Radiation and Dispersion of Internal Waves 



iJ 



l- ut H 



Fig. 5 - Internal waves in steady flows 



(U Icoscpl < N//3 = [-2gPo/p;] '/2) _ 



27tU 



1/2 



4gH; 



1/2 



(H = -P./Po) 



(65a) 



(65b) 



When the condition u < N/p is met, (63) indicates that the stationary waves would 

 be located on the entire spherical surface with diameter OQ if these waves had 

 been propagated with phase velocity c . It is of interest to note that the wave- 

 length ^ of the stationary internal waves depends only on the property of me- 

 dium and free stream velocity, and, in contrast with ship waves in a homogeneous 

 water, is independent of the angle of wave propagation. Generally /3 is very 

 small (H = 1/2/3 ~ 8000 meters for atmosphere), hence for sufficiently small U 

 the last factor of (65b) in the square bracket is nearly unity, then \ is propor- 

 tional to u. This feature is also in contrast with two-dimensional irrotational 

 small waves in deep water, which have wavelength k = l-nV^/g in steady motion. 



Since the wave energy is propagated with velocity equal to c^, the final con- 

 figuration of the stationary waves must be determined on this basis. Consider 

 first the two-dimensional motions in the x-z plane. The final location of a sta- 

 tionary wave packet emitted at Q in the direction making an angle f? with the 

 vertical evidently has the coordinates 



565 



