Dynamic mode decomposition for the inspection of three-regime separated transitional boundary layers using a least squares method

Abstract

Transitional boundary layers undergoing separated flow transition for different free stream turbulence intensity levels and Reynolds numbers have been inspected by applying dynamic mode decomposition (DMD) to time-resolved particle image velocimetry data. The identification of the unstable modes responsible for transition suffers from nonlinear effects if the whole dataset is considered for the construction of the snapshot matrix underlying the flow evolution. To overcome this limit, piecewise linear models aimed at the identification of the different regimes in the entire transition process are proposed. In particular, the flow is initially laminar (i.e., stable), it becomes unstable due to transition, and once transition is completed, the fully turbulent condition leads the boundary layer to a stable regime. The norm of the residuals resulting from the application of DMD on a variable streamwise extension of the dataset shows a trend that is associated with the variation of regime. This trend is analyzed by means of the least squares method, which allows identifying the change in the regime with stable, unstable, and turbulent behaviors. The validity of this procedure is proved by comparing it with previously published results. Moreover, since the DMD is applied to limited temporal snapshots, it provides a temporal resolution of growth rate and positions of switch between the boundary layer states. Such information is used to extract from the big dataset under analysis the time sequences characterized by the largest growth rate, hence quickly highlighting the flow physics driving transition.