Velocity,temperature, and Reynolds-stress scaling in the wall region of turbulent boundary layer on a permeable surface

A finite total number of flow parameters in the wall region of a turbulent boundary layer points to universal behavior of turbulent shear stress as a function of mean-velocity gradient and turbulent heat flux as a function of both mean-velocity and mean-temperature gradients. Combined with dimensional arguments, this fact is used to reduce the momentum and heat equations to first-order ordinary differential equations for temperature and velocity profiles amenable to general analysis. Scaling laws for velocity and temperature in boundary layer flows with transpiration are obtained as generalizations of well-known logarithmic laws. Scaling relations are also established for shear stress and rms transverse velocity fluctuation. The proposed method has substantial advantages as compared to the classical approach (which does not rely on fluid-dynamics equations 1–3]). It can be applied to establish scaling laws for a broader class of near-wall turbulence problems without invoking closure hypotheses.