Advection
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Advection is transport of a some conserved scalar quantity in a vector field. A good example is the transport of pollutants or silt in a river: the motion of the water carries these impurities downstream (see pigpen problem). Any substance 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. Advection follows isobaric surfaces and is therefore predominantly horizontal. The advection operator in height (z) and pressure (p) coordinates is
- <math>\mathbf{v} \cdot \nabla = u \frac{\partial}{\partial x} + v \frac{\partial}{\partial y} + w \frac{\partial}{\partial z} = u \frac{\partial}{\partial x} + v \frac{\partial}{\partial y} + \omega \frac{\partial}{\partial p}</math>.
where the vector v and the scalars u and v denote the horizontal components of the fluid flow, w denotes the vertical component of the flow and x and y denote horizontal position.
