Abstract
An analysis is presented of how a plane boundary affects the structure of turbulence in a sheared free stream. A uniform-shear boundary layer (USBL) is formulated with the slip velocity condition at the surface, and inhomogeneous rapid distortion theory is applied. The effects of ‘blocking’ by the surface on the turbulence structure in the USBL are compared with those in the shear-free boundary layer (SFBL).
Shear produces highly anisotropic eddies elongated in the flow direction. The distinctive peaks of the spanwise spectra of the streamwise velocity, Θ 11(κ 3; y), suggest the existence of the streaky structures in the flow. The mean streak spacing estimated from the energy spectra increases with the distance from the surface, in qualitative agreement with previous measurements and computations.
The vertical velocity variance, \( \overline {{v^2}} \), is reduced with shear at all heights, roughly in proportion to the reduction in the homogeneous value, but the shape of the profile remains unchanged only near the surface: \( \overline {{v^2}} /\overline {{v^{{2(H)}}}} \sim {y^{{2/3}}} \). The turbulent shear stress, - \( \overline {uv} \), increases with total shear at all distances from the boundary. Scaled with the homogeneous value, the profile of the shear stress does not vary with time. The universal profile near the surface is \( \overline {uv} /{\overline {uv}^{{(H)}}} \sim {y^{{2/3}}} \), similar to the vertical variance profile.
The streamwise integral length scales increase with shear, indicating elongation of the streamwise extent of eddies. At given total shear, the spanwise extent of the streaks determined from L zuu widens as the boundary is approached. The smallest of the integral scales, L (z)vv , is a measure of the dissipation scale, and decreases with shear in a self-similar way: L (z)vv ~ y.
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Lee, M.J., Hunt, J.C.R. (1991). The Structure of Sheared Turbulence Near a Plane Boundary. In: Durst, F., Launder, B.E., Reynolds, W.C., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76087-7_9
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DOI: https://doi.org/10.1007/978-3-642-76087-7_9
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