Fractional-Order Modeling of Turbulent Flows Using Generalized Navier-Stokes Equations in MATLAB

This paper presents a numerical investigation into the application of fractional-order calculus to the modeling of turbulent fluid flows using generalized Navier-Stokes equations. Traditional Navier-Stokes equations are extended to incorporate Caputo fractional derivatives in the time domain, capturing memory effects inherent in turbulent flows. A simplified 1D time-fractional Burgers’ equation is used to demonstrate the method. The results showcase the impact of fractional order on velocity field evolution, providing a foundational framework for advanced 2D and 3D extensions.