Secondary Flow near an Undulatory Surface Induced by Wall Blocking Effect

Secondary mean motions of Prandtl's second kind near an undulatory surface are explained in terms of the turbulent blocking effect and kinematic boundary conditions at the surface, and the order of magnitude is estimated. The isotropic turbulence is distorted by the undulatory surface with a low slope h/λ, where λ is the wavelength and h is the amplitude. The prime mechanism for generating the mean flow is that the far-field isotropic turbulence is distorted by the nonlocal blocking effect of the surface to become the anisotropic axisymmetric turbulence near the surface with a principal axis that is not aligned with the local curvature (slope) of the undulation. Then, the local analysis can be applied and the mechanism is similar to that of the mean flow generation by the impingement of homogeneous axisymmetric turbulence over a planar surface, i.e. the gradient of the Reynolds stress caused by the turbulent blocking effect generates the mean motion. The results from this simple analysis are consistent with the previous exact analysis, in which the effects of the curvature are taken into account. The results also qualitatively agree with the flow visualization over an undulatory surface in a mixing box.