# Dictionary Definition

advection n : (meteorology) the horizontal
transfer of heat or other atmospheric properties

# User Contributed Dictionary

## English

### Noun

- The horizontal movement of a body of atmosphere (or other fluid) along with a concomitant transport of its temperature, humidity etc.
- The transport of a scalar by bulk fluid motion

# Extensive Definition

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. 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.

## Meteorology

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.
Advection is important for the formation of orographic cloud and
the precipitation of water from clouds, as part of the hydrological
cycle.

## Other quantities

The advection equation also applies if the
quantity being advected is represented by a
probability density function at each point, although accounting
for diffusion is more difficult.

## Mathematics of advection

The advection equation is the
partial differential equation that governs the motion of a
conserved scalar
as it is advected by a known velocity
field. It is derived using the scalar's conservation
law, together with Gauss's
theorem, and taking the infinitesimal limit.

Perhaps the best image to have in mind is the
transport of salt dumped in a river. If the river is originally
fresh water and is flowing quickly, the predominant form of
transport of the salt in the water will be advective, as the water
flow itself would transport the salt. If the river was not flowing
the salt would simply disperse outwards from its source in a
diffusive
manner, which is not advection.

In Cartesian coordinates the advection operator
is

- \mathbf \cdot \nabla = u \frac + v \frac + w \frac.

where the velocity vector v has components u, v
and w in the x, y and z directions respectively.

The advection equation for a scalar
\psi , such as temperature, is expressed mathematically as: \frac
+\nabla\cdot\left( \psi\right) =0

where \nabla\cdot is the divergence operator and \bold
u is the vector field. Frequently, it is assumed that the velocity
field is solenoidal,
that is, that \nabla\cdot=0. If this is so, the above equation
reduces to

\frac +\cdot\nabla\psi=0.

For a vector
\bold a, such as magnetic field or velocity, in a solenoidal field
it is defined as: \frac + \left( \cdot \nabla \right) =0.

In particular, if the flow is steady,
\cdot\nabla\psi=0 which shows that \psi is constant along a
streamline.

The advection equation is not simple to solve
numerically:
the system is a
hyperbolic partial differential equation, and interest
typically centers on discontinuous
"shock" solutions (which are notoriously difficult for numerical
schemes to handle).

Even in one space dimension and constant
velocity, the system remains difficult to simulate. The equation
becomes

\frac+u\frac=0

where \psi=\psi(x,t) is the scalar being advected
and u the x component of the vector \bold u = (u(x),0,0).

According to , numerical simulation can be aided
by considering the skew
symmetric form for the advection operator.

\frac \cdot \nabla + \frac \nabla ( )

where \nabla ( ) is a vector with components
[\nabla ( u_x),\nabla ( u_y),\nabla ( u_z)] and the notation =
[u_x,u_y,u_z] has been used.

Since skew symmetry implies only complex
eigenvalues, this
form reduces the "blow up" and "spectral blocking" often
experienced in numerical solutions with sharp discontinuities (see
Boyd )

## See also

## References

advection in Catalan: Advecció

advection in German: Advektion

advection in Spanish: Advección

advection in French: Advection

advection in Norwegian: Adveksjon

advection in Norwegian Nynorsk: Adveksjon

advection in Polish: Adwekcja

advection in Romanian: Advecţie

advection in Finnish: Advektio

advection in Russian: Уравнение
переноса