Eddy coefficient

Whereas the kinematic viscosity fx/p, the thermal diffusivity k/Cpp, and the diffusivity D are physical properties of the system and can therefore be taken as constant provided that physical conditions do not vary appreciably, the eddy coefficients E, Eh, and ED will be affected by the flow pattern and will vary throughout the fluid. Each of the eddy coefficients is proportional to the square of the mixing length. The mixing length will ... 

The equation of motion and the equation of energy balance can also be time averaged according to the procedure indicated above (SI, pp. 336 et seq. G7, pp. 191 et seq. pp. 646 et seq.). In this averaging process there arises in the equation of motion an additional component to the stress tensor t(,) which may be written formally in terms of a turbulent (eddy) coefficient of viscosity m(I) and in the equation of energy balance there appears an additional contribution to the energy flux q(1), which may be written formally in terms of the turbulent (eddy) coefficient of thermal conductivity Hence for an incompressible fluid, the x components of the fluxes may be written... 

Deardorff JW (1971) On the magnitude of the subgrid scale eddy coefficient. J Comput Phys 7(l) 120-l-33... 

Here, H = 8500 m denotes the atmospheric scale height. Radon obviously would be a good tracer for turbulent mixing in the troposphere. Unfortunately, it is hard to measure. It should be noted that the assumption of a constant Kz in the troposphere is a reasonable approximation only for the region outside the planetary boundary layer (zs=2km). The air motions close to the earth surface are greatly influenced by friction, which causes the eddy coefficients to decrease from their values in the free troposphere. 

The evaluation of these statistical second moments is the goal of turbulence models. These models fall into two categories. First are models in which the turbulent fluxes are expressed in the same functional form as their laminar counterparts, but in which the molecular properties of viscosity, thermal conductivity, and diffusion coefficient are supplemented by corresponding eddy viscosities, conductivities, and diffusivities. The primary distinction is the recognition that the eddy coefficients are properties of the turbulent flow field, not the... 

Once a model has been selected, an additional conservation or continuity equation Is required to describe the transient species of Interest. The eddy coefficients that govern the transport of the transient have been taken to be the same as those for heat transport [see e.g., ( ]. Thus, the temporal development of the transient can be modeled along with the development and diurnal variation of the stability of the water column. In this manner, the effects of wlnd-stlrrlng and surface heat flux as well as of photochemical processes on the vertical profile of a transient can be Investigated. 

K is a parameter characterizing the atmospheric and topological conditions in the surroundings of the point of release, the eddy coefficient in m s ... 

The K-model of Eq. (10.81) is a substantial simplihcation, because it is based on the assumption that the eddy coefficient and the wind speeds are constants. In addition, many of the parameters of influence on atmospheric dispersion presented above cannot be accounted for. This motivated numerous further developments. If the following relationship between the eddy coefficient an the atmospheric standard deviation is used... 

The cr-values are the standard deviations of the concentration in the direction of the wind, at a right angle from the wind direction and vertically upwards. They can easier be determined experimentally than the eddy coefficient K. The standard deviations depend on the atmospheric conditions and the distance from the source in the direction of the wind. In [26] relationships are given for them which depend on the weather condition (stable, neutral, unstable), the velocity of the wind and the surface roughness Zq (vid. Table 10.5). Separate values for and are provided for Cy the same value as for is used. For distances < 100 m the standard deviations are not verified. That is why results in that range have to be treated with caution. The integration of further factors of influence in the dispersion process is described in [26]. 

---