Data-Driven Dynamical System Models of Roughness-Induced Secondary Flows in Thermally Stratified Boundary Layers

The goal of this work is to investigate the feasibility of constructing data-driven dynamical system models of roughness-induced secondary flows in thermally stratified turbulent boundary layers. Considering the case of a surface roughness distribution which is homogeneous and heterogeneous in the streamwise and spanwise directions, respectively, we describe the streamwise averaged in-plane motions via a stream function formulation, thereby reducing the number of variables to the streamwise velocity component, an appropriately introduced stream function, and the temperature. Then, from the results of large-eddy simulations, we perform a modal decomposition of each variable with the proper orthogonal decomposition and further utilize the temporal dynamics of the modal coefficients to construct a datadriven dynamical system model by applying the sparse identification of nonlinear dynamics (SINDy). We also present a novel approach for enforcing spanwise reflection symmetry within the SINDy framework to incorporate a physical bias.