Data-driven fractional order model for drag-reduced wall bounded turbulent flows

We develop a data-driven fractional-order mathematical model that unifies and generalizes the formulation of drag-reducing mean flow in wall-bounded turbulence with polymer additives. Our model incorporates the nonlocality of complicated interactions between coherent turbulent structures, which is formulated with fractional-order operators applied to stress tensor. The variable fractional order involved in the model is learned from available computational and experimental data obtained from both direct numerical simulations with different micro-rheological models and laser doppler anemometer measurements in pipe flow experiments. Results show that the data-driven fractional-order model uncovers a universal formulation of wall-bounded turbulent flows, which is able to correctly predict the mean velocity profiles of various viscoelastic turbulent flows, valid for a large range of Reynolds numbers and various polymer concentrations. The proposed model provides a convenient way to effectively evaluate the drag-reduction in wall-turbulence and offers new insights to understanding the hidden fluid physics of how polymer additives change the complicated interactions in coherent turbulent structures in wall-bounded flows.