  This paper deals with the optimal streaky perturbations (which maximize the
perturbed energy growth) in a wedge flow boundary layer. These three
dimensional perturbations are governed by a system of linearized boundary layer
equations around the Falkner-Skan base flow. Based on an asymptotic analysis of
this system near the free stream and the leading edge singularity, we show that
for acute wedge semi-angle, all solutions converge after a streamwise transient
to a single streamwise-growing solution of the linearized equations, whose
initial condition near the leading edge is given by an eigenvalue problem first
formulated in this context by Tumin (2001). Such a solution may be regarded as
a streamwise evolving most unstable streaky mode, in analogy with the usual
eigenmodes in strictly parallel flows, and shows an approximate
self-similarity, which was partially known and is completed in this paper. An
important consequence of this result is that the optimization procedure based
on the adjoint equations heretofore used to define optimal streaks is not
necessary. Instead, a simple low-dimensional optimization process is proposed
and used to obtain optimal streaks. Comparison with previous results by Tumin
and Ashpis (2003) shows an excellent agreement. The unstable streaky mode
exhibits transient growth if the wedge semi-angle is smaller than a critical
value that is slightly larger than $\pi/6$, and decays otherwise. Thus the
cases of right and obtuse wedge semi-angles exhibit less practical interest,
but they show a qualitatively different behavior, which is briefly described to
complete the analysis.
