Unsupervised modelling of a transitional boundary layer

Abstract

A data-driven approach for the identification of local turbulent-flow states and of their dynamics is proposed. After subdividing a flow domain in smaller regions, the -medoids clustering algorithm is used to learn from the data the different flow states and to identify the dynamics of the transition process. The clustering procedure is carried out on a two-dimensional (2-D) reduced-order space constructed by the multidimensional scaling (MDS) technique. The MDS technique is able to provide meaningful and compact information while reducing the dimensionality of the problem, and therefore the computational cost, without significantly altering the data structure in the state space. The dynamics of the state transitions is then described in terms of a transition probability matrix and a transition trajectory graph. The proposed method is applied to a direct numerical simulation dataset of an incompressible boundary layer flow developing on a flat plate. Streamwise-spanwise velocity fields at a specific wall-normal position are referred to as observations. Reducing the dimensionality of the problem allows us to construct a 2-D map, representative of the local turbulence intensity and of the spanwise skewness of the turbulence intensity in the observations. The clustering process classifies the regions containing streaks, turbulent spots, turbulence amplification and developed turbulence while the transition matrix and the transition trajectories correctly identify the states of the process of bypass transition.