Shallow-layer models

D (either two horizontal dimensions—typical for shallow layer models—or downwind distance or travel time and plume height—typical for plume trajectory models—are independent variables)... 

The thin-film model is the simplest and, therefore, most commonly used approach to estimate air-sea fluxes of gases. In this model, molecular diffusion is assumed to present a barrier to gas exchange in each of two layers. As illustrated in Figure 6.5, one layer is composed of a shallow region of the atmosphere that lies in direct contact with the sea surface. The second is a shallow layer of seawater tliat lies at the sea surface. These layers have depths less than 100 (am and, hence, are referred to as thin films. 

Some results of the simulation experiment are given in Figures 6.5 and 6.6. Figure 6.5 shows the tendency vs. time of the average content of radionuclear pollution on the whole Arctic water area. The distribution with depth is represented by a three-layer model, upper waters (z < 1 km), deep water (z > 1 km), and sediments. Bottom depth is taken as 1.5 km. More realistic depth representations of both shallow seas and the deeper Arctic Basin will be considered in a future refinement of the model. The curves describe the vertical distribution with time of the radionuclide content in two water layers and in sediments. The transfer of radionuclides from upper water to deep water occurs at a speed which results in the reduction of radionuclear pollution in upper water by 43.3% over 20 years. Such distributions for each Arctic sea are given in Table 6.11. 

State-of-the-art modeling, however, is based on the solution of the so-called shallow-layer equations, a non-linear differential equation system which takes into account the conservation of mass and momentum. This allows the tracking of the dynamic behavior... 

Thomas described a two-layer model of the liquid-gas interface that is based on a Henry s Law constant and mass-transfer coefficients. To illustrate the relative volatilities of the solvents in water, the half-lifes of each solvent in a shallow stream were compiled (Table 16.1.8). The stream was assumed to be 1.0 meter deep and flowing at a rate of 1.0 meter per second. It was also assumed that there was a breeze blowing across the stream at a rate of 3.0 meters per second. Under these conditions, the predicted half-lives of many of the solvents in Table 16.1.1 are less than 10 hours, indicating that volatilization into the atmosphere can be a relatively rapid pathway for solvents that have been released to surface water. The volatilization of nitrobenzene, isobutyl alcohol, n-butyl alcohol, cyclohexanone, and, in particular, o-cresol may be a slow process, and other fate processes may be more important in water. 

The diSuse scatter arises because dislocations are defects which rotate the lattice locally in either direction. This gives rise to scatter, from near-core regions, which is not travelling in quite the same direction as the diffraction from the bulk of the crystal. This adds kinematically (i.e. in intensity not amplitude) and gives a broad, shallow peak that mnst be centred on the Bragg peak of the dislocated layer or substrate since all the local rotations are centred on the lattice itself. We can model the diffuse scatter quite well by a Gaussian or a Lorentzian function of the form ... 

In Part IV we repeatedly used box models for describing the dynamics of chemicals in lakes. In this chapter we will summarize this information. As a first step, Fig. 23.1 illustrates the one-box model approach for the average total concentration of a chemical, Ct, in a well-mixed water body such as a pond, a shallow lake, a subcompartment of a deep lake or ocean (e.g., the mixed surface layer), or even an engineered system like a completely stirred reactor. 

Both of the models presented here are based on the flow of nitrogen through ecosystems in one case a nearshore kelp-bed system and in the other a general offshore plankton community. The klep bed model was developed to explore the hypothesis that nitrogen flow is affected by horizontal water transport in shallow water marine systems here wave action or mixing associated with horizontal transport are likely to retain nitrogen in the photic zone and the benthic community is of fixed location so that boundaries of the system can be easily defined. In pelagic systems, on the other hand, the community tends to move horizontally with water in the mixed layer, and vertical transport into and out of the mixed layer is an important feature of the system dynamics. 

---