Direct Numerical Simulation of Fully Developed Turbulent Channel Flow Based on the Corrected Navier-Stokes Equations

Abstract

Direct numerical simulations (DNS) of fully developed turbulent channel flows at Re_tau = 550 were performed to investigate the corrected Navier-Stokes (CNS) equations. Grounded in the fluid kinematics of Rortex, the CNS abandons the Stokes' isotropic hypothesis and applies the shearing-only constitutive relation by explicitly eliminating the controversial stretching terms in the stress tensor. Comparisons with the DNS data from the traditional Navier-Stokes (TNS) suggest that the CNS inherently rectifies the near-wall momentum transport. The removal of stretching-induced dissipation shifts the inner- and buffer-layer boundaries towards the wall and effectively suppresses the overshoot in the mean velocity profile in TNS. The turbulence statistics demonstrate a multiscale kinetic energy redistribution that intensifies the near-wall production-dissipation cycle. Furthermore, the topological delineation of instantaneous coherent structures, namely the discovery and definition of rotational/non-rotational interface (RNRI) via the velocity gradient tensor (VGT) discriminant (Delta = 0), confirms that the CNS is capable of capturing the highly complex and interwoven vortical structures. Ultimately, the spectral proper orthogonal decomposition (SPOD) unveils and elucidates that the shearing-only mechanisms intrinsically modulate the spatiotemporal energy cascade, promoting denser and more inclined vortices while enhancing turbulence intermittency by fragmenting the coherent packets. Overall, by isolating and detecting the shearing-only mechanism with physics purity, the DNS based on the CNS provides a more refined perception of the intrinsic dynamics of wall-bounded turbulence, offering a more physical soundness model to capture the interactions among the multiscale coherent structures and the improved capability in predicting the wall-bounded turbulence.