Studies on the Motion of Viscous Flows— III 



iterations use lower iteration solutions which have already used a condition at 

 this distance. 



The domain within a radius hf has viscous effects, whereas beyond h* the 

 potential flow represents the real flow. In this sense one may say that hf is the 

 thickness of a boundary layer surrounding the cylinder; indeed, this thickness 

 may be several times the diameter of the cylinder for some values of the Reyn- 

 olds number. However, we must expect this domain to become smaller, i.e., h* 

 to decrease, with increasing Reynolds number when the flow is time-independent. 

 Even for a temporal flow we should expect the part of the domain close to the 

 cylinder to become smaller with increasing Reynolds number. 



Hence we have the following conditions to be satisfied by u^ and v^^, n > 1 



at ht: 



First Iteration — 



d^^ 



-l(hr^,t)=(,_j =0 for all t ^^^33^ 



v,(h*,.,t) = i-^j =0 fo.all t . ^^^3^^ 



r = h' 



Second Iteration — 



u^ih\,e,t) = I7— -) = for all t 



r = h=' 



V2(h?,0,t) =1- 1 =0 for all t 



.= u* 



Higher Iterations ( n > 3) — 



30 

 "n(h*^^.t) =1--^) =0 for all t 



30 

 ^n(h*.^,t) = (- -^ ) = . for all t 



553 



(1.85) 



(1.86) 



r 3^y - " ^"' -"'' ' , ..^ ,. (1.87)- 



r- h . .--....'... 



(1.88) 



