Advection fluxes, calculation

Acridine char nitrogen, retention as function of burnoff, 307/, 308/ Advection fluxes, calculation, 41-43 Aerosol particle size distribution, molecular clusters, 317 Aerosol scavenging pathway, acetic and formic acid formation, 223 Aerosol species, transformation over the western Atlantic, 52 Aerosol sulfate airborne determination, 298 See also Sulfate... 

The advective flux (mol cm-2 s-1) of component i (Eqn. 20.11) across the left side of the control volume is calculated as,... 

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 ... 

The offshore advective flux for Si shown in Fig. 17.3 (30 X 10 mol d l) was calculated by difference, based on the total flux of dissolved Si supplied to the shelf system (32 X 10 mol Si d-1), the estimated deltaic burial rate (1-3 x 10 mol Si d ), and the nearshore particulate flux (0.1-0.7 x 10 mol Si d ). This advective flux is in good agreement with the results of Daley (1997), who estimated that 30 x 10 mol d of Si leave the shelf, based on seasonal field data and a multibox model for the shelf. Most of the silicate (94%) supplied to the shelf by external sources appears to be transported to the open ocean in either dissolved or particulate form. Approximately 36% of the Si leaving the outer shelf is in particulate form according to these calculations. Biogenic silica export may have contributed to the lack of closure in the Edmond et al. (1981) silicate budget for the shelf, although deltaic burial also remains as a potentially important sink. 

This relation can be solved for the superficial velocity, provided that the density is known from a appropriate EOS. For gas mixtures the ideal gas law is often used, thus the changes in composition is taken into account through the average molecular mass of the mixture. Moreover, the continuity equation can be integrated from the inlet z = 0 to any level z = z, to show that the mass flux is constant in the tube pv ) z = (/W ) in = Constant kg/m s). In particular, this integral relationship is frequently used to simplify the models, calculating the convective/advective flux terms from the known inlet values. 

Some examples for the second case were provided by Schultheiss and McPhail (1986). By using an analytical instrument that freely sinks to the ocean floor, they were able to measure pressure differences between pore water, located 4 m below the sediment surface, and the bottom water directly. At some locations, deep sea sediments of the Madeira Abyssal Plain displayed pressure differences of about 0 Pa, at other locations, however, the pressure in pore water 4 m below the sediment surface was significantly lower (120 or 450 Pa) than in bottom water. With regard to the porosity (([)) and the permeability coefficient of the sediment (k), the advective flux is calculated according to the following equation ... 

In this equation, known as the Darcy Equation, and which is applied in hydrogeology for calculating advective fluxes in groundwater, vjm s ] denotes the velocity with which a particle/solute crosses a definite distance in aqueous sediments. Ap refers to the pressure altitude measured in meters of water column (10 Pa = 1 bar 750 mm Hg 10.2 m water column) and Ax [m] is the distance across which the pressure difference is measured. In the example shown above ((]) = 0.77, k = 7-10 m s ), this distance amounts to 4 m. Insertion into Equation 3.30 yields ... 

In particular, this integral relationship is frequently used to simplify the models, calculating the convective/advective flux terms from the known inlet values. 

Pahlow et al. [67] have also carefully examined the role of cell shape on nutrient uptake by diatoms in the presence of advection, under the assumption that nonspherical cells will rotate intermittently. In that case, the relative increase in transport capacity is small for solitary, nonspherical cells with respect to spheres [67], These authors found that advection could significantly increase transport for cell chains, even though it did not compensate for the loss in diffusive flux when calculations were made on a cell surface area basis. Therefore, although advection has a much greater effect on the supply of solute to chains than it does to solitary cells, solitary cells will always maintain an advantage over chains. 

To assess the relative importance of the volatilisation removal process of APs from estuarine water, Van Ry et al. constructed a box model to estimate the input and removal fluxes for the Hudson estuary. Inputs of NPs to the bay are advection by the Hudson river and air-water exchange (atmospheric deposition, absorption). Removal processes are advection out, volatilisation, sedimentation and biodegradation. Most of these processes could be estimated only the biodegradation rate was obtained indirectly by closing the mass balance. The calculations reveal that volatilisation is the most important removal process from the estuary, accounting for 37% of the removal. Degradation and advection out of the estuary account for 24 and 29% of the total removal. However, the actual importance of degradation is quite uncertain, as no real environmental data were used to quantify this process. The residence time of NP in the Hudson estuary, as calculated from the box model, is 9 days, while the residence time of the water in the estuary is 35 days [16]. 

Now we need the corresponding expression for advective transport. Note that the advective velocity along the x-axis, vx, can be interpreted as a volume flux (of water, air, or any other fluid) per unit area and time. Thus, to calculate the flux of a dissolved chemical we must multiply the fluid volume flux with the concentration of... 

To calculate the profile you need two boundary conditions. The first one is given by C(z = 0) = C0= 10 x 10 12mol L 1. The second one is less obvious. You observe that no CFC-12 is entering the lake at the bottom (nor at another depth). If CFC-12 is nonreactive, the sum of the vertical advective and diffusive fluxes anywhere in the profile must be zero. Thus, from Eq. 22-3 ... 

Consider the same profile as in P 22.1. In addition to diffusion, an advective velocity v acts on the profile, (a) Calculate the corresponding additional contribution to the flux and to dC /dt. (b) Determine the relation between v and the other parameters (.D, a, C0) such that the profile, given in P22.1 between x = 0 and x = °° corresponds to a steady-state. Is such a steady-state possible if v > 0 ... 

A summary of physical and biochemical parameters for the Amazon shelf are presented in Table 17.1. These data were used to develop the mass balance calculations described in the remainder of the paper. The rate of Amazon River sediment discharge that is cited in most studies (Meade et al. 1985) characterizes the flux at Obidos, which is hundreds of kilometers from the river mouth. The sediment fluxes that have been documented for the Amazon coastal area are the fine-grained sediment accumulation rate on the shelf (6.3 x 10 g yr, Kuehl et al. 1986, 1996) and the advection rate of particulate material northward out of the study area, primarily in nearshore environments (-1.2 X 10 g yr, Allison et al. 1995). Because some sediment may be deposited between Obidos and the river mouth, we have chosen to use the sum of the shelf... 

An important conclusion of the Toggweiler and Carson (1995) study is that the EUC is the most important source of N to the equatorial zone paradoxically, NO3 concentration in the EUC is lower than in the surrounding waters. The resolution of this apparent paradox lies in the nonconservative nature of bioactive elements such as N. The primary mass balance for N is between zonal advection by the EUC and sedimentation of particulate N, while the mass balance for water is between zonal advection and poleward advection of surface waters that have been depleted of N by the biota. This is not intended to minimize the importance of vertical advection, which is of course very important for equatorial ecosystems, but to understand sources to the region as a whole, by calculating fluxes in and out of a box encompassing the upper equatorial ocean down to the base of the thermocHne. 

---