Advection
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Advection is transport in a fluid. The fluid is described mathematically for such processes as a vector field, and the material transported is described as a scalar concentration of substance, which is present in the fluid. A good example of advection is the transport of pollutants or silt in a river: the motion of the water carries these impurities downstream (see pigpen problem). Another commonly advected substance is heat, and here the fluid may be water, air, or any other heat-containing fluid material. Any substance, or conserved property (such as heat) can be advected, in a similar way, in any fluid.
Advection is important for the formation of orographic cloud and the precipitation of water from clouds, as part of the hydrological cycle.
In meteorology and physical oceanography, advection often refers to the transport of some property of the atmosphere or ocean, such as heat, humidity (see moisture) or salinity. Meteorological or oceanographic advection follows isobaric surfaces and is therefore predominantly horizontal.
In Cartesian coordinates the advection operator is
.
where the velocity vector v has components u, v and w in the x, y and z directions respectively.