Vertical fluxes, calculation

Development in recent years of fast-response instruments able to measure rapid fluctuations of the wind velocity (V ) and of fhe tracer concentration (c ), has made it possible to calculate the turbulent flux directly from the correlation expression in Equation (41), without having to resort to uncertain assumptions about eddy diffusivities. For example, Grelle and Lindroth (1996) used this eddy-correlation technique to calculate the vertical flux of CO2 above a foresf canopy in Sweden. Since the mean vertical velocity w) has to vanish above such a flat surface, the only contribution to the vertical flux of CO2 comes from the eddy-correlation term c w ). In order to capture the contributions from all important eddies, both the anemometer and the CO2 instrument must be able to resolve fluctuations on time scales down to about 0.1 s. 

Aerosol particles Table 3.13 shows the percentage change in the actinic flux calculated by Peterson (1976) and Demerjian et al. (1980) for two cases (1) a particle concentration of zero, corresponding to a very clean atmosphere, and (2) a total particle concentration doubled compared to the base case. The actinic flux is predicted to increase if the total particle concentration is zero and decrease if it doubles (note, however, as discussed later, the sensitivity to the vertical distribution of particles and the relative importance of light scattering compared to absorption). 

In Illustrative Example 19.2 we discussed the flux of trichloroethene (TCE) from a contaminated aquifer through the unsaturated zone into the atmosphere. The example was based on a real case of a polluted aquifer in New Jersey (Smith et al., 1996). These authors compared the diffusive fluxes, calculated from measured TCE vapor concentration gradients, with total fluxes measured with a vertical flux chamber. They found that the measured fluxes were often several orders of magnitude larger than the fluxes calculated from Fick s first law. In these situations the vapor profiles across the unsaturated zone were not always linear. The authors attributed this to the influence of advective transport through the unsaturated zone. In order to test this hypothesis you are asked to make the following checks ... 

Calculate the vertical steady-state profile of benzene as well as the total vertical flux of benzene, XFbenzene (expressed as mass per unit time), if the following conditions hold ... 

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. 

The advantage of the k-profile scheme is its treatment of the convective limit. Since convection implies strong vertical mixing that destroys vertical gradients, the calculation of vertical fluxes from gradient formulas becomes inaccurate. This problem is circumvented in the k-profile approach by a special term in the expression for the turbulent vertical tracer fluxes, ww(J), which is active in the convective case and redistributes the surface flux, ivx(O), of a tracer X over the surface boundary layer in depth d. 

Jaeschke ei al. (1978) have shown the importance of this process in the following indirect way. They measured the vertical concentration gradient of H2S and calculated the vertical flux by using the gradient method (see Section 5.1). They have... 

Fig. 7-13. Vertical flux of sea-spray droplets according to Monahan (1968), compared with the number density size distribution of sea-salt particles 6 m above the ocean surface (Chaen, 1973, as reported by Blanchard and Woodcock, 1980). Both follow a Junge (r ) power law. Numbers next to points indicate the wind speed (m/s). The solid line for the droplet flux was calculated from ejection velocities given by Wu (1979).

FIGURE 15.118 Effect of mass flux on critical heat flux in upward water flow in a vertical tube (calculated from the Bowring [293] correlation for a tube length of 1 m, a tube diameter of 0.01 m, and zero inlet subcooling) (from Hewitt [291], with permission from The McGraw-Hill Companies). 

In contrast to the vertical fluxes, horizontal subgrid-scale fluxes in mesoscale models are not realistically represented. They are included only to smooth the model calculations horizontally. 

Table 3.10 shows the calculated percentage increase in the actinic flux at the earth s surface for an elevation of 1.5 km and atmospheric pressure of 0.84 atm (corresponding approximately to Denver) as a function of zenith angle for four wavelength intervals. In this calculation, it was assumed that the vertical 03 and particle... 

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