DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

quence, luminosity of the advection dominated
disk can be much lower than that of a standard
thin accretion disk. Advection dominated disks
are expected to form if the accretion rate is above
the Eddington limit, or on the other end, if the
accretion rate is very low. Low accretion rate,
advection dominated disks have been used to
model the lowest luminosity active galactic nuclei,
the galactic center, and quiescent binary
systems with a black hole candidate. See active
galactic nuclei, black hole, Eddington limit.
advective heat transfer (or advective heat
transport) Transfer of heat by mass movement.
Use of the term does not imply a particular
driving mechanism for the mass movement
such as thermal buoyancy. Relative to a
reference temperature T0, the heat flux due to
material of temperature T moving at speed v is
q=vρc(T −T0), where ρ and c are density
and specific heat, respectively.
aeolian See eolian.
aerosol Small size (0.01 to 10 µm), relatively
stable suspended, colloidal material, either
natural or man-made, formed of solid particles
or liquid droplets, organic and inorganic,
and the gases of the atmosphere in which these
particles float and disperse. Haze, most smokes,
and some types of fog and clouds are aerosols.
Aerosols in the troposphere are usually removed
by precipitation. Their residence time order
is from days to weeks. Tropospheric aerosols
can affect radiation processes by absorbing, reflecting,
and scattering effects, and may act
as Aitken nuclei. About 30% of tropospheric
aerosols are created by human activities. In the
stratosphere, aerosols are mainly sulfate particles
resulting from volcanic eruptions and usually
remain there much longer. Aerosols in the
stratosphere may reduce insolation significantly,
which is the main physics factor involved in
climatic cooling associated with volcanic eruptions.
aesthenosphere Partially melted layer of the
Earth lying below the lithosphere at a depth of
80 to 100 km, and extending to approximately
200 km depth.
© 2001 by CRC Press LLC
African waves
affine connection A non-tensor object which
has to be introduced in order to construct the covariant
derivatives of a tensor. Symbol: Ɣ α βγ .
Under the general coordinate transformation
x µ −→x ′µ =x µ +ξ µ (x) the affine connection
possesses the following transformation rule:
Ɣ α′
β ′ γ ′=∂xα′
∂x µ
∂xν ∂xβ′ ∂xλ µ
∂xγ′Ɣ νλ +∂xα′
∂xτ ∂2xτ ∂xβ′ ∂xγ′ while for an arbitrary tensor TA =T µ1...µl
ν1...νk one
has
T α1 ′...αl
β1 ′...βk ′ = ∂xα1 ′
∂x µ1 ...∂xα l ′
∂x µl
∂xν1 ∂xβ1 ′
... ∂xνk
∂xβk ′Tµ1...µl
ν1...νk
The non-tensor form of the transformation of
affine connection guarantees that for an arbitrary
tensorT αβ...γ
ρν...α its covariant derivative
∇µT αβ...γ
ρν...α
= Tαβ...γ ρν...α,µ +Ɣα σµ Tσβ...γ ρν...α +...
−Ɣ σ ρµ Tαβ...γ σν...α −...
is also a tensor. (Here the subscript “µ” means
∂/∂X µ .) Geometrically the affine connection
and the covariant derivative define the parallel
displacement of the tensor along the given
smooth path. The above transformation rule
leaves a great freedom in the definition of affine
connection because one can safely add to Ɣα βγ
any tensor. In particular, one can provide the
symmetry of the affine connection Ɣα βγ = Ɣα γβ
(which requires torsion tensor = 0) and also
metricity of the covariant derivative ∇µgαβ = 0.
In this case, the affine connection is called the
Cristoffel symbol and can be expressed in terms
of the sole metric of the manifold as
Ɣ α 1
βγ =
2 gαλ
∂βgγλ + ∂γ gβλ − ∂λgβγ
See covariant derivative, metricity of covariant
derivative, torsion.
African waves During the northern hemisphere
summer intense surface heating over the
Sahara generates a strong positive temperature
gradient in the lower troposphere between the
equator and about 25 ◦ N. The resulting easterly
thermal wind creates a strong easterly jet core
near 650 mb centered near 16 ◦ N. African waves