Data-Driven Dynamics Description of a Transitional Boundary Layer

Cluster analysis is applied to a DNS dataset of a transitional boundary layer developing over a flat plate. The stream-wise-span-wise plane at a wall normal distance close to the wall is sampled at several time instants and discretized into small sub-regions, which are the observations analysed in this work. Using K-medoids clustering algorithm, a partition of the observations is sought such that the medoids in each cluster represent the main local states. The clustering has been carried out on a two-dimensional reduced-order feature space, constructed with the multi-dimensional scaling technique. The clustered feature space provides a partitioning which consists of five different regions. The observations are automatically classified as laminar, turbulent spots, amplification of disturbances, or fully-developed turbulence. The Lagrangian evolution of the regions and the state transitions are described as a Markov process in terms of transition probability matrix and transition trajectory graph to determine the transition dynamics between different states. PITUFLOW-CM-UC3M, funded by the call "Programa de apoyo a la realización de proyectos interdisciplinares de I+D para jóvenes investigadores de la Universidad Carlos III de Madrid 2019-2020" under the frame of the Convenio Plurianual Comunidad de Madrid-Universidad Carlos III de Madrid. COTURB, funded by the European Research Council, under grant ERC-2014-AdG-669505.