DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

are distinguished according to the nature of the
airmassesseparatedbythefront, thedirectionof
the front’s advance, and stage of development.
The term was first devised by Professor V. Bjerknes
and his colleagues in Norway during World
War I.
frontogenesis Processes that generate fronts
which mostly occur in association with the developing
baroclinic waves, which in turn are
concentrated in the time-mean jet streams.
frostpoint Thetemperaturetowhichairmust
be cooled at constant pressure and constant mixing
ratio to reach saturation with respect to a
plane ice surface.
Froude number A non-dimensional scaling
number that describes dynamic similarity in
flows with a free surface, where gravity forces
must be taken into consideration (e.g., problems
dealing with ship motion or open-channel
flows). The Froude number is defined by
Fr≡ U
√ gl
where g is the constant of gravity, U is the
characteristic velocity, and l is the characteristic
length scale of the flow. Even away from
a free surface, gravity can be an important role
in density stratified fluids. For a continuously
stratified fluid with buoyancy frequencyN,itis
possible to define an internal Froude number
Fri≡ U
Nl .
However, in flows where buoyancy effects are
important, itismorecommontousetheRichardson
number Ri = 1/Fr 2 i .
frozen field approximation If the turbulent
structure changes slowly compared to the time
scale of the advective (“mean”) flow, the turbulence
passing past sensors can be regarded
as “frozen” during a short observation interval.
Taylor’s (1938) frozen field approximation implies
practically that turbulence measurements
as a function of time translate to their corresponding
measurements in space, by applying
k=ω/u, wherek is wave number [rad m −1 ],ω
© 2001 by CRC Press LLC
“frozen-in” magnetic field
is measurement frequency [rad s −1 ], andu is advective
velocity [m s −1 ]. The spectra transform
by φ(k)dk =uφ(ω)dω from the frequency to
the wavenumber domain.
frozen flux If the conductivity of a fluid
threaded by magnetic flux is sufficiently high
that diffusion of magnetic field within the fluid
may be neglected, then magnetic field lines behave
as if they are frozen to the fluid, i.e., they
deform in exactly the same way as an imaginary
line within the fluid that moves with the fluid.
Magnetic forces are still at work: forces such as
magnetic tension are still communicated to the
fluid. With the diffusion term neglected, the induction
equation of magnetohydrodynamics is:
∂B
∂t
=∇×(u × B) .
By integrating magnetic flux over a patch that
deforms with the fluid and using the above equation,
it can be shown that the flux through the
patch does not vary in time. Frozen flux helps
to explain how helical fluid motions may stretch
new loops into the magnetic field, but for Earthlike
dynamos some diffusion is required for the
dynamo process to work. The process of calculating
flows at the surface of the core from
models of the magnetic field and its time variation
generally require a frozen flux assumption,
or similar assumptions concerning the role of
diffusion. See core flow.
“frozen-in” magnetic field A property of
magnetic fields in fluids of infinite electrical
conductivity, often loosely summarized by a
statement to the effect that magnetic flux tubes
move with the fluid, or are “frozen in” to the
fluid. An equivalent statement is that any set of
mass points threaded by a single common magnetic
field line at time t = 0 will be threaded
by a single common field line at all subsequent
times t.
It is a quite general consequence of Maxwell’s
equations that for any closed contour C that comoves
with a fluid, the rate of change of magnetic
flux contained within C is (cgs units)
d
dt =
E + 1
c V×B
· dx ,
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