Statistical Modelling of Laminar-to-Turbulent Transition in a Blasius boundary layer*

Transient, non-modal growth of a perturbation can cause significant energy amplification and ultimately trigger transition to turbulence, even when the LNS operator is stable as defined by its eigenvalues. Transient growth is typically characterized by the optimal energy growth and initial condition.  However, Frame & Towne (2024) demonstrated via statistical analysis that, within a temporal stability framework, the optimal energy growth is generally much larger than the realized energy growth.  Our current work seeks to expand this statistical framework to spatial stability within a boundary layer. Using a compressible Blasius boundary layer as a proof of concept, we apply the statistical framework and show a disparity between the downstream responses of the optimal inlet condition and an ensemble of realizations of inlet conditions drawn from a PDF with a physically informed correlation length.  The downstream response is simulated using a linear One-Way Navier-Stokes solver and used to estimate the mean and PDF of the perturbation energy amplification. Given some transition threshold energy, we can then predict the likelihood of laminar-to-turbulent transition as a function of the streamwise direction.

 

Frame, P. & Towne, A. (2024). Beyond optimal disturbances: a statistical framework for transient growth. Journal of Fluid Mechanics, 983, A2.