Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer

Abstract

This paper is concerned with the effect of free-stream turbulence on the pretransitional flat-plate boundary layer. It is assumed that either the turbulent Reynolds number or the downstream distance (or both) is small enough that the flow can be linearized. The dominant disturbances in the boundary layer, which are of the Klebanoff type, are governed by the linearized unsteady boundary-region equations, i.e. the linearized Navier–Stokes equations with the streamwise derivatives neglected in the viscous and pressure-gradient terms. The turbulence is represented as a superposition of vortical free-stream Fourier modes and the corresponding Fourier component solutions to the boundary-region equations are obtained numerically. The results are then superposed to compute the root mean square of the fluctuating streamwise velocity in the boundary layer produced by the actual free-stream turbulence. It is found that the disturbances computed with isotropic free-stream turbulence do not reach the levels measured in experiments. However, good quantitative agreement is obtained with the relatively low turbulent Reynolds number data of Kendall when the measured strong anisotropy of the low-frequency portion of his spectrum is accounted for. Data at higher turbulent Reynolds numbers are affected by nonlinearity, which manifests itself through the generation of small spanwise length scales. We attempt to model this within the context of the linear theory by choosing a free-stream spectrum whose energy is concentrated at larger transverse wavenumbers and achieve very good agreement with the data. The results suggest that even small deviations from pure isotropy can be an important factor in explaining the large amplitudes of the Klebanoff modes in the pre-transitional boundary layer, and also point to the importance of nonlinear effects. We discuss some additional effects that may need to be accounted for in order to obtain a complete description of the Klebanoff modes.