Numerical simulation of flow over urban-like topographies and evaluation of turbulence temporal attributes

We have used large-eddy simulation with an immersed boundary method to study turbulent flows over distributions of uniform height, staggered cubes. The computational domains were designed such that both the roughness sublayer and a region of the inertial layer are resolved. With this, we record vertical profiles of time series of fluctuating streamwise and vertical velocity at different locations throughout the domain. Contour images of these fluctuating quantities shown relative to elevation and time are studied; contour images of Reynolds shear stresses owing to ‘sweeps’ and ‘ejections’ are also studied. These images show that periods of momentum excess (deficit) in the inertial-layer precede excitation (subdual) of cube-scale coherent vortices in the roughness sublayer. We compute this time lag (termed advective lag) and demonstrate that it scales linearly with wall-normal elevation. The advective lag is attributed to coherent, low- and high-momentum regions in the aloft inertial layer. Vortex identification is used to illustrate the presence of hairpin packets encapsulating low-momentum regions. Based on this, the reported inclination angle associated with hairpin packets is used to guide the development of a model for prediction of advective lag with height. The model captures the advective lag profiles reasonably well. In the interest of generality, additional cases of flow over homogeneous roughness (aerodynamic drag imposed with the equilibrium logarithmic law) are considered. We again observe that advective lag scales linearly with wall-normal elevation. Advective lag predictions from the aforementioned model agree well with results for these cases.