PART II 



C. S. Cox 



4. Differential Equations 



The equations governing the motion of waves through initially still water on 

 a rotating sea have been treated extensively by Love (1891), Fjeldstad (1933), 

 Groen (1948) and Eckart (1960). Let 



ijj{z) exp[i{kx — cot)] 



(1) 



represent the vertical displacement of water particles from an equilibrium 

 condition in free waves (Fig. 22). Then the first order equation is 



I d / di/j 



pdz\Pdz}^Hco^-Q^ 



ifj = 



where p is the undisturbed density, 



---m-W' 



(2) 



(3) 



////////, '//////■■'//// 



Fig. 22. The z axis is directed vertically upward. \\}{z) is the amplitude of internal oscilla- 

 tions. 



is Vaisala's frequency (Chapter 2, Eq. 35), and Q is the inertial frequency equal 

 to twice the angular velocity of the earth times the sine of latitude. Boundary 

 conditions are 



dx\s gk^ 



.Q2 



ifj = 



at the surface and 



at a level bottom. 



ijj = Q 



752 



(4) 



(5) 



