  Stochastic Structural Stability Theory (SSST) provides an autonomous,
deterministic, nonlinear dynamical system for evolving the statistical mean
state of a turbulent system. In this work SSST is applied to the problem of
understanding the formation of the roll/streak structures that arise from
free-stream turbulence (FST) and are associated with bypass transition in
boundary layers. Roll structures in the cross-stream/spanwise plane and
associated streamwise streaks are shown to arise as a linear instability of
interaction between the FST and the mean flow. In this interaction incoherent
Reynolds stresses arising from FST are organized by perturbation streamwise
streaks to coherently force perturbation rolls giving rise to an amplification
of the streamwise streak perturbation and through this feedback to an
instability of the combined roll/streak/turbulence complex. The dominant
turbulent perturbation structures involved in supporting the
roll/streak/turbulence complex instability are non-normal optimal perturbations
with the form of oblique waves. The cooperative linear instability giving rise
to the roll/streak structure arises at a bifurcation in the parameter of STM
excitation parameter. This structural instability eventually equilibrates
nonlinearly at finite amplitude and although the resulting statistical
equilibrium streamwise streaks are inflectional the associated flows are
stable. Formation and equilibration of the roll/streak structure by this
mechanism can be traced to the non-normality which underlies interaction
between perturbations and mean flows in modally stable systems.
