A note on the absolute instability of wakes

The family of wake profiles formed from the Falkner–Skan boundary-layer solutions with negative pressure gradient, m, was shown in (Woodley and Peake, 1997) to be inviscidly absolutely unstable. However, due to numerical difficulties, the limit m→ 0 was not considered there, although the results that were found appeared to indicate that the double Blasius profile (m = 0) is absolutely unstable. In this note we repeat those calculations using an alternative formulation, and show that in fact the absolute instability present form< 0 becomes neutral as m→ 0, so that the flatplate wake is only convectively, and not absolutely, unstable. In addition, the effects of viscosity are included here using the Orr–Sommerfeld equation, and two sets of saddle points are now found, one set corresponding to the inviscid family, which can be either pinching or non-pinching depending on the values of m and the Reynolds number, and another set which is always pinching, but which is stable for m close to zero.  Elsevier, Paris absolute instability / wakes