studies on the Motion of Viscous Flows — V 

 o e e e e o o 



"2.t + "2^2,1 + "2^2,2 + "3^2,3 = -^% " ^^2 + ^^'^2 ' 



e o o o o e e 



"3,t + "l"3,l + ^2^3, 2 + "3^3,3 = "^^ " ^^ + ^^^^3 ^ 



o e e e e o o 



Consequently, 



and 



"i.t = -P'i + ^v^u, , (12) 



Ui,i = -P?i . ' „ (13) 



u. i = . (14) 



Let Wi = eijku^ j be vorticity. Here e^^ is the permutation symbol. Then, 

 from Eq. (12), 



= ^V^Ce^.^u^ j) 



Thus, 



'i,t = ^^'^k • (15) 



Each component of vorticity obeys the heat conduction equation in an anti- 

 symmetrical flow. (A similar argument was previously given by Lieber and 

 Wan in Ref . 1.) 



Also from Eq. (13), we have 



e . . , u • w, = e ■ • , u • e, „ u „ 

 ijk J k 1 j k ] kf m m, f 



= (1/2 UjU.) i + P^. 

 = (P^+ 1/2 u.u.)_i . 



685 



