OCEAN CURRENTS RELATED TO THE DISTRIBUTION OF MASS 103 



nearly the same at both stations, and the difference will be an error of 

 absolutely negligible amount. In practice one can therefore consider 

 the numbers that represent the geometric depth in meters as representing 

 absolute pressure in decibars. Interpreting the depth in meters at which 

 either directly observed or interpolated values of temperatures and 

 salinities are available as representing pressures in decibars, one can 

 compute, by means of a few simple tables, the anomaly of specific volume 

 at the given pressure. By multiplying the average anomaly of specific 

 volume between two pressures by the difference in pressure in decibars 

 (which is considered equal to the difference in depth in meters), one 

 obtains the geopotential anomaly of the isobaric sheet in question, 

 expressed in dynamic meters. By adding these geopotential anomalies, 

 one can find the corresponding anomaly between an}^ two given pressures. 

 An example of a complete computation is given in table 13. 



As has been repeatedly stated, these computations give information 

 only for the field of pressure that is related to differences in density. 

 The total field of pressure may be composed of this internal field and 

 of a field that may be related to piling up or removal of mass. If actual 

 piling up of water takes place, the slopes of the isobaric surfaces remain 

 constant from the surface to the bottom, and this pressure field is called 

 the slope field, in contrast to the internal field. 



Currents in Stratified Water 



Some of the outstanding relationships between the distribution of 

 mass and the velocity field are brought out by considering two water 

 masses of different density, p and p', where p is greater than p'. In the 

 absence of currents, the boundary surface between the two water masses 

 is a level surface, the water mass of the lesser density, p, lying above the 

 denser water. On the other hand, if the water of densit}^ p' moves at a 

 uniform velocity v' and the water of greater density moves at another 

 uniform velocity v, the boundary must slope. For the sake of simplicity, 

 it will be assumed that both water masses move in the direction of the 

 y axis and that the acceleration of gravity, g, can be considered constant. 

 The dynamic boundary condition (p. 96) then takes the form 



\{pv - pV)dx + g{p - p')dz = 0. (VI, 24) 



From this equation one obtains the slope of the boundary surface: 



dz X pv' — pv ,^r^ __. 



iB = -r = - 7- (VI, 25) 



dx g p - p' 



The slope of the isobaric surfaces is obtained from (VI, 6), which, on the 

 above assumptions, gives 



2p = - - v' and tp = - - V. (VI, 26) 



g 9 



