Features of surface physical quantities and temporal-spatial evolution of wall-normal enstrophy flux in wall-bounded flows

This paper presents a concise derivation of the temporal-spatial evolution equation of the wall-normal enstrophy flux on a no-slip flat wall. Each contribution to the evolution is explicitly expressed using the two fundamental surface quantities: skin friction (or equivalently surface vorticity) and surface pressure which are coupled through the boundary enstrophy flux (BEF). The newly derived relation is then used to explore, in a preliminary manner, the physical features of surface quantities and their dynamical roles in wall-bounded laminar and turbulent flows. It is confirmed that the BEF usually changes its sign near the separation and attachment lines in the skin friction field. For the simulated incompressible turbulent channel flow at Re-tau = 180, violent variations of different terms in the derived formulation are observed in the regions below the strong wall-normal velocity events (SWNVEs) when compared to other common regions. Near the SWNVEs, the evolution of the wall-normal enstrophy flux is found to be dominated by the wall-normal diffusion of the vortex stretching term which is relatively weak or negligible for laminar flows. Combined with our previous research results, it is conjectured that the strong interaction between the quasi-streamwise vortex and the channel wall intensifies the temporal-spatial evolution of the wall-normal enstrophy flux on the wall, which accounts for the highly intermittent feature of the viscous sublayer.