SECT. 3] DYNAMICS OF OCEAN CURRENTS 393 



higher, their infiiience on the baroclinic waves is large. Moreover, in the presence 

 of steady barocHnic flow, the interface cannot be level. Variations in depth of 

 the upper layer would have significant effects on the baroclinic wave modes. If 

 we consider, to a first approximation, that the variation of layer depth can be 

 taken into account by replacing / by hofjh, where h is the mean depth of the 

 upper layer at any point and ho the average depth over the region, we see that 

 baroclinic Rossby waves cannot be generated for steady westward flow for 

 which //A is constant. On the other hand, the effective value of the variation of 

 hoflh may be considerably larger than /3 for steady eastward flow. 



Analysis of the time-dependent response of an unbounded two-layer ocean 

 to fluctuations of wind stress has been carried out by Veronis and Stommel 

 (1956). They considered a one-dimensional model and did not include steady 

 flow components. They found that the response for periods of wind fluctuations 

 of the order of one to seven weeks was principally in the form of barotropic 

 Rossby waves. For longer periods, the baroclinic Rossby waves become in- 

 creasingly important. The contribution to the velocity in the upper layer by 

 barotropic and baroclinic waves is about equal for periods of about one year. 

 For very long periods ( > 100 years), the response is purely baroclinic. Veronis 

 (1956) calculated the proportion of energy that appears in geostrophic and non- 

 geostrophic motions for winds of short duration. He concluded that a large 

 fraction of the energy of the resultant motion appears as high-frequency 

 {co>f) wave motion if momentum is added impulsively. However, if the same 

 amount of momentum is added over a period of a half-pendulum day, only 

 about one-tenth of the energy goes into the high-frequency waves. Thus, for 

 wind duration of the order of a half -pendulum day or longer, the high-frequency 

 wave modes can be neglected and the induced motion can be considered 

 approximately geostrophic. 



The studies of the forced response of an unbounded ocean have given us a 

 qualitative description of the effects of variations of wind stress. However, it 

 appears likely that the results will be modified significantly by the presence of 

 boundaries and components of steady flow. Further investigations of the time- 

 dependent equations are required both to improve our understanding of the 

 mechanism of Rossby waves and to determine in more detail the response 

 characteristics of a partially or fully enclosed ocean. 



References 



Arons, A. B. and H. Stommel, 1956. A ^S-plane analysis of free periods of the second class 

 in meridional and zonal oceans. Deep-Sea Res., 4, 23-31. 



Bjerknes, V., 1898. Uber einen hydrodynamischen Fundamentalsatz und seine Anwen- 

 dung, besonders auf die Mekanik der Atmosphare und des Weltmeeres. Kgl. Svenska 

 Veteitskapsakad. Handl., 31, 1-35. 



Bjerknes, V. and J. W. Sandstrom, 1910. Dynamic meteorology and hydrography. 

 Statics. Puhl. Car?iegie Inst. Wash., No. 88, Part I, 1-146. 



Bjerknes, V., Th. Hesselberg and O. Devik, 1911. Dynamic meteorology and hydro- 

 graphy. Kinematics. Publ. Carnegie Inst. Wash., No. 88, Part II, 1-175. 



