Advection is the transport of a conserved scalar quantity that is transported in a vector field. A good example to have in mind would be the transport of pollution in a river: the motion of the water carries the polluted water downstream (see pigpen problem).

In meteorology and physical oceanography, advection usually refers to the predominantly horizontal transport of an atmospheric property or oceanic fluid by the wind, e.g. moisture or heat advection. In this context, the advection operator (in z and p vertical coordinates) is

[itex]\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}[itex].

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