Turbulence eddy spectrum

Turbulent eddies larger than the cloud size, as such, tend to move the cloud as a whole and do not influence the internal concentration distribution. The mean concentration distribution is largely determined by turbulent motion of a scale comparable to the cloud size. These eddies tend to break up the cloud into smaller and smaller parts, so as to render turbulent motion on smaller and smaller scales effective in generating fluctuations of ever smaller scales, and so on. On the small-scale side of the spectrum, concentration fluctuations are homogenized by molecular diffusion. 

Since for all dispersion organs in the ranges which are important for the practice the gas dispersion occurs due to turbulence mechanisms it is to be expected that there is a relationship between the turbulence properties and the efficiency of gas dispersion. It has already been pointed out that efficient gas dispersion is only possible, if the microeddy size is smaller than de cind if the percentage of microturbulence is high enough. Therefore the power spectrum of turbulence should influence the efficiency of gas dispersion. Fig. 10 shows one-dimensional power spectra in stirred teink reactors of different sizes according to van der Molen and van Maanen (22). As usual, the energy content of turbulent eddies was plotted as a function of the wave number, K, which is inversely proportional to the diameter of the... 

The turbulent eddies that cause an odor plume to disperse occur simultaneously over a range of sizes in the atmosphere. Energy derived from the largest eddies is passed down into smaller and smaller eddies until it dissipates as heat. As pointed out by Slade (1968), Mason (1973), Aylor (1976) and Aylor et al. (1976) the dispersion of an instantaneous odor plume is driven by eddies that are about the same size as the plume. Eddies that are smaller than the plume redistribute the pheromone within the plume whereas the larger eddies cause the plume to meander downwind intact. At the small end of the spectrum there exists a lower eddy size limit below which molecular viscosity causes the eddies to break down and dissipates their energy as heat. Typically, the minimum eddy size is in the order of 1 mm. 

Eddy size in the inertial subrange of the turbulence energy spectrum (m)... 

If rjc is increased by adding high polymers, this may readily lead to turbulence depression. This is of special importance in the regime TI. It has been studied by Walstra, who showed that addition of polymers caused d to increase and ci (the spread in droplet size) to decrease. This would agree with the smallest eddies being removed from the eddy spectrum. 

In RANS-based simulations, the focus is on the average fluid flow as the complete spectrum of turbulent eddies is modeled and remains unresolved. When nevertheless the turbulent motion of the particles is of interest, this can only be estimated by invoking a stochastic tracking method mimicking the instantaneous turbulent velocity fluctuations. Various particle dispersion models are available, such as discrete random walk models (among which the eddy lifetime or eddy interaction model) and continuous random walk models usually based on the Langevin equation (see, e.g.. Decker and... 

Davies (Turbulence Phenomena, Academic, New York, 1972) presents a good discussion of the spectrum of eddy lengths for well-developed isotropic turbulence. The smallest eddies, usually called Kolmogorov eddies (Kolmogorov, Compt. Rend. Acad. Sci. URSS, 30, 301 32, 16 [1941]), have a characteristic velocity fluctuation given by... 

Flow in the atmospheric boundary layer is turbulent. Turbulence may be described as a random motion superposed on the mean flow. Many aspects of turbulent dispersion are reasonably well-described by a simple model in which turbulence is viewed as a spectrum of eddies of an extended range of length and time scales (Lumley and Panofsky 1964). 

Usually, however, the stresses are modeled with the help of a single turbulent viscosity coefficient that presumes isotropic turbulent transport. In the RANS-approach, a turbulent or eddy viscosity coefficient, vt, covers the momentum transport by the full spectrum of turbulent scales (eddies). Frisch (1995) recollects that as early as 1870 Boussinesq stressed turbulence greatly increases viscosity and proposed an expression for the eddy viscosity. The eventual set of equations runs as... 

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