One-dimensional advective-diffusive

The ratio vJD can then be used to calculate a chemical reaction rate for a nonconservative solute, S. To do this, the one-dimensional advection-diffusion model is modified to include a chemical reaction term, J. This new equation is called the one-dimensional advection-diffusion-reaction model and has the following form ... 

Depth profiles of (a) salinity (%o), (b) dissolved oxygen (ml /L), and (c) percent saturation of dissolved oxygen in the Southeastern Atlantic Ocean (9°30 W 11°20 S). Samples were collected in March 1994. Dotted lines represent the curves generated by the one-dimensional advection-diffusion model (see text for details). The values of Dz, Vz, and J are the ones that best fit the data. Data are from Java Ocean Atlas (http /odf.ucsd.edu/joa). Values of percent saturation of oxygen less than 100 reflect the effects of aerobic respiration. Values greater than 100 indicate a net input, such as from photosynthesis. (See companion website for color version.)... 

If the solute imdergoes any chemical changes, a reaction term must be added to Eq. 12.4. In the absence of specific rate law information, diagenetic reactions are generally assumed to be first-order with respect to the solute concentration. Thus, the one-dimensional advection-diffusion equation far a nonconservative solute is given by... 

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... 

As we saw with the steady-state water-column application of the one-dimensional advection-diffusion-reaction equation (Eq. 4.14), the basic shapes of the vertical concentration profiles can be predicted from the relative rates of the chemical and physical processes. Figure 4.21 provided examples of profiles that exhibit curvatures whose shapes reflected differences in the direction and relative rates of these processes. Some generalized scenarios for sedimentary pore water profiles are presented in Figure 12.7 for the most commonly observed shapes. 

After making these adjustments for diffusion in sediments, the mass balance and vertical concentration patterns of nonconservative solutes in saturated sediments can be described by the following one-dimensional advective-diffusive general diagenetic equation (GDE) (Berner, 1980 Aller, 2001 Jprgensen and Boudreau, 2001) ... 

The mass balance and vertical concentration patterns of nonconservative solutes in saturated sediments can be described by the one-dimensional advective-diffusive general diagenetic equation (GDE). 

This classification has been discussed extensively within the context of a one-dimensional advection-diffusion model, along with simple solutions to the relevant equations (Craig, 1969). It should be noted, however, that specific tracers may fall into different categories depending on the nature of the specific application. For example, radiocarbon is a transient tracer in the surface waters of the ocean because its natural inventory (due to cosmic ray production) has been affected... 

Magnesium concentrations as a function of depth (meters below the sea floor) in sediment porewaters from the western flank of the Juan de Fuca Ridge near 48° N in the North Pacific Ocean. The concentration decreases with depth because it is removed from solution by reaction with crustal rocks at the sediment-crustal boundary. The curves are convex upward because of porewater upwelling along the upward-flowing limb of a convection cell. Velocities of the upwelling are determined by using a one-dimensional advection-diffusion model and are indicated by the numbers on the curves. Redrafted from Wheat and MottI (2000). 

The concentrations of compounds dissolved in the water change over time and distance as the compounds dissolve from the slick into the water, volatilize from the water to the atmosphere, and disperse in the river. The one-dimensional advection-diffusion equation for... 

The general one-dimensional advective-diffusive dynamics for a reactive pollutant can be written as a differential equations [10] [11] [12]. This one-dimensional in the x-direction model can be appropriate only for small rivers that is characterizing by small fluctuations on vertical and horizontal coordinates. This assumption wouldn t be appropriate for large rivers. Two- and three-dimensional representations are also possible, but they have considerable computational complexity. Neglecting the diffusion term yields [13] ... 

---