Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence

Abstract

The problem of closing the Reynolds-stress and dissipation-rate equations at low Reynolds numbers is considered, specific forms being suggested for the direct effects of viscosity on the various transport processes. By noting that the correlation coefficient$\overline{uv^2}/\overline{u^2}\overline{v^2} $is nearly constant over a considerable portion of the low-Reynolds-number region adjacent to a wall the closure is simplified to one requiring the solution of approximated transport equations for only the turbulent shear stress, the turbulent kinetic energy and the energy dissipation rate. Numerical solutions are presented for turbulent channel flow and sink flows at low Reynolds number as well as a case of a severely accelerated boundary layer in which the turbulent shear stress becomes negligible compared with the viscous stresses. Agreement with experiment is generally encouraging.