*J.(s,Of) - 0(s T ) at infinity 



j_ 



which corresponds to the strong singularity V<J> - 0(x~ 2 ). With that 



choice of E(s) the solution is still not unique, because the wake 

 strength A is undetermined. We can argue that conditions are such 

 that there should be no jump in tangential velocity across the extension 

 of the plate, in which case A ■ 0, V<(i - 0(x~ ) and <f> - 0(x 2 ) near the 

 plate edge and we have a situation essentially the same as was examined 

 in $8. Because the. radiation is emitted into uniformly moving fluid 

 the "stationary phase" formula (8.29) is not immediately applicable, but 

 we shall show in a moment how it can be generalized to the moving fluid 

 case. 



We can alternatively argue that a wake will adjust itself to 

 eliminate the high velocities which would otherwise exist at the trail- 

 ing edge, and that a Kutta condition of finiteness of the velocities 

 at th» edge should be imposed whenever possible. The physical basis 

 for such a condition in unsteady trailing edge flow is a matter of 

 controversy at tha moment, but that does not concern us here as our 

 interest is merely in seeing if and how such a condition can be applied 

 in this model problem. 



Expand the ©part of (9.18) as b + » in R . We have 



/ k lvD(-q) 5 (-q)\ 1 I 

 ♦• + (s,0) - {u£J- -jf) + ° g( _ q) " J (1 + M) 2 s" T 



3 



+ 0(s" T ) (9.19) 



the term given explicitly corresponding to v\J> - 0(x ) the second to 



i 

 V$ - 0(x ). Thus we can impose a Kutta condition, that the velocities 



67 



