The idea of Fourier-Averaged-Navier-Stokes formulations for turbulent flow modeling

Periodic or quasi-periodic flow behaviour is commonly observed in many turbulent flows in engineering problems. The power spectra of periodic fluid motion often have distinct peaks in frequency space, suggesting that large-scale, energetic and predictable motions are present in the flow. Conventional Reynolds-Averaged-Navier-Stokes (RANS) formulations commonly fail to accurately model these inhomogenous and anisotropic structures. Eddy-viscosity models assume that all variations are isotropic and uncorrelated in space and time. Therefore, a formulation for turbulence models that is inherently capable of capturing these periodic variations is desirable. By deriving transport equations for the Fourier coefficients of a periodic flow, we are proposing a class of models that would directly capture periodic flow behaviour. The intention of this modeling paradigm is to simplify and limit the number of computational resources needed to capture large, anisotropic, regularly occurring structures, while increasing the accuracy of turbulence modeling. The newly proposed Fourier-Averaged-Navier-Stokes (FANS) formulations are tested against Direct Numerical Simulation results for 2D wake of a square cylinder, Couette flow and Hagen-Poiseuille flow with an oscillating pressure gradient.