The Representation of Oceanic Movements and Kinematics yjl 



amount in the considered space. For example, the silicate content is q at three oceanographic stations 

 a, b and c, where the vertical salinity distribution is s. For a prism taken by these stations down to a 

 definite level, there will be current amounts M^, Mj, M3 passing through each side in unit time and a 

 current flow M^ through the bottom surface. If it is then assimied that no water enters or leaves through 

 the upper sea surface (zero precipitation and evaporation) then the constancy of the water volume 

 requires that 



Ml + M2 + M3 + M„ = 0. 



If further the corresponding mean amounts of salt and silicate passing through the three surfaces of 

 the prism are indicated by s^, s^, s^ and q^, q<i, q^, respectively, and the amounts of salt and silicate in 

 the prism are taken as constant, then 



s^Mi + S2M2 + .ygMg + s^M^, = 

 and 



^iMi + q^M^ + q^M^ + qJA^ = 0. 



If the current amount or the current at one of the lateral surfaces of the prism are known the three 

 equations are sufficient for a calculation of the other three unknown currents. 



Okada (1934) has used these methods to study the oceanographic conditions in the Sagami Bay; 

 and they have been used in a more extended form by Hidaka (1940a, b) to reduce the relative velocity 

 distribution calculated from the oceanographic structure at different stations to the absolute values. 

 Unfortunately, however, these methods cannot be used in most cases just for numerical reasons, since 

 the coefficients of the equations diffisr numerically by so little that the determination of the un- 

 knowns becomes illusory. In the second and third of the above equations the mean salinity and 

 silicate values at the three surfaces of the prism differ very little, so that the equations are only in- 

 significantly different from the first. Small errors in the determination of the values of 5 and <? and other 

 random effects such as inaccuracies in the positions of the stations thus play such an important part 

 in the solution that no reliance can be put on it. 



In using the continuity equation for the determination of the current amount it 

 should be borne in mind that the distribution of the characteristic water properties is 

 largely controlled by exchange processes, so that these cannot be neglected since the 

 magnitude of these effects is the same as that of the simple transport terms. To be 

 strictly correct the equation (XII. 12) should also take into account the effects of 

 mixing processes. This leads then to an equation which has already been used in 

 Pt. I (see p. 120) in the explanation of the phenomena occurring during the spreading 

 of a water mass into surrounding waters. For stationary conditions it takes the form 



dpus dpvs 8pws d / 8s\ 8 / 8s\ 8 



8x 



8pvs 8p\vs 8 1 8s\ 8 1 8s\ 8 [ 8s\ 



Integrating this equation from the sea surface down to the sea bottom the last term 

 on the right-hand side gives 



8s \ I 8s 



'k- 



The first term of this expression is zero since A^ vanishes at the sea bottom. The 

 second represents the difference between evaporation and precipitation per unit area 

 at the surface of a water prism. 



Neglecting the effect of the vertical component of velocity on the left-hand side of equation (XII. 15) 

 on account of its smallness and retaining on the right-hand side only the term for the vertical exchange, 

 then for p Y^ 1 and A^ = const, an approximately correct equation is obtained 



ds ds d'^s 



