Reverse transition in a two dimensional boundary layer flow

Abstract

Experiments on reverse transition were conducted in two-dimensional accelerated incompressible turbulent boundary layers. Mean velocity profiles, longitudinal velocity fluctuations u′u'u′ (i.e., u′2‾\overline{u'^2}u′2), and the wall shear stress were measured. The results show that reverse transition in a two-dimensional boundary layer occurs in three consecutive stages: (i) Reduction in heat transfer rate near the wall (ii) Breakdown of the law of the wall (iii) Decay of turbulent intensity The mean velocity profiles show that the profiles near the wall adjust to laminar condition in the same region where the turbulent intensity begins to decay. The mean velocity profiles in the outer region take a longer time to adjust. The decay of turbulent intensity occurred when the momentum thickness Reynolds number RθR_\thetaRθ​ decreased roughly below 400 in all the experiments conducted, indicating that there is a critical Reynolds number Rθ=300±100R_\theta = 300 \pm 100Rθ​=300±100 for reverse transition in a two-dimensional boundary layer flow. The u′2u'^2u′2 profiles exhibit near similarity in the decay region. Exponential decay was noticed when u′2/U2u'^2 / U^2u′2/U2 was plotted with respect to a suitable time coordinate. During the reverse transition process, increase in shape parameter HHH is accompanied by a decrease in CfC_fCf​. The location of the minimum value of HHH coincides with that of the breakdown of the law of the wall, and this breakdown occurs when Λ=dU∗/dxU∗\Lambda = \frac{dU^*/dx}{U^*}Λ=U∗dU∗/dx​ (where U∗U^*U∗ is the friction velocity) equals -0.0245, as predicted by Patel and Head