Statistical Prediction of Laminar-turbulent Transition

Stochastic versions of stability equations are considered as a means to develop integrated models of transition and turbulence. Two types of stochastic models are considered: probability density function evolution equations for stability mode amplitudes, and Langevin models based on representative stability theories including the resonant triad model and the parabolized stability equations. The rst type of model can describe the e ect of initial phase di erences among disturbance modes on transition location. The second type of model describes the growth of random disturbances as transition proceeds and provides a natural framework in which to couple transition and turbulence models. Coupling of parabolized stability equations with either subgrid stress models or with conventional turbulence models is also discussed as an alternative route to achieve the goal of integrated turbulence and transition modeling.