Basic Principles of the General Oceanic Circulation 589 



charts without taking into account the deviations. It might also be due to the imper- 

 fections in the present knowledge of the relationships between wind velocity and wind 

 stress (see pp. 421 and 586) or due to the use of plane co-ordinates instead of spherical 

 ones for the calculation of conditions on the curved surface of the earth. It is note- 

 worthy that Hidaka has obtained good numerical agreement for transport in the Kuro- 

 shio Current using spherical co-ordinates. The most probable reason however is that 

 the actual dynamics of the strong western boundary currents (such as the Gulf Stream 

 and the Kuroshio) are left essentially unexplained by the Stommel-Munk theory. In 

 order to explain the narrowness of these boundary currents it is necessary to take an 

 eddy viscosity so large that the eddy sizes would be comparable to the width of the cur- 

 rent. This can never be the case. Pressure inertia and the variations of Coriolis para- 

 meter with latitude all seem to play an important part in the dynamics of these boundary 

 currents (see p. 550). It is striking that there is no indication of a "westward intensifi- 

 cation" of ocean currents in the Southern Hemisphere; the Brazil Current and the 

 East Australian Current for instance are not so strongly developed along the east 

 coast of the continents as the Gulf Stream and the Kuroshio. It wouid be expected 

 that if the planetary vorticity were the only cause of the westward intensification in the 

 oceans of the Northern Hemisphere it would show the same effect in the South Atlantic 

 and South Pacific. It appears however that the vertical structure of the ocean also 

 plays a role in the theory since the depth d is correlated with the oceanic structure and 

 the magnitude of d cannot be chosen arbitrarily, d denotes the depth over which an 

 integration has to be performed in order to eliminate the effect of the vertical oceanic 

 stratification and of internal vertical friction. Usually the depth of no motion has been 

 taken as d and only the horizontal velocity of the water movement has been taken in- 

 to consideration; the vertical velocity is presumed to be zero or so small that it can 

 be neglected. This assumption is certainly incorrect and may lead to an entirely false 

 picture of the horizontal circulation. Stommel (1956) has given a detailed discussion 

 showing that the existence of a level of no motion in the ocean where all the three 

 velocity components vanish cannot be substantiated; in fact the maximum vertical 

 velocity occurs at the depth of no meridional \Q\ocity (see p. 499). A paper by Neumann 

 (1955) is of interest here. He has re-examined the theory for a horizontal wind-driven 

 ocean current taking into account the spherical shape of the earth the average vertical 

 density stratification and the variable depth of the lower boundary of the circulation 

 system. The latter assumption is the same as the assumption that the depth d is the 

 depth of the layer of no meridional motion. Integration of the usual equations of 

 motion for the geostrophic wind taken over the depth _ between +^ and —d and with 

 P = p(x,y,z) gives the equations of transport 



dP 81, cd, 



■^ -^ cy ^^^^ cy ^^ ^ dy 



CP CL dx. 



(XVIII.21) 



Introducing 



' T+d 



p(-) dz; P(-d) = gp(i + rf) and P = p dz = 2f (? + df 



I 



gP 



