Atmospheric mixing eddy diffusion

If the lake is stratified, vertical transport is commonly the time-limiting step for complete mixing. This was the reason for applying the two-box model to the case of PCE in Greifensee (Illustrative Example 21.5). Now we go one step further. We consider a vertical water column of mean depth h with a constant vertical eddy diffusion coefficient Ez. The flux Fa/VJ of PCE escaping to the atmosphere is given by Eq. 20-la ... 

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). 

Clark (55) reviewed the laboratory data and concluded that there was no homogeneous gas phase process capable of accounting for the CO and O2 mixing ratio limits at any altitude. More recently, McElroy and McConnell (93) have concluded that vertical transport with high eddy diffusion coefficients may explain the mixing ratios in the Mars upper atmosphere. The same mechanism cannot, however, account for the lower atmosphere. 

As indicated earlier, vertical exchanges associated with turbulent mixing such as that caused by gravity wave breaking below the homopause are often represented as eddy diffusion. When expressed in terms of number density in an atmosphere following hydrostatic equilibrium conditions, the effective vertical eddy diffusion velocity becomes... 

As indicated, the flux may be expressed either in units of molecules/m2 s or in units of kg/m2 s. Here, p and n are the density and number density of air, respectively, and K is called the eddy diffusion coefficient. This quantity must be treated as a tensor because atmospheric diffusion is highly anisotropic due to gravitational constraints on the vertical motion and large-scale variations in the turbulence field. Eddy diffusivity is a property of the flowing medium and not specific to the tracer. Contrary to molecular diffusion, the gradient is applied to the mixing ratio and not to number density, and the eddy diffusion coefficient is independent of the type of trace substance considered. In fact, aerosol particles and trace gases are expected to disperse with similar velocities. 

Fig. 12-2. Partial pressure (in bar, solid line) and mixing ratio (dashed line) of hydrogen in the primitive atmosphere on Earth according to Eqs. (12-7) and (12-8). K2 = 102m2/s, H = 9 km, A = 3 x KT4. The eddy diffusion coefficient corresponds to present conditions at the homopause. If K2 in the primitive atmosphere had been smaller by a certain factor, the hydrogen partial pressure would have been greater by the same factor and vice versa.

The water photolysis under low O2 pressure always led to a loss of hydrogen into space. The diffusion rate of the H2 (or H after it has been broken down by photolysis) through the homopause and exobase is limited. The definition of the homopause (80-90 km altitude) is the point at which the molecular and eddy diffusion coefficients are equal or, in other words, the critical level below which an atmosphere is well-mixed. The exobase ( 550 km) is the height at which the atmosphere becomes collisionless above that height the mean free path of the molecules exceeds the local scale height (RTIg). 

While molecular diffusivity is commonly independent of direction (isotropic, to use the correct expression), turbulent diffusivity in the horizontal direction is usually much larger than vertical diffusion. One reason is the involved spatial scales. In the troposphere (the lower part of the atmosphere) and in surface waters, the vertical distances that are available for the development of turbulent structures, that is, of eddies, are generally smaller than the horizontal distances. Thus, for pure geometrical reasons the eddies are like flat pancakes. Needless to say, they are more effective in turbulent mixing along their larger axes than along their smaller vertical extension. 

As the plane continues to climb, the ride becomes smooth. Coffee served in open cups does not spill, providing testimony that in the tropopause [at approximately 10,000 m (33,000 ft)] and the still higher stratosphere (Fig. 4-1), the size and energy of atmospheric eddies decrease. Weather phenomena are confined almost entirely to the troposphere. Being at the edge of the stratosphere is comparable to being in the thermocline of a stratified lake (Section 2.2.2) turbulent diffusion is suppressed, and vertical Fickian transport is slowed. Chemicals released into the air near Earth s surface may mix... 

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