THE SECONDARY RESONANCE WAVE FIELD DUE TO 

 SWELL IN CASE OF AN EXPONENTIALLY STRATIFIED SEA 



With reference to observations described in the following section, we eval- 

 uated the resonance part of solution (52), using (59), (60), (66), (67), and (68). 

 The results are based on the following numerical values: 



The swell frequencies of the two primary waves are co^ = 3.808 • 10"! sec'l 

 and &)£ = 3.900 ■ 10"^ sec "l. The corresponding wave numbers for a water depth 

 of H= 18 m are fe^ = 3.00 • 10-4 cm-l, feg = 3.08 • 10-4 cm-1. The density strati- 

 fication is given by Fq = 5.811 ■ 10-''' cm-l. The corresponding periods and wave- 

 lengths of the primary waves are r^ = 16-50 seconds, t2 = 16.11 seconds. Aj = 

 209.4 m, ^2 = 204.0 m. Furthermore, for surface waves we have a„ = i\k„\. 

 ^m = 'l^ml- The product between the amplitudes A„and A^ of the vertical com- 

 ponents of the velocity is supposed to be A1A2 = 400 cm2 sec-2. The corresponding 

 amplitude product of the two swell waves is ^1(^2 = 889.76 cm^, which may be 

 based on 4-^ = 50 cm and ^2 = 17.8 cm. 



Because of these swell frequencies we expect an internal wave of frequency 

 C02 - oji = 0.0092 sec-l or period T2.1 = 11-38 minutes. The result is shown in 

 figure 2, which contains the amplitude of this internal wave after an interaction 



CM 



Figure 2. Amplitude (cm) of infernal waves due to modulated 

 swell after an interaction time of 10^ seconds (16.6 minutes) as 

 a function of the angle between the two primary waves. 



23 



