There- 

 fore from equation (177), assuming 



W = f l (z)f 2 (y) (179) 



we have 



/i(2 )W =0 (180) 



To solve equation (180) let 



df(z} 



(181) 



dz 

 where M is a constant. Then from equation (176) and (180) 



dy \4 / 



