Application of the Telegraph Equation to Oceanic Diffusion: Another Mathematical Model.
JOHNS HOPKINS UNIV BALTIMORE MD CHESAPEAKE BAY INST
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The solution of the conventional diffusion equation has an obvious shortcoming that is, the substance concentration will rise instantaneously everywhere when substance is introduced at some point in the sea. Although such instantaneous propagation of substance makes a negligibly small contribution to the concentration at large distances from the source, it might cause serious error in predicting water pollution, microorganism distributions, etc. A diffusion equation which overcomes this difficulty is the telegraph equation characterized by a finite propagation velocity. An ad hoc derivation of the telegraph equation from a set of hydromechanical equations identifies the parameters involved in the equation. Thus the propagation velocity is related to the correlation tensor of turbulent velocity. As a result, the one-particle dispersion law by Taylor and the relative diffusion law by Richardson can be deduced from the telegraph equation. Author
- Physical and Dynamic Oceanography