DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

is lifted adiabatically. It can be determined by
the adiabatic chart.
adiabatic cooling In an adiabatic atmosphere,
when an air parcel ascends to upper
lower pressure height level, it undergoes expansion
and requires the expenditure of energy and
consequently leading to a depletion of internal
heat.
adiabatic deceleration Deceleration of energetic
particles during the solar wind expansion:
energetic particles are scattered at magnetic
field fluctuations frozen into the solar wind
plasma. During the expansion of the solar wind,
this “cosmic ray gas” also expands, resulting in a
cooling of the gas which is equivalent to a deceleration
of the energetic particles. In a transport
equation, adiabatic deceleration is described by
a term
∇·vsowi
3
∂
∂T (αTU)
with T being the particle’s energy, To its rest
energy,U the phase space density, vsowi the solar
wind speed, and α=(T + 2T o)/(T +T o).
Adiabatic deceleration formally is also
equivalent to a betatron effect due to the reduction
of the interplanetary magnetic field strength
with increasing radial distance.
adiabatic dislocation Displacement of a virtual
fluid parcel without exchange of heat with
the ambient fluid. See potential temperature.
adiabatic equilibrium An equilibrium status
when a system has no heat flux across its
boundary, or the incoming heat equals the outgoing
heat. That is, dU =−dW, from the first
law of thermodynamics without the heat term, in
which dU is variation of the internal energy, dW
is work. Adiabatic equilibrium can be found, for
instance, in dry adiabatic ascending movements
of air parcels; and in the closed systems in which
two or three phases of water exist together and
reach an equilibrium state.
adiabatic index Ratio of specific heats:
Cp/CV where Cp is the specific heat at constant
pressure, and CV is the specific heat at
constant volume. For ideal gases, equal to
(2+degrees of freedom )/(degrees of freedom).
© 2001 by CRC Press LLC
ADM form of the Einstein–Hilbert action
adiabatic invariant A quantity in a mechanical
or field system that changes arbitrarily little
even when the system parameter changes substantially
but arbitrarily slowly. Examples include
the magnetic flux included in a cyclotron
orbit of a plasma particle. Thus, in a variable
magnetic field, the size of the orbit changes as
the particle dufts along a guiding flux line. Another
example is the angular momentum of an
orbit in a spherical system, which is changed if
the spherical force law is slowly changed. Adiabatic
invariants can be expressed as the surface
area of a closed orbit in phase space. They are
the objects that are quantized (=mh) in the Bohr
model of the atom.
adiabatic lapse rate Temperature vertical
change rate when an air parcel moves vertically
with no exchange of heat with surroundings. In
the special case of an ideal atmosphere, the adiabatic
lapse rate is 10 ◦ per km.
ADM form of the Einstein–Hilbert action
In general relativity, by introducing the ADM
(Arnowitt, Deser, Misner) decomposition of
the metric, the Einstein–Hilbert action for pure
gravity takes the general form
1
SEH =
16 πG
d 4
1/2
xαγ Kij K ij − K 2 + (3)
R
− 1
d
8 πG
a ta
3 xγ 1/2 K + 1
8 πG
dt d 2
1/2
xγ Kβ i − γ ij
α,j ,
b
x i b
where the first term on the r.h.s. is the volume
contribution, the second comes from possible
space-like boundaries ta of the spacetime
manifold parametrized by t = ta, and
the third contains contributions from time-like
boundaries xi = xi b . The surface terms must
be included in order to obtain the correct equations
of motion upon variation of the variables
γij which vanish on the borders but have nonvanishing
normal derivatives therein.
In the above,
Kij = 1
2 α
βi|j + βj|i − γij,0