III. DYNAMICS OF OCEAN CURRENTS 



N. P. ForoNOFF 



During the past two decades there has been a marked increase of interest in 

 the theory of ocean currents and dynamical processes in the ocean in general. 

 A measure of success has been achieved in explaining certain gross features of 

 ocean circulation in terms of steady-state theory. This success is responsible, 

 at least in part, for spurring activity in the more difficult fields of time-dependent 

 and convective circulations in the ocean. 



The classical works of Bjerknes (1898), Ekman (1905), Bjerknes and 

 Sandstrom (1910) and Bjerknes, Hesselberg and Devik (191 1) have had aremark- 

 ably strong influence on subsequent development of dynamical theories of 

 ocean currents. Sverdrup, Johnson and Fleming (1942, chaps. XII and XIII) 

 and Dietrich (1957, chap. VII) follow the classical ideas closely in their treat- 

 ment of statics, kinematics and dynamics, including a discussion of the circula- 

 tion theorem and the Ekman theory of ocean currents. 



In recent years, the Ekman theory of wind drift and gradient currents has 

 been developed and generalized for application to the steady and time- 

 dependent circulation in shallow seas. The theory is not considered in detail 

 here and the interested reader is referred to Sverdrup, Johnson and Fleming 

 (1942, chap. XIII) or to the recent and more complete summary by Felsenbaum 

 (1956) for the details. i 



Shtokman (1946) recognized the deficiencies of the Ekman theory in ex- 

 plaining steady-state ocean currents in a non-homogeneous ocean and derived 

 equations for total transport in which the density structure does not appear 

 explicitly. Sverdrup (1947) was able to show that, if the variation of the Coriolis 

 parameter 2 with latitude is taken into account, a realistic distribution of 

 transport can be deduced from surface-wind stress. Stommel (1948) showed 

 that the circulation can be completed by an intensified meridional flow along 

 the western boundary of the ocean provided the variation with latitude of the 

 Coriolis parameter is retained in the equations governing the flow. These 

 developments were followed by a more complete and rigorous application of 

 the theory by Munk (1950), who was able to deduce the major features of ocean 

 circulation from estimates of the actual wind stress over the ocean surface. 

 Further developments have been restricted to modifications of the theory of 

 formation of the intensified meridional currents along the western boundaries 

 of the ocean. 



1 Other recent papers on the Ekman theory include Ichiye (1949, 1950), Sarkisian (1954, 

 1957), Welander (1957), Felsenbaum (1956a), Ozmidov (1959) and Saint-Guily (1959). 



2 Defined as twice the magnitude of the vertical component of the earth's rotation 

 vector. 



[MS received November, 1960] 323 



