The factor (co„ tw,,) A^^, t/iig^lk^ ± ^J^) in (57) is dimensionless; W± (z) 

 and Wy (z) are velocities and Wf^(z) is an acceleration. 



From (57) to (61) we conclude that the primary waves create new waves 

 of wave number fe^ ±k„ and frequency com - con with amplitudes depending on 

 the driving forces F^„ (z) and G,^„ (0). These new waves grow linearly with 

 time if the resonance condition (56) is met. The amplitude factor A^,,^ is given 

 according to (58) by 



H 



/ 



Ur-(co^±co,f]-p ^±j,,,,±^,),. 



(62) 



Jlgr-(co„,±cof~]-pW^u) dz 



If more than one internal mode is to be considered, G;,7'„(0) has to be expanded 

 into eigenfunctions, too, and evaluated at £ = 0. Formulas similar to (58) and 

 (62) will hold then for g|„ (0). 



Fllzl, GlM ANDA^,„, IN CASE OF AN 

 EXPONENTIALLY STRATIFIED SEA 



In order to evaluate solution (57) of the secondary resonance waves, we 

 have to know the eigenfunctions of W-fe), which are given by (59). They depend 

 on the mean stratification p(z) and determine the amplitude factor A^~^, given 

 by (62). Equations (59) can be solved numerically for any stable stratified fluid, 

 and it is known that the eigenvalues may vary considerably due to density changes. 

 However, solving (59) for an exponentially stratified sea, where ro= const, may 

 be sufficient at the present time where only the magnitude of the effects is of 

 interest. „ 



Using 'p(z) = Pqc 0~ as density distribution, W,, is given as solution of 

 (46) to (48) 



where 



£o _ g^^n 2 



9 2 



19 



