Eddy diffusion coefficients profile

Figure 5.7 gives some relationships for eddy diffusion coefficient profiles under different conditions that will be handy in applications of turbulent diffusive transport. 

Figure 5.7. Profiles of eddy diffusion coefficient for various types of applications.

We will apply equation (5.20) to solve for the concentration profile of suspended sediment in a river, with some simplifying assumptions. Suspended sediment is generally considered similar to a solute, in that it is a scalar quantity in equation (5.20), except that it has a settling velocity. We will also change our notation, in that the bars over the temporal mean values will be dropped. This is a common protocol in turbulent transport and will be followed here for conformity. Thus, if an eddy diffusion coefficient, e, is in the transport equation,... 

Above 120 km. the atmosphere is essentially in diffusive equilibrium (34). For the altitude interval between 80 and 120 km. Colegrove et al. (6) estimated an average vertical eddy diffusion coefficient of 4 X 106 cm.2 sec."1 by a careful evaluation of the 0/02 concentration ratio profile over this altitude interval. Using their eddy diffusion coefficient and following the procedure of Kellogg (22) it is estimated that molecular... 

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). 

It is not to be expected that the straight-line Equation 21 would apply to the thermocline layers of other lakes. Both N and K were calculated from temperature profiles the shape of which depends in a complex manner on the climate of the area, thermal regime, depth, and volume of the lake. It seems, however, that by arguments presented earlier in this section, an inverse relationship between the stability frequency and eddy diffusion coefficient would, in general, hold in the pycnocline layers of lakes. If such a relationship is established, it would be possible to obtain estimates of K from the values of the stability frequency N, which are much easier to compute. 

The distribution of a number of dissolved species (02, C-14, Ra-226, salinity) in the Central Pacific water column, at depths between 1 and 4 km, has been shown (11) to be consistent with a steady-state model of the water column in which the concentration-depth profiles are stationary and the concentrations at the boundaries 1 and 4 km are stipulated at their present values. The physical model of the water column is based on two transport mechanisms vertical eddy diffusion (eddy diffusion coefficient K — 1.3 cm2 sec"1) and upwelling of deep water (advection velocity U = 1.4 X 10 5 cm sec"1, or approximately 1 cm per day) (11). 

Computed as explained in the text using initial stationary concentration (Ct 0) given by profile 1 in Figure 12 and new steady-state given by profile 2. Time to steady-state shown for different values of eddy diffusion coefficient (K) and advective velocity (U). Time to steady-state defined as the time when the oxygen concentration has attained 95% of the concentration difference between the new and initial steady-state profiles C — Ct 0 = 0.95(Ct x — Ct= 0). 

The profiles of the vertical eddy diffusion coefficients for different stability categories were estimated using the correlations presented in Pasquill (1974). 

Axial mixing effects commonly are taken into account by using a diffusion analogy and an axial mixing coefficient E, also called the longitudinal dispersion coefficient or eddy diffusivity, to account for the spreading of the concentration profiles. At steady state, the conservation equation has the general form... 

Different profiles have been proposed using first order closure models which specify a simple eddy diffusivity, K, and a drag coefficient, Cd, to describe that portion of the mean wind profile which exists beneath the forest ceiling for constant foliage distribution ... 

The axial dispersion coefficient is determined from the concentration profile of a non-penetrating tracer (Tl). A reasonable approximation for its velocity dependence goes back to van Deemter et al. (1956). The axial dispersion coefficient is the sum of the contributions of eddy diffusion and molecular diffusion (Chapter 2.3.4) ... 

In chromatographic systems with relatively large effective mass transfer coefficients kefy (i.e. low mass transfer resistance) the influence of axial dispersion, especially eddy diffusion, dominates the concentration profile. HETPj and Nj is then independent of the interstitial velocity. 

It follows from equation [5.1] that the dry deposition of trace gases (vs = 0) may be calculated by measuring their concentration gradient and the eddy (or molecular) diffusion coefficient This procedure, called the gradient method, is widely used to determine the dTy deposition velocity. Thus, Atkins and Garland (1974) studied the dry deposition of S02 in this way. They determined the diffusion coefficient from wind profile observations. Using equation [5.3] these authors were able to calculate... 

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