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 data-driven 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.

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