This study examines the statistical predictability of local wind conditions in a real urban environment under realistic atmospheric boundary layer conditions by means of Large-Eddy Simulation (LES). The computational domain features a highly detailed description of a densely built coastal downtown area, which includes vegetation. A multi-scale nested LES modelling approach is utilized to achieve a setup where a fully developed boundary layer flow, which is also allowed to form and evolve very large-scale turbulent motions, becomes incident with the urban surface. Under these nonideal conditions, the local scale predictability and result sensitivity to central modelling choices are scrutinized via comparative techniques. Joint time–frequency analysis with wavelets is exploited to aid targeted filtering of the problematic large-scale motions, while concepts of information entropy and divergence are exploited to perform a deep probing comparison of local urban canopy turbulence signals. The study demonstrates the utility of wavelet analysis and information theory in urban turbulence research while emphasizing the importance of grid resolution when local scale predictability, particularly close to the pedestrian level, is sought. In densely built urban environments, the level of detail of vegetation drag modelling description is deemed most significant in the immediate vicinity of the trees.

The Maxey-Riley equation and its simplified versions represent the most widespread tool to investigate dynamics and dispersion of inertial small particles in turbulent flows. The numerical solution of such models is often very challenging, and some of their terms, such as the molecular diffusivity or the Basset history force, are often neglected to reduce the complexity upon suitable approximations. Here, we propose exact results with regard to the rate of transport on large time scales in random shear flows. These can be expediently used as a benchmark to develop and assess algorithms when solving this class of stochastic integrodifferential problems on large time scales.

One of the cornerstones of turbulent dispersion is the celebrated Taylor's formula. This formula expresses the rate of transport (i.e., the eddy diffusivity) of a tracer as a time integral of the fluid velocity autocorrelation function evaluated along the fluid particle trajectories. Here, we review the hypotheses which permit us to extend Taylor's formula to particles of any inertia. The hypotheses are independent of the details of the inertial particle model. We also show by explicit calculation that the hypotheses encompass cases when memory terms such as Basset's and Faxén's corrections are taken into account in the modeling of inertial particle dynamics.

One of the principal tools to tackle turbulent dispersion problems is the celebrated Taylor-Green-Kubo formula. By virtue of this formula, the rate of transport (i.e. the eddy diffusivity) of a tracer can be evaluated as the time integral of the fluid velocity auto-correlation function along the fluid trajectories. Here, we show that Taylor-Green-Kubo formula can be generalized to include external forces and other terms describing the inertia of the particles. This result therefore applies to determine the eddy diffusivity of inertial particles of any inertia. Afterwards, we will show a simple model where generalized Taylor-Green-Kubo formula yields the exact expression for the eddy diffusivity of inertial particles, regardless of their density and at any Stokes number. These general and exact results may open new scenarios in the field of turbulent dispersion of inertial particles, and closure modeling in the sea and in the atmosphere.