Asymptotic behaviour at the wall in compressible turbulent channels

The asymptotic behaviour of Reynolds stresses close to walls is well established in incompressible flows owing to the constraint imposed by the solenoidal nature of the velocity field. For compressible flows, thus, one may expect a different asymptotic behaviour, which has indeed been noted in the literature. However, the transition from incompressible to compressible scaling, as well as the limiting behaviour for the latter, is largely unknown. Thus, we investigate the effects of compressibility on the near-wall, asymptotic behaviour of turbulent fluxes using a large direct numerical simulation (DNS) database of turbulent channel flow at higher than usual wall-normal resolutions. We vary the Mach number at a constant friction Reynolds number to directly assess compressibility effects. We observe that the near-wall asymptotic behaviour for compressible turbulent flow is different from the corresponding incompressible flow even if the mean density variations are taken into account and semi-local scalings are used. For Mach numbers near the incompressible regimes, the near-wall asymptotic behaviour follows the well-known theoretical behaviour. When the Mach number is increased, turbulent fluxes containing wall-normal components show a decrease in the slope owing to increased dilatation effects. We observe that $R_{vv}$ approaches its high-Mach-number asymptote at a lower Mach number than that required for the other fluxes. We also introduce a transition distance from the wall at which turbulent fluxes exhibit a change in scaling exponents. Implications for wall models are briefly presented.

Modeling and simulation of air pollutant distribution in street canyon area with Skytrain stations

This paper focuses on effects of the wind flow velocity on the air flow and the air pollution dispersion in a street canyon with Skytrain. The governing equations of air pollutants and air flow in this study area are the convection–diffusion equations of species concentration and the Reynolds-averaged Navier–Stokes (RANS) equations of compressible turbulent flow, respectively. Finite element method is utilized for the solution of the problem. To investigate the impact of the air flow on the pattern of air pollution dispersion, three speeds of inlet wind in three different blowing directions are chosen. The results illustrate that our model can depict the airflows and dispersion patterns for different wind conditions.