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Statistical inverse analysis and stochastic modeling of transition

A computational method is introduced to infer statistical information on boundarylayer perturbations upstream of laminar-turbulent transition in a supersonic boundary layer. The method uses the intermittency function as a basis, which specifies the amount of time a flow is turbulent at a given streamwise location. The methods yields a joint probability density function for amplitude and frequency of boundary-layer perturbations upstream of transition. It relies on linear stability theory to link the probability density function with the intermittency. In order to infer parameters governing the function, we perform a statistical inverse analysis using the Markov chain Monte Carlo method. The approach is applied to a synthetic test case and to experimental data. The knowledge of the location of laminar to turbulent transition is essential for numerous engineering applications. For a hypersonic vehicle, an accurate prediction of the transition location may allow to precisely define the dimensions of the vehicle’s thermal protection system. Transition does not only affect the performance of an atmospheric re-entry vehicle, it also plays a key role in the safety of the vehicle and its payload. The development of credible engineering models for the prediction of laminar-turbulent transition is therefore an important task. The transition location depends on a large number of parameters and is, consequently, difficult to predict. In particular, perturbations in the boundary layer upstream of transition are known to affect the transition process. Except in studies performed within a carefully controlled laboratory environment, transition is a highly random process due to its strong sensitivity to these perturbations. Instead of trying to determine fixed values of the most important governing parameters, in particular those relating to boundary-layer perturbations, we should characterize them in a statistical way in order to account for the stochastic nature of transition. The laminar-turbulent transition process may be divided into three stages: receptivity, linear disturbance evolution and nonlinear breakdown to turbulence. Most transition modeling approaches are deterministic and rely on empirical data (Langtry & Menter 2009), but they do not capture the stochastic nature of the physical processes active during these stages. Only the nonlinear breakdown stage, including the formation of turbulent spots, has been modeled in a probabilistic way (Vinod & Govindarajan 2004; Pyecnik et al. 2011).