Influences of boundary layer scale separation on the vorticity transport contribution to turbulent inertia

Abstract

In the flows of interest, the mean effect of turbulent inertia can be expressed as the difference of two velocity vorticity correlations. This difference must be sufficiently non-zero if turbulent inertia is to have a net influence on the mean dynamics. One of the correlations is physically related to change of scale effects, while the other is related to advective vorticity transport. The vorticity transport mechanism is studied under the influence of increasing scale separation. Through the use of both laboratory and field data, the scale separation between the fluctuations of wall-normal velocity, v, and spanwise vorticity ωz, are shown to increase with distance from the wall and Reynolds number. Time-delayed correlations between these quantities reveal that only slight variations in their average phase would cause significant variations in the mean transport of momentum. Spectra are used to explore previous observations of scale selection between v and ωz. The wavelengths corresponding to the peaks in the v and ωz spectra are used to describe scale separation effects. The variations in the wavelength ratios are shown to correlate with the scaling properties that follow from the magnitude ordering of terms in the mean momentum equation. Scale separation is seen to result from two mechanisms: spatial confinement and spatial dispersion. The influence of vorticity stretching apparently generates motions bearing concentrated vorticity that, with increasing Reynolds number, are confined to a smaller fraction of the region where the mean viscous force is of leading order. Where the mean dynamics are inertially dominated, the characteristic vortical motions are advectively dispersed. The width of this domain asymptotically grows like the boundary layer thickness. In the region y+ ≲ 40, the streamwise correlation lengths of v and ωz are shown to scale with the square root of the Reynolds number. This is consistent with inner-outer interactions suggested by the scaling structure of the mean momentum equation.