Advection defined

As characterized in Fig. 6.7, once a chemical is released into the atmosphere, it is rapidly transported by the average wind and subjected to dispersion, defined as spreading as a result of thermal or density gradients and/or turbulence, and advection, defined as movement as... 

Time scales of transport can also be applied to situations when no well-defined reservoirs can be defined. If the dominant transport process is advection by mean flow or sedimentation by gravity, the time scale characterizing the transport between two places is simply tadv = L/V where L is the distance and V the transport velocity. Given a t)q)ical wind speed of 20 m/s in the mid-latitude tropospheric westerlies, the time of transport around the globe would be about 2 weeks. 

In this model, two level-set functions (d, p) are defined to represent the droplet interface (d) and the moving particle surface (p), respectively. The free surface of the droplet is taken as the zero in the droplet level-set function 0> and the advection equation (Eq. (3)) of the droplet level-set function (droplet surface. The particle level-set function (4>p) is defined as the signed distance from any given point x in the Eulerian system to the particle surface ... 

Let us consider a medium moving with velocity v (components vx, Vy, vz). A medium with non-zero velocity is said to be advective. Let us first define in the most general way the flux of volume at a point M of the familiar 3D space this is simply the quantity of volume moving across the unit surface perpendicular to v per unit time. For an arbitrary surface 6S next to M and perpendicular to v (Figure 8.1) and during time dt, the volume will be... 

Organic chemicals dissolved in groundwater originate from a release source, which may be point source (defined leak) or it may emanate from an area source, such as a mass of contaminated soil. Once dissolved, the chemicals disperse into the ground-water by molecular diffusion and advection (combined as dispersion), both of which are influenced by equilibrium distribution relationships with the aquifer materials. 

These solutions to the one-dimensional advection-diffusion model can be used to estimate reaction rate constants Ck) from the pore-water concentrations of S, if and s are known. More sophisticated approaches have been used to define the reaction rate term as the sum of multiple removals and additions whose functionalities are not necessarily first-order. Information on the reaction kinetics is empirically obtained by determining which algorithmic representation of the rate law best fits the vertical depth concentration data. The best-fit rate law can then be used to provide some insight into potential... 

Quantification of NAPL transport usually is considered by using advection-dispersion equations for each of the water and NAPL phases and defining relative permeabilities (as noted previously). Alternatively, if the emphasis is on contamination... 

Advection is generally defined as the displacement of a portion of matter with respect to the point of observation under the influence of force fields (Lerman, 1979). An advection flux g/(sec X cm )] of a material with density p (g/cm ) moving at velocity V (cm/sec) with respect to the point of observation is given by... 

Nevertheless, the process of encystment dictates when a substantial fraction of a Gonyaulax population leaves the water column, regardless of the ability of motile cells to persist for extended periods. The encystment/excystment cycle can thus define the temporal limits of some blooms. More work is needed to evaluate the importance of this process relative to bloom termination from factors such as grazing or advection that decrease the numbers of motile cells. 

Contaminated bed sediments exist at numerous locations in the United States and around the world. These result mainly from past indiscriminate pollution of our aquatic environments and consist of freshwater and marine bodies including streams, lakes, wetlands, and estuaries. The bed sediments contain many hydrophobic organic compounds and metal ions that in the course of time act as sources of pollutants of the overlying aqueous phase. There are a number of transport pathways by which pollutants are transferred to the aqueous phase from contaminated sediments. One of the lesser known, but potentially important, modes of transport of pollutants from bed sediments is by diffusion and advection of contaminants associated with colloidal-size dissolved macromolecules in pore water. These colloids are measured in the aqueous phase as dissolved organic compounds (DOCs). (These are defined operationally as particles with a diameter smaller than 0.45 micrometer.)... 

Remember that from the nondimensional version of the advection-dispersion equation, Eq. 25-18, the Peclet Number Pe was identified as the only parameter that determines the shape of the concentration distribution in the aquifer. By introducing relative coordinates for space ( ,) and time (9) as defined in Eq. 25-16, Eq. 25-20 takes the form ... 

The construction of a mass balance model follows the general outline of this chapter. First, one defines the spatial and temporal scales to be considered and establishes the environmental compartments or control volumes. Second, the source emissions are identified and quantified. Third, the mathematical expressions for advective and diffusive transport processes are written. And last, chemical transformation processes are quantified. This model-building process is illustrated in Figure 27.4. In this example we simply equate the change in chemical inventory (total mass in the system) with the difference between chemical inputs and outputs to the system. The inputs could include numerous point and nonpoint sources or could be a single estimate of total chemical load to the system. The outputs include all of the loss mechanisms transport... 

If particle mixing is assumed to be analogous to diffusion with sediment accumulation and radionuclide decay, the steady-state profile for excess activity of a nonexchangeable radionuclide is defined by an advective-diffusion equation. 

Further tests and previous experiences in other geographic locations confirmed that minimum Kz is a relevant (and often neglected) parameter to model properly the dispersion during weak wind and very stable conditions. Unfortunately no general value for minimum Kz can be defined, while proper values depend on season and local climatology, as well as on numerical diffusion in the advection scheme. 

The horizontal wind components, potential temperature and specific humidity are used in METRAS as forcing fields. Changes in the scalar quantities temperature and humidity are mainly induced by advection and diffusion, i.e. processes that depend on the wind. Therefore, we define the conditions for writing the model results only in dependence of changes in the horizontal wind components. The model results were alternatively written at regular intervals (3 h, 6 h), if the... 

Harvie, D. J. E., and Fletcher, D. F. (2001) A New Volume of Fluid Advection Algorithm The Defined Donating Region Scheme, International Journal for Numerical Methods in Fluids, Vol. 35(2), pp. 151-172. 

FIGURE 2-4 Transport of a chemical in a river. At time zero, a pulse injection is made at a location defined as distance zero in the river. As shown in the upper panel, at successive times C, t2, and t3, the chemical has moved farther downstream by advection, and also has spread out lengthwise in the river by mixing processes, which include turbulent diffusion and the dispersion associated with nonuniform velocity across the river cross section. Travel time between two points in the river is defined as the time required for the center of mass of chemical to move from one point to the other. Chemical concentration at any time and distance may be calculated according to Eq. [2-10]. As shown in the lower panel, Cmax, the peak concentration in the river at any time t, is the maximum value of Eq. [2-10] anywhere in the river at that time. The longitudinal dispersion coefficient may be calculated from the standard deviation of the concentration versus distance plot, Eq. [2-7]. 

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