Secondary flow near an undulatory surface induced by wall blocking effect

Prandtl's secondary mean motions of the second kind near an undulating surface were explained in terms of turbulent blocking effect and kinematic boundary conditions at the surface, and its order of magnitude was estimated. Isotropic turbulence is distorted by the undulating surface of wavelength λ and amplitude h with a low slope, so that h « λ. The prime mechanism for generating the mean flow is that the far-field Isotropic turbulence is distorted by the non-local blocking effect of the surface to become anisotropic axisymmetric turbulence near the surface with principal axis that is not aligned with the local curvature of the undulation. Then the local analysis can be applied and the mechanism is similar to the mean flow generation mechanism for homogeneous axisymmetric turbulence over a planer surface, i.e. gradients of the Reynolds stress caused by the turbulent blocking effect generate the mean motions. The results from this simple analysis are consistent with previous exact analysis in which the effects of curvature are strictly taken into account. The results also qualitatively agree with flow visualization over an undulating surface in a mixing-box.

The dynamic effect of a piled-foundation building on an incident vibration field from an underground railway tunnel

This paper presents a three-dimensional comprehensive model for the calculation of vibration in a building based on pile-foundation due to moving trains in a nearby underground tunnel. The model calculates the Power Spectral Density (PSD) of the building's responses due to trains moving on floating-slab tracks with random roughness. The tunnel and its surrounding soil are modelled as a cylindrical shell embedded in half-space using the well-known PiP model. The building and its piles are modelled as a 2D frame using the dynamic stiffness matrix. Coupling between the foundation and the ground is performed using the theory of joining subsystems in the frequency domain. The latter requires calculations of transfer functions of a half-space model. A convenient choice based on the thin-layer method is selected in this work for the calculations of responses in a half-space due to circular strip loadings. The coupling considers the influence of the building's dynamics on the incident wave field from the tunnel, but ignores any reflections of building's waves from the tunnel. The derivation made in the paper shows that the incident vibration field at the building's foundation gets modified by a term reflecting the coupling and the dynamics of the building and its foundation. The comparisons presented in the paper show that the dynamics of the building and its foundation significantly change the incident vibration field from the tunnel and they can lead to loss of accuracy of predictions if not considered in the calculation.