Navier–Stokes equations in Fractional Time and Multi‑Fractional Space
- 1Hydraulics Laboratory, Department of Civil Engineering, Middle East Technical University, Ankara, 06800, Turkiye
- 2Hydrologic Research Laboratory and J. Amorocho Hydraulics Laboratory, Department of Civil and Environmental Engineering, University of California, Davis, CA, 95616, USA
This presentation focuses on the governing equations of incompressible and compressible flow in fractional time and multi-fractional space as developed recently by the authors in DOI: 10.1038/s41598-022-20911-3. Mathematical differentiation has found many applications in real-life problems in the last two decades, before which it was mainly utilized by mathematicians and theoretical physicists. The proposed fractional governing equations for fluid flow may be interpreted as the general forms of the classical Navier–Stokes equations; as they reduce to the classical ones when integer values are replaced with their fractional powers in space and time. Due to their nonlocal structure, proposed governing equations in factional time/space can reflect the initial conditions for long times, and the boundary conditions for long distances. Results of numerical applications are presented for flow due to a wall suddenly set into motion. It is found that the proposed equations have the potential to model both sub-diffusive and super-diffusive flow cases.
How to cite: Ercan, A. and Kavvas, M. L.: Navier–Stokes equations in Fractional Time and Multi‑Fractional Space, EGU General Assembly 2023, Vienna, Austria, 24–28 Apr 2023, EGU23-6138, https://doi.org/10.5194/egusphere-egu23-6138, 2023.
