Roll/streak dynamics in turbulent shear flow

Stochastic Structural Stability Theory (SSST) provides an autonomous, deterministic, nonlinear dynamical system for evolving a turbulent mean state. In this work SSST is applied to the problem of understanding the origin and dynamics of roll/streak structures associated with both transition to turbulence and maintenance of the turbulent state. Roll structures in the cross-stream/spanwise plane and associated streamwise streaks are shown to arise spontaneously from interaction between the mean flow and the turbulence. Turbulent Reynolds stress divergence is configured in this interaction to force rolls that produce streamwise streaks that in turn organize the turbulence to support the roll/streak/turbulence complex. The dominant turbulent perturbation structures involved in supporting the roll/streak/turbulence complex are roller and hairpin eddies. The cooperative instability giving rise to the roll/streak structure arises as a bifurcation in the parameter of free stream turbulence intensity. This structural instability equilibrates nonlinearly at finite amplitude and although the resulting statistical equilibrium velocity profiles are inflectional, the associated flows are stable and both formation and equilibration of the roll/streak structure can be traced to the non-normality of the underlying shear flow dynamics. At sufficiently high turbulence intensity the fixed point equilibrium roll/streak/turbulence complex loses structural stability at a second bifurcation leading to a limit cycle in which the roll/streak structure repeatedly collapses and reforms.