Eddy diffusion coefficients horizontal

The second stage realizes a two-step procedure that re-calculates the ozone concentration over the whole space S = (tp, A, z) (, A)e l 0atmospheric boundary layer (zH 70 km), whose consideration is important in estimating the state of the regional ozonosphere. These two steps correspond to the vertical and horizontal constituents of atmospheric motion. This division is made for convenience, so that the user of the expert system can choose a synoptic scenario. According to the available estimates (Karol, 2000 Kraabol et al., 2000 Meijer and Velthoven, 1997), the processes involved in vertical mixing prevail in the dynamics of ozone concentration. It is here that, due to uncertain estimates of Dz, there are serious errors in model calculations. Therefore the units CCAB, MFDO, and MPTO (see Table 4.9) provide the user with the principal possibility to choose various approximations of the vertical profile of the eddy diffusion coefficient (Dz). 

Figure 6.16 Solutions to a horizontal ventilation model of denitrification for waters of the eastern tropical North Pacific for d NOa vs J, the fraction of nitrate remaining, i.e., the measured nitrate minus the nitrate deficit. Nitrate deficit was calculated as NOa deficit) = M.8 x PO4—NO3, where NO3 and PO4 are the measured concentrations.The two equations describing the steady-state nitrate isotope distrihution are 0[ NO3]/0t—J[ N03] + 0 [ NO3]/0a and0[ NO3]/0t—aQ/[ N03] + ri0 pNO3]/0x where is the eddy diffusion coefficient in the x direction, J is the denitrification rate, a is the fraction factor, and Q is a N N ratio that makes the system non-linear. (See Voss et at, 2001 for solution details). Solutions for three different values of are given ( = [l-0(] x 1000).

Many of the questions about the origin of the suboxic zone and the redox reaction zones would be easier to answer if we could calculate vertical fluxes. Unfortunately, neither the mechanism nor the rate of vertical transport are well understood. Estimates of the vertical advection velocity (w) and eddy diffusion coefficients (K.) are available in the literature (e.g., 5, 32, 39, 40), but they are probably not realistic, considering the importance of horizontal ventilation discussed earlier. 

It turns out that turbulent diffusion can be described with Fick s laws of diffusion that were introduced in the previous section, except that the molecular diffusion coefficient is to be replaced by an eddy or turbulent diffusivity E. In contrast to molecular diffusivities, eddy dififusivities are dependent only on the phase motion and are thus identical for the transport of different chemicals and even for the transport of heat. What part of the movement of a turbulent fluid is considered to contribute to mean advective motion and what is random fluctuation (and therefore interpreted as turbulent diffusion) depends on the spatial and temporal scale of the system under investigation. This implies that eddy diffusion coefficients are scale dependent, increasing with system size. Eddy diffusivities in the ocean and atmosphere are typically anisotropic, having much large values in the horizontal than in the vertical dimension. One reason is that the horizontal extension of these spheres is much larger than their vertical extension, which is limited to approximately 10 km. The density stratification of large water bodies further limits turbulence in the vertical dimension, as does a temperature inversion in the atmosphere. Eddy diffusivities in water bodies and the atmosphere can be empirically determined with the help of tracer compounds. These are naturally occurring or deliberately released compounds with well-estabhshed sources and sinks. Their concentrations are easily measured so that their dispersion can be observed readily. 

The Gaussian expressions are not expected to be valid descriptions of turbulent diffusion close to the surface because of spatial inhomogeneities in the mean wind and the turbulence. To deal with diffusion in layers near the surface, recourse is generally made to the atmospheric diffusion equation, in which, as we have noted, the key problem is proper specification of the spatial dependence of the mean velocity and eddy diffusivities. Under steady-state conditions, turbulent diffusion in the direction of the mean wind is usually neglected (the slender plume approximation), and if the wind direction coincides with the jc axis, then =0. Thus it is necessary to specify only the lateral, Ky, and vertical, A --, coefficients. It is generally assumed that horizontal homogeneity exists so that u and A are independent of y. Hence (18.52) becomes... 

In lateral mixing, the horizontal diffusion written in Equation 16 is subjected to the eddy kinematic viscosity. Conventionally, the vertical diffusion coefficient v, which is related to the vertical velocity distribution is applied by simply multiplying a constant even in horizontal mixing as v,, and furthermore, the value given for flow on the area without vegetation, as follows ... 

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