Near-wall flow structures and related surface quantities in wall-bounded turbulence

Abstract

By applying the Taylor-series expansion solution of the Navier–Stokes equations, an analysis is given to elucidate the relationships between near-wall flow structures and the fundamental surface quantities (skin friction and surface pressure). The derived results are used to understand the physical features of near-wall flow structures around a typical strong wall-normal velocity event (SWNVE) in a turbulent channel flow based on the direct numerical simulation data at $R{e}_{\tau }=180$ . The simulation is carefully done using a multiple-relaxation-time lattice Boltzmann method combined with an improved on-wall bounce-back implementation. It is found that both the skin friction divergence and the Laplacian of surface pressure have good correspondence with sweep and ejection motions induced by the quasi-streamwise vortex above the viscous sublayer. Interestingly, the surface pressure variation induced by a quasi-streamwise vortex tends to attenuate the wall-normal velocity magnitude in both the sweep and ejection sides through the Laplacian of surface pressure. Similar physical effects of surface-pressure-related terms are also observed for the near-wall Reynolds stress. The concentrated enstrophy and dissipation are associated with the SWNVE and high skin friction magnitude. It is found that the SWNVE is dynamically important in generating the boundary enstrophy flux, greatly enhancing the intermittency of turbulence inside the viscous sublayer. In addition, by applying the methods of differential geometry, the near-wall Taylor-series expansions are generalized for a stationary curved surface in a general curvilinear coordinate system. The generalized results could be useful in evaluating the curvature effect in the near-wall region for complex flows.