Substituting (23) and (21 ) in (18) gives the identity 



proving the consistency of the solution, Next, suostituting (23) and (17) 

 into (22) gives 



-<rk\n_ , oottt ^-p 1 ! -^ 



UTT ^ ' olTlc • (29) 



Hence* 





■f 



since J^= y£ 



In shallow water, i.e., when l\ << L. ? Q ~* j* , and it is seen 

 that the period would be approximately the same as in the case of instability 

 eddies, or 21.7 hours. However, since h/L is positive, even though small, 

 the denominator in (30) is greater than 1, and hence <£=■ 1,- is less than 

 f . The period is then somewhat greater than 21»7 hours. 



The physical effect of the inertial motion described above may be seen 

 by considering the motion in the horizontal (xy) plane. In this case, for 

 a fixed z, equations (9) through (12) reduce to 



(JL - eos (Tkx-KPfc) * A c£>s —£~ 



V - t=/n Ck,x+$t) * C 00s -£- ( 31 ) 



p •= -s.Vi £k*+cr-fc)- dty . 



L6 



