627 



a 



FIGURE 5. The onset of wave breaking for )( > . The waves are moving to the left. The mean Richardson number at the in- 

 terface in the accelerating flow is approximately (a) 2.5 (b) 0.73 (c) 0.36 (d) 0.25 (e) 0.18 (f) 0.14 (g) 0.11 (h) 0.09 

 (i) 0.07 (j) 0.06 [from Thorpe (1968)]. Convective overturn is seen to begin at (c) and K-H.I at (i). The instability is 

 not seen at the critical value of Ri because of the time needed for growth in the accelerating flow. 



not be unaffected by it. This process may be 

 important in producing asymmetric directional wave 

 spectra in the seasonal thermocline. 



In practice of course unidirectional flows and 

 long trains of internal waves do not occur in the 

 ocean. The component of the mean flow velocity 

 normal to the direction of wave propagation appears 

 to play no part in the breaking or dynamics of the 

 waves, and the results should be valid for long 

 crested waves even in (Ekman) spiral flows. A 

 periodic shear flow applied to a wave, as when one 

 internal wave moves through another, may produce 

 locally the conditions for convective overturn of 

 the kind we have described. The final stages of 

 the experiments of Keulegan and Carpenter (1961) 

 or Davis and Acrivos (1957) illustrate this process. 

 In these experiments a short second mode wave is 

 driven by resonant interaction from a long first 

 mode wave, itself generated by a wavemaker. The 

 shorter wave eventually breaks in the shear field 

 of the longer first mode wave . 



Flow acceleration accompanies both the periodic 

 flows in a wave field and the motion of the upper 

 layers of the ocean during periods of wind forcing. 

 In the experiments shown here breaking was induced 

 by allowing the flow to accelerate uniformly. It 

 was discovered that the energy of the fluctuating 

 wave components was reduced very rapidly as a 

 result of this acceleration. The consequent Rey- 

 nolds stress working on the mean velocity gradient 

 transferred energy to the mean flow. This inter- 

 action may have important consequences on the 

 development of the seasonal thermocline during 



(a) 



(b) 



X<0, R| 



X>0,R 



FIGURE 6. Stability diagrams corresponding 

 to the waves described in Figure 2, based 

 on a calculation extended to t±iird order 

 (Thorpe, 1968). (a) Couette flow (b) Hyper- 

 bolic tangent profiles. 



