Multi-Scale Modeling of Turbulent Flows Using Coupled Fractional-Order Navier-Stokes and Deep Learning-Based Closure Models

This research presents a hybrid turbulence modeling framework that couples fractional-order Navier-Stokes equations with a machine learning-based subgrid-scale stress closure model. The objective is to enhance the accuracy of turbulent flow simulations by incorporating long-range memory and non-local effects via fractional calculus, alongside neural network-inspired closures. A simplified 1D fractional-order Burgers' equation is used with a synthetic ML-based stress term to illustrate the method. Results show improved flow representation, highlighting the model’s potential for broader applications in fluid mechanics.