  Although the roll/streak structure is ubiquitous in pre-transitional
wall-bounded shear flow, this structure is linearly stable if the idealization
of laminar flow is made. Lacking an instability, the large transient growth of
the roll/streak structure has been invoked to explain its appearance as
resulting from chance occurrence in the free-stream turbulence (FST) of
perturbations configured to optimally excite it. However, there is an
alternative interpretation which is that FST interacts with the roll/streak
structure to destabilize it. Statistical state dynamics (SSD) provides analysis
methods for studying instabilities of this type which arise from interaction
between the coherent and incoherent components of turbulence. Stochastic
structural stability theory (S3T), which implements SSD in the form of a
closure at second order, is used to analyze the SSD modes arising from
interaction between the coherent streamwise invariant component and the
incoherent FST component of turbulence. The least stable S3T mode is
destabilized at a critical value of a parameter controlling FST intensity and a
finite amplitude roll/streak structure arises from this instability through a
bifurcation in this parameter. Although this bifurcation has analytical
expression only in SSD, it is closely reflected in both the dynamically similar
quasi-linear system, referred to as the restricted non-linear (RNL) system, and
in DNS. S3T also predicts a second bifurcation at a higher value of the
turbulent excitation parameter. This second bifurcation is shown to lead to
transition to turbulence. Bifurcation from a finite amplitude roll/streak
equilibrium provides a direct route to the turbulent state through the S3T
roll/streak instability.
