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Mathematical Modeling of Earth's Dynamical Systems by Rudy Slingerland, Lee Kump

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CHAPTER7

Advection and Diffusion (Transport) Problems

 

Consider a property P that is conserved. It could be mass such as the amount of a dissolved species in a river or the mass of particulate load suspended in a flow, or it could be a vector property of a mudflow like momentum. Further assume that P is passively carried along by the medium in which it exists at the flow speed u; that is, it is advected along. Also assume that within the medium, P moves from one point to another in proportion to its gradient; that is, it diffuses according to a first-order rate law. Finally, assume that there is a source and/or sink for P in the medium such as might occur if P is converting to another chemical species at a known rate. The resulting PDE is called ...

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