380 FOFONOFF [sect. 3 



Weddell Sea. The observational evidence for these sources, although indirect, 

 is convincing. However, although we know approximately where the sources 

 are, we do not have a clear understanding of the processes that control their 

 strength. It is evident that the formation of deeja water is ultimately controlled 

 by the distribution of fluxes of heat and water across the ocean surface but we 

 do not know the details of the processes involved. The model for the con- 

 vergent Ekman transport yields larger meridional gradients of temperature 

 for weaker upward flow. The larger gradients may, in turn, favour an increased 

 rate of formation of deep water. Hence, the thermal circulation may tend to 

 be self-regulating. In this sense, the interpretation that the thermocline 

 mechanism "demands" a certain upward flux of water from below, suggested 

 by Stommel and Arons (1960a), may be justified. In any case, the model of 

 convective circulation constructed by Robinson and Stommel deserves further 

 study and elaboration. 



7. Time-Dependent Motion 



The theoretical study of time-dependent motion in bodies of water of oceanic 

 scale has been confined for the most part to the investigation of various types 

 of waves that can be propagated in a homogeneous or two-layer ocean without 

 interaction with the steady flow\ We shall, therefore, confine our attention to 

 these two idealizations of the structure of the real oceans and consider primarily 

 wave modes with periods greater than a half-pendulum day {'l-nlf). Waves of 

 shorter period have been studied in greater detail in connection with tidal 

 theory and the study of surface waves and swell. 



Rossby (1939) showed that the variation of the Coriolis parameter with 

 latitude enables the ocean to execute a low-frequency wave motion that 

 propagates westwards relative to the particle motion. These waves, called 

 planetary or Rossby waves, provide a mechanism for transporting energy on a 

 time-scale greater than a half-pendulum day. One of their characteristics, 

 pointed out in the section on dimensional analysis of the momentum equations, 

 is that the horizontal velocities in the wave are nearly geostrophic. Thus, in a 

 sense, the waves can be considered as moving current systems. These low- 

 frequency waves play a fundamental role in the approach of ocean circulation 

 to the steady state and in the transient response of the ocean to variations in 

 the driving forces that maintain the steady circulation. 



Our present knowledge of the time-dependent modes of response of the ocean 

 is far from adequate. For example, we have a poor understanding of the 

 interactions between wave modes and the steady flow. We have seen that the 

 steady flow can be concentrated into intense currents near the ocean bound- 

 aries. In the boundary regions the relative vorticity can become as large as the 

 Coriolis parameter so that the Rossby number is unity. Under these conditions 

 the interaction terms between the steady flow and time-dependent modes of 

 flow are not negligible, and appreciable exchanges of energy between the modes 

 may occur. However, boundaries are extremely difficult to incorporate into the 



