Forced internal Waves 



starting with the perturbation equations, 



p—+fxtip + yp + pV(f> + K = 



dt 



dt dz 



(52) 



V-0 = O 



and eliminating the horizontal components of velocity, pressure, p , and 

 density, p , in order to get a differential equation for the vertical component 

 of velocity w : 



v.^ 



d^w 



d w 



+ gr v^^iv + 



dt^ dz^dt^ 



+ f^ 



d-^w 



d^w 



dw 



dz dt^ * 



1/p 



dK^ 



f Vx 



d^K 

 dz dt 



(53) 



Surface tides are excluded from the boundary conditions so that in the case of a 

 horizontal bottom 



w = o for 2 = o and z = H 



(54) 



must hold. 



The inhomogeneous term in (53) is simplified to 



k^exp[i{KoX + r]Qy + ajQt)] with /Jq=10~^^ cm"l see" (55) 



where the magnitude of k^ follows from the expression 



K=fK^, Ky.K^) =3M 



Rp — 3zRp 



exp [ i (kqX + rj^y + WQi)]gm cm"^ sec" 



with 



M = mass of the moon, assuming the mass of the earth to be unity 



r= distance between the center of the earth and the center of the moon 



Rg = radius of the earth 



22 



