SECT. 1] THE EQUATIONS OF MOTION OF SEA- WATER 39 



8. Definitions Related to Convective Motion 



One first remarks that the quantity 



C = Go-V-ho- Hp,o V • Soldo (47) 



is known from the zeroth approximation ; it will be called the convectomotive 

 force. The quantity 



Be = podoN^ie/ (48) 



is also known, and will be called the convective resistance. Then (41) and (46) 

 become 



^ - pogui • Vx + poco^ V • ui = poCoHN^Ig)CIRc, (49) 



and 



^-ui-Vx = -01 Re. (60) 



It remains to justify the terminology used in these definitions. The quantity 



tv — Ui- V;\; 



is the vertical component of velocity. If steady solutions only are considered, 

 so that 8ldt = 0, (50) becomes 



wRc = C, (51) 



which is reminiscent of Ohm's law. The convectomotive force is essentially the 

 net accession of heat due to all causes, and w is the vertical component of the 

 convective motion resulting from the heating of the fluid. Equation (49) then 

 becomes 



V,.„..^(^VA)._^^. (52) 



lie \ g CoV po -fic 



Equations similar to (51) and (52) are discussed in Chapter 3 of Eckart (1960). 

 On the other hand, if (7 = 0, (50) becomes 



|i = »; (53) 



in the absence of a convectomotive force, gi is thus the vertical displacement of 

 the fluid to the accuracy of the present approximation. 



Finally, it is to be remarked that the unknown Si does not appear in (45), 

 (49) and (50). These may, therefore, be solved without regard to (40), the 

 solution of which is trivial once Ui has been determined from the other three 

 equations. 



