On some properties of Lagrangian dispersion models with non-Gaussian noise

The properties of a stochastic model with non-Gaussian random noise describing turbulent dispersion have been investigated, with reference to its Mathematical structure and to its behaviour simulating the inertial subrange. The process is Markovian, mean-square continuous and with correlated increments. The model is influenced by the turbulence inhomogeneities also at the smallest scales, that is, it does not correctly simulate the existence of a well-developed inertial subrange. Some numerical computations have been performed confirming the theoretical results

Stability analysis of solid particle motion in rotational flows

A two-dimensional model of a rotational flow field is used to perform the stability analysis of solid particle motion. It results that the stagnation points are equilibrium points for the motion of particles and the stability analysis allows to estimate their role in the general features of particle motion and to identify different regimes of motion. Furthermore, the effects of Basset history force on the motion of particles lighter than the fluid (bubbles) are evaluated by means of a comparison with the analytical results found in the case of Stokes drag. Specifically, in the case of bubbles, the vortex centres are stable (attractive) points, so the motion is dominated by the stability properties of these points. A typical convergence time scale towards the vortex centre is defined and studied as a function of the Stokes number St and the density ratio γ. The convergence time scale shows a minimum (nearly, in the range 0.1 < St < 1), in the case either with or without the Basset term. In the considered range of parameters, the Basset force modifies the convergence time scale without altering the qualitative features of the particle trajectory. In particular, a systematic shift of the minimum convergence time scale toward the inviscid region is noted. For particles denser than the fluid, there are no stable points. In this case, the stability analysis is extended to the vortex vertices. It results that the qualitative features of motion depend on the stability of both the centres and the vertices of the vortices. In particular, the different regimes of motion (diffusive or ballistic) are related to the stability properties of the vortex vertices. The criterion found in this way is in agreement with the results of previous authors (see, e.g., Wang et al. (Phys. Fluids, 4 (1992) 1789))

A re-evaluation of surface layer turbulence from Antarctic data

A data set of velocity and temperature variances measured in the surface layer over a glacier in Antarctica is analysed in terms of the Monin-Obukhov Similarity Theory. The presence of surface inhomogeneities, flow unsteadiness, and other uncontrolled disturbances affects the shape of the distribution of normalised variances for intervals of the stability parameter. The modal value of the distribution, instead of the mean, is used to estimate the numerical coefficients of the similarity functions to minimize the influence of the (positive) outliers on the estimates. The overall agreement of the present results with previuos investigations is good, and also the spread of the numerical values noted by different authors is confirmed. In particular the investigation points out the need to use a similarity function for the temperature variance which diverges in near neutral conditions, as the heat flux goes to zero, and the occurrence of a large stability region where the variances of velocity and temperature are characterised by a behaviour almost independent of the momentum flux

Evaluation of the dispersion coefficient for numerical simulations of tropospheric transport

Data of velocity spectra in wave number and frequency space available in literature are analysed to estimate climatological values of the dissipation rate of kinetic energy ε. In the frame of Kolmogorov (1941) theory, the relationship between diffusion coefficient and spectral window is used to determine the diffusion coefficient as a function of resolved scale. To exploit frequency spectrum data with a limited knowledge of flow conditions, a hypothesis on the relationship between the Eulerian time scale and the sampling temporal window was formulated, and the implied empirical constant was determined. Using the obtained values and some recent similarity relationships for the boundary-layer, a parameterisation of ε was adopted to propose an expression of the horizontal dispersion coefficient for different heights and different scales, which is suitable for use in numerical models with special reference to climate applications

Modeling turbulence perturbation in a laboratory boundary layer flow over hills

A second-order closure was used to investigate the effect of a gentle slope hill on the second moments of velocity. An approximated equation system was solved in streamlines coordinates and the mean flow was obtained by means of a linearized model. Results are tested on a very rich data set of two experiments with different slopes

Investigations on convective boundary layer turbulence using SODAR data

Acoustic sounding (SODAR) data collected in convective conditions were analysed to estimate high order statistics of the vertical velocity in the lower half of the Convective Boundary Layer (CBL). Limitations of the instrumentation system were assessed and it turned out that spatial and temporal fi ltering have little effect on skewness and kurtosis, and do not prevent a reliable evaluation of these parameters, provided that a suffi ciently long time period is analysed. Vertical profi les of skewness are grouped into two broadly defi ned classes, one which increases almost linearly with height and the other which shows a constant-with-height behaviour. Both behaviours are shown to be consistent with different parameterisations used in literature. Kurtosis profi les are found to be fairly well described adopting a quadratic relationship between skewness and kurtosis, provided that the correct parameterisation of skewness is used

Longitudinal spectra of wind velocity in the atmospheric surface layer perturbed by a small topographic ridge

Turbulence measurements carried out in the near neutral surface layer are presented. The wind velocity components were measured with sonic anemometers at 2 and 10 m height. Three masts are considered, placed about 4 km upwind, on the top and about 6 km downwind of Inexpressible Island, a relief 300 m high and 1 km in cross-section. Spectral features are discussed in detail. Local equilibrium is found in the inertial subrange and in (at least in part of) the intermediate range, characterized by different slopes upwind and downwind (k−1 and k−5/3, respectively) for the components parallel to the terrain

Numerical vs. turbulent diffusion in geophysical flow modelling

Numerical advection schemes induce the spreading of passive tracers from localized sources. The effects of changing resolution and Courant number are investigated using theWAF advection scheme, which leads to a sub-diffusive process. The spreading rate from an instantaneous source is compared with the physical diffusion necessary to simulate unresolved turbulent motions. The time at which the physical diffusion process overpowers the numerical spreading is estimated, and is shown to reduce as the resolution increases, and to increase as the wind velocity increases

Nudging technique for scale bridging in air quality/climate atmospheric composition modelling

Abstract. The interaction between air quality and climate involves dynamical scales that cover a very wide range. Bridging these scales in numerical simulations is fundamental in studies devoted to megacity/hot-spot impacts on larger scales. A technique based on nudging is proposed as a bridging method that can couple different models at different scales. Here, nudging is used to force low resolution chemical composition models with a run of a high resolution model on a critical area. A one-year numerical experiment focused on the Po Valley hot spot is performed using the BOLCHEM model to asses the method. The results show that the model response is stable to perturbation induced by the nudging and that, taking the high resolution run as a reference, performances of the nudged run increase with respect to the non-forced run. The effect outside the forcing area depends on transport and is significant in a relevant number of events although it becomes weak on seasonal or yearly basis

Reliability of third-order moment parameterization for models of turbulent boundary layer over gentle topography

An analysis is made of the transport equation of Reynolds shear stress, written in a streamline coordinate system, starting from the fields of first- and secondorder moments of wind velocity, measured in a terrain-following system over gentle topography, in order to verify the usual parameterizations of third-order moments. The equation is split into two parts: the first contains the terms which can be calculated directly from measurements, the second involves the pressure-velocity correlation considering the terms of rapid distortion, curvature and return to isotropy and the transport of triple velocity-correlation modelled assuming a flux-gradient approximation. Moreover, the error estimates associated with both parts have been computed using a Monte Carlo technique which takes into account the experimental errors. This analysis is performed on wind tunnel data over a gently shaped two-dimensional valley and hill. The comparison between the measured and modelled parts is good near the surface, whereas, at higher levels, where the pertubations induced by the topography are significant, there are large zones generally characterized by streamlines with concave curvature in which the flux-gradient approximation used to compute the triple product correlation cannot be applied