Yih 



If for c = a-e or c = b+c, and any e ~ , M is less than 

 TrV{y_ - y, )^ for all y, and yg between zero and 1, then there can 

 be no waves propagating with c equal to a or b, or outside of the 

 range of U. On the other hand, if U' = at the point of maximum 

 or minimum U, and, a fortiori, if there is a region of constant U 

 where U = a or b, it can be easily shown that waves of auiy finite 

 wave length and any finite number of internal zeros n can propagate 

 with c < a or c > b. All this is in contrast with waves propagating 

 in a layer of homogeneous fluid with a free surface and In shear flow. 

 In that case [ Ylh 1970] , If U is monotonically increasing with y, 

 waves of all wave lengths can propagate with c greater than b, and 

 only sufficiently long waves can propagate with c less than b. 



ACKNOWLEDGMENT 



This work has been supported by the National Science Foundation, 



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Howard, L. N. , "Note on a Paper of John W. Miles," J. Fluid 

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