On the wave structure of the wall region of a turbulent boundary layer

Abstract

Following the ideas suggested by Landahl (1967, 1975), some model calculations of the fluctuating velocity field in the wall region of a turbulent boundary layer have been carried out. It was assumed that the turbulent stresses are generated intermittently on small scales in time and space owing to bursting-type motions. The Reynolds-stress distribution during bursting periods and the mean velocity profile were assumed to be known, and the linear large-scale response to a random system of bursts was computed using an idealized model for the joint probability distribution in time and space of the occurrence of bursts. Computed energy spectra of the streamwise velocity fluctuations display scales in the spanwise and streamwise directions and time which are in good agreement with measurements by Morrison, Bullock & Kronauer (1971). However, the wavenumber band-widths of the computed spectra are narrower than those of the measured ones. This discrepancy is probably due to the crudeness of the model employed for the Reynolds stress during bursting.