Formation of longitudinal vortices in the sublayer due to boundary-layer turbulence

Abstract

A number of experiments have indicated that the behaviour of longitudinal vortices in the sublayer of a turbulent boundary layer has a significant effect on the equilibrium of the whole flow field, but the formation of such longitudinal vortices remains unclarified. In the present paper, paying attention to the random turbulent motions normal to the wall which induce a dynamic instability causing the generation of the regular longitudinal vortices, a turbulence model is introduced to analyse the generation of the longitudinal vortices in the sublayer of a turbulent boundary layer.By integrating the results of the analysis with previous experimental results for the behaviour of developing longitudinal vortices, a feedback loop linking regular and irregular motions in the turbulent boundary layer is presented.It has been experimentally confirmed that even at low Reynolds number, regular longitudinal vortices are formed when a disturbance is applied to a boundary layer. As for the stability region described in terms of the intensity of the disturbance and the wavenumber of the longitudinal vortices, no conflict between analysis and experiment is observed. Using the thermodynamic argument of irreversible processes the formation of longitudinal vortices close to the wall by the turbulence in the boundary layer is shown to be physically reasonable.