158 Thermohaline Features 



These equations are of the same form as equation (5), but contain an 

 additional term because of the vertical mass flux associated with the ther- 

 mohahne circulation. The sum of the two equations is exactly the same as 

 equation (5) ; and hence we see that the introduction of the thermohaline 

 circulation in this manner does not produce any net transport over both 

 layers in the interior of the ocean, but does result in a kind of internal mode 

 of circulation. As we shall see, there is every reason to suppose that the 

 flow induced in each layer may be of the same order of magnitude as that 

 produced by the wind stress. Since there is so much uncertainty in choosing 

 the depth of no motion for a reference level in dynamic computations from 

 actual hydrographic data, it is important to form a clear idea of the role of 

 this internal thermohahne mode. Indeed, one of the theses of this study is 

 that the apparent discrepancy between the theoretical Gulf Stream trans- 

 port and that computed 'dynamicaUy' (Munk, 1950) is simply a result 

 of a confusion of this sort. In a later section this wall be considered in 

 some detail. 



In order to obtain some idea of the magnitude of the velocity w^ required 

 to produce a transport equal to that produced by wind stress, we note that 

 Munk (1950) gives the value curl t = —0-7 x lO^g./sec./sec. at 35° N. latitude 

 in the North Atlantic Ocean. An upward flux of (/ow?), = 0-85 x 10~* cm. /sec, 

 (roughly 8-5 cm. /day or 30 m./year) produces an equivalent transport. This 

 is not an exorbitantly high vertical velocity. It corresponds closely to 

 values premised by Riley (1951). It may be compared with what little is 

 known of global heat-budget considerations. For example, suppose that in 

 subtropical regions there is a net do\vnward heat flux of 150 g.cal. /day/cm. ^ 

 into the sea surface, and that this heat is used to heat water flowing up from 

 below. The average temperature increase is in the neighborhood of 15° C, 

 hence the vertical flow is 10 cm. /day. These figures should be regarded as 

 maximum heat fluxes near the equator : they would require that the ocean 

 transport more of the equatorial heat surplus toward the poles than does 

 the atmosphere. 



From the point of view of equation (13) the level of no horizontal 

 divergence is also the level of no meridional motion. Moreover, if there is a 

 small but finite interval of depth in which there is no horizontal divergence, 

 this interval will also be a layer of no motion and no vertical shear of geo- 

 strophic motion. This may be in part an explanation for Defant's (1941) 

 intuitive choice of the level of no motion in the Atlantic Ocean. In all that 

 follows I have been forced to make the assumption that the level of no 

 horizontal divergence is of finite thickness, in order to make it a level of no 

 motion as well. 



It is perhaps worth while to reemphasize at this point that all we have 

 done in this section is to introduce new fields of horizontal divergence 



