DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

critical level
they are recorded from ionograms with a frequency,
rather than electron density, scale. See
ionogram, plasma frequency.
critical level A level at which the mean flow
speed is equal to the wave speed.
critical phenomena in gravitational collapse
Discrete scaled-similar, or continuous scaledsimilar
behavior in the gravitational collapse of
physical fields, near the threshold of black hole
formation. Discovered by Choptuik in 1993.
critical point In an expanding flow, the location
of a transition from subsonic to supersonic
flow. The concept of the critical point plays a
centralroleintheoriesoftheexpansionofthesolar
wind. The term is frequently generalized to
refer to a point of transition through the Alfvén
speed or the fast or slow magnetoacoustic wave
speed.
critical temperature In thermodynamics,
theupperlimitingtemperatureatwhichagascan
be forced to condense (to a liquid or a solid) by
compression at constant temperature. For water,
the critical temperature is 374 ◦ C. The corresponding
pressure is 221 bar. In superconductors,
it is the temperature above which the superconducting
behavior disappears. In a permanent
magnet, it is the temperature above which the
magnetism disappears. Also called Curie point.
In symmetry breaking particle theories relevant
to early universe cosmology, the critical temperatureTc
for a particular model separates temperature
zones in which the effective potential has
very different qualitative features. For temperatures
above Tc, simple potentials will have the
form of a generalized paraboloid, with its minimum
attained for a vanishing field. However,
at temperatures belowTc, a degenerate space of
minima develops (e.g., as in the “Mexican-hat”
potential) and the field, in trying to minimize its
potential energy, will select one of these minima,
hence breaking the symmetry previously
possessed by the system. See cosmic phase transition,
Kibble mechanism, spontaneous symmetry
breaking.
© 2001 by CRC Press LLC
criticalvelocity Thevelocityoftheflowinan
open channel corresponding to a Froude number
of unity. See critical depth.
cross helicity One of the quadratic invariants
occurring in the theory of hydromagnetic turbulence.
The cross helicity within a volume V is
defined as
HC = V ·Bd 3 x,
where V is the velocity, B is the magnetic field,
and the integral is taken over V. In an incompressible
dissipation-free fluid, for suitable
boundary conditions, HC is conserved. In fully
developed three-dimensional dissipative hydromagnetic
turbulence, the cross helicity, as well
as the energy, cascades from large eddies down
to smaller eddies where dissipation can occur.
See helicity, hydromagnetic turbulence, magnetic
helicity.
cross-section Any of several quantities with
units of area, which describe the interaction of
an object with an incident flux of particles or of
radiation.
cross-shore Perpendicular to the general
trend of a coastline. A beach profile represents
a slice through a beach in the cross-shore direction.
cross slip Refers to the manner of dislocation
motion. With Burgers vector parallel to the
dislocation line, screw dislocations are not tied
to specific slip planes, and they can move from
one plane to another intersecting plane which
contains the same Burgers vector. This is called
cross slip. Cross slip is an important mechanism
of deformation at high temperature, and it
is involved in the way recovery takes places.
cross waves Waves in an open channel which
propagate across the channel, normal or nearly
normal to the direction of flow.
crust The outermost layer of a differentiated
solid-surfaced body; on Earth, the outer layer of
the solid earth, above the Mohorovicic discontinuity.
Its thickness on Earth averages about
35 km on the continents and about 7 km below
the ocean floor. The crust is composed