Diffusion and advection

Taking into account both advective and diffusive transport, the evolution of the concentration of a passive non-reactive substance in an incompressible flow is governed by the advection-diffusion equation 

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Great care has to be given to the physics of rotation and to the treatment of its interaction with mass loss. For differentially rotating stars, the structure equations need to be written differently [9] than for solid body rotation. For the transport of the chemical elements and angular momentum, we consider the effects of shear mixing, meridional circulation, horizontal turbulence and in the advanced stages the dynamical shear is also included. Caution has to be given that advection and diffusion are not the same physical effect. 

In order to provide AMS analyses to the broad ocean sciences research community, the National Ocean Sciences Accelerator Mass Spectrometry Facility (NOSAMS) was established at Woods Hole Oceanographic Institution (Massachusetts) in 1989. Studies performed there include identification of sources of carbon-bearing materials in the water column and sediment, dating of sedimentary samples, investigations of paleocirculation patterns (e.g., from observations of differences in 14C relative abundances in planktonic and benthic foraminifera, and coral cores and cross sections), as well as studies of modern oceanic carbon cycling and circulation. In fact, much that is known about advective and diffusive processes in the ocean comes from measurements of chemical tracers, such as 14C, rather than from direct measurements of water mass flow. 

Egan, B. A., and J. R. Mahon. Numerical modeling of advection and diffusion of urban area source pollutants. J. Appl. Meteorol. 11 312-322, 1972. 

The tube models consider the oceanic mass of water as subdivided into columns. Mass transfer between columns takes place by advection and diffusion. Examples of tube models may be found in Munk (1966) and Bieri et al. (1966), to whom we refer readers for further clarification. 

In fact, wherever we look at a compartment of the environment, we usually find the simultaneous actions of advective and diffusive motion. In this chapter we focus on the latter. 

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