DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

dispersion
dispersion A phenomenon in which wave velocity
(phase velocity, group velocity) changes
with its wavelength. In seismology, for a layered
structure, phase velocity becomes closer
to S-wave velocity of the lower and upper layers
for longer and shorter wavelengths, respectively.
Phenomena in which phase velocity increases
anddecreaseswithincreasingwavelengtharerespectively
referred to as normal dispersion and
reverse dispersion. (This is the case for visible
light in glass and is the usual case in seismology.)
In seismology, curves representing the
relation between surface wave velocity and its
wavelength are called dispersion curves, from
which the velocity structure of the crust and the
mantle can be estimated.
dispersionless injection A sudden rise in the
intensity of energetic ions in the Earth’s nightside
equatorial magnetosphere, in general at or
beyond synchronous orbit, occurring simultaneously
over a wide range of energies. It is
widely held that such particles must have been
accelerated locally because if their acceleration
occurred some distance away, the faster ones
would have arrived first.
dispersion measure (DM) The integral
along the line of sight distant source of the electron
number density.
The pulse arrival time for two different frequenciesf2,f1is
related by
t =e 2
/(2πmec) f −2
DM .
dispersive Tending to spread out or scatter;
having phase and group velocities that depend
on wavelength. Used to describe both physical
and numerical processes.
displacement vector In a Euclidean space,
the difference vector between position vectors
to two points. The displacement vector is often
thought of as the difference in position of a
particular object at two different times.
dissipation In thermodynamics, the conversion
of ordered mechanical energy into heat.
In computational science, deliberately added to
differential equations to suppress short wave-
© 2001 by CRC Press LLC
length oscillations that appear in finite representations
of differential equations, but have no
analog in the differential equations themselves.
dissipation of fields One of the basic concepts
of magnetohydrodynamics. In the case of
a finite conductivity, the temporal change of the
magnetic flux in a plasma can be written as
∂B
∂t
= c2
4πσ ∇2 B
with B being the magnetic flux, σ the conductivity,
andc the speed of light. Formally, this is
equivalent to a heat-conduction equation, thus
by analogy we can interpret the equation as describing
the temporal change of magnetic field
strength while the magnetic field lines are transported
away by a process that depends on conductivity:
the field dissipates. Note that while
the magnetic flux through a given plane stays
constant, the magnetic energy decreases because
the field-generating currents are associated with
ohmic losses. Magnetic field dissipation seems
to be important in reconnection. See reconnection.
Aside from the conductivity, the temporal
scale for field dissipation depends on the spatial
scale of the field. With τ being the characteristic
time scale during which the magnetic field
decreases to 1/e and L being the characteristic
spatial scale of the field, the dissipation time can
be approximated as
τ ≈ 4πσ
c2 L2 .
Thus, the dissipation depends on the square
of the characteristic scale length of the field:
Smaller fields dissipate faster than larger ones.
Thus in a turbulent medium, such as the photosphere,
where the field lines are shuffled around
and therefore a polarity pattern on very small
spatial scales results, the field dissipates rather
quickly. Or in other words, turbulence can accelerate
magnetic field dissipation.
Note that for infinite conductivity the dissipation
time becomes infinite as well, leading to
frozen-in fields.
dissipation of temperature variance For
scales smaller than the Batchelor scale temperature
fluctuations T ′ become extinguished by the