BibTeX
@MISC{Farrell10roll/streakdynamics,
author = {Brian F. Farrell and Petros J. Ioannou},
title = {Roll/streak dynamics in turbulent shear flow},
year = {2010}
}
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Abstract
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 themeanflow andtheturbulence. Turbulent Reynolds stress divergence isconfigured 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/streakstructure arises asabifurcationin theparameter of freestream turbulence intensity. This structural instability equilibrates nonlinearly at finite amplitude and although the resulting statistical equilibrium velocity profiles are inflectional, the associatedflowsarestableandbothformationandequilibrationoftheroll/streakstructurecanbetracedtothenon-normalityoftheunderlyingshearflowdynamics. Atsufficiently 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. a)
Keyphrases
turbulent shear flow roll streak dynamic roll streak turbulence complex roll streak structure structural instability structural stability freestream turbulence intensity work ssst high turbulence intensity turbulent mean state roll streakstructure nonlinear dynamical system associated streamwise streak limit cycle asabifurcationin theparameter cooperative instability themeanflow andtheturbulence cross-stream spanwise plane turbulent state turbulent reynolds stress divergence stochastic structural stability theory second bifurcation statistical equilibrium velocity profile hairpin eddy finite amplitude dominant turbulent perturbation structure
