DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

F star
where E and B are the electric and magnetic
fields, V is the fluid velocity,c is the (vacuum)
speed of light, and the integral is taken about
the contour C. In fluids of infinite electrical
conductivity (and for that matter, to an excellent
approximation in most situations involving
collisionless plasmas)
so that
E + 1
V ×B = 0 ,
c
d
dt
= 0 .
When this condition is satisfied, the magnetic
flux through any closed contourC that co-moves
with a fluid is constant; it is in this sense that
magnetic flux tubes may be considered to “move
with a fluid”. This result is sometimes called
Alfvén’s theorem.
F star Star of spectral type F. Canopus and
Procyon are F stars.
Fukushima’s theorem In two articles in
1969 and 1976, Naoshi Fukushima showed that
the main contributions to the magnetic field, observed
on the ground from field aligned currents
which flow in and out of the Earth’s ionosphere,
tended to cancel (the mathematical principle
might have been known before, but was not
applied to the ionosphere). He showed that with
a uniformly conducting spherical ionosphere,
linked to infinity by straight conducting filaments
(an idealization of the actual geometry),
thereisnomagneticeffectbelowtheionosphere.
It explained why the main magnetic effect seen
on the ground comes from secondary currents,
the Hall currents which form the auroral electrojets.
fully arisen sea A sea condition whereby
continued energy input by wind will not increase
wave energy.
fully rough flow Hydrodynamic flow near a
boundary in which the Reynolds number computed
using the typical surface irregularity scale
ɛ as the length exceeds approximately 100:
© 2001 by CRC Press LLC
186
uɛ/ν ≥ 100
where u is the velocity and ν is the kinematical
viscosity. See kinematic viscosity, Reynolds
number.
fulvic substance In oceanography, high
molecular weight organic compounds resulting
from plant decay, especially phytoplankton. See
colored dissolved organic matter.
fundamental tensors of a worldsheet A cosmic
string is a type of cosmic topological defect
which may play a role in producing the structures
and features we see in our present universe.
It can be conveniently described as long
and infinitely thin, but a line evolving in space
and time and describing a two-dimensional “surface”
called a worldsheet, whose evolution is
known provided one knows its dynamics and
its geometry. Fundamental tensors provide the
knowledge of the worldsheet geometry, while
the equation of state allows one to compute its
dynamics.
The position of the worldsheet in spacetime
requires knowledge of its coordinates x µ (ℓ, τ)
depending on two variables internal to the
worldsheet: a curvilinear space coordinate ℓ
and a time τ, denoted collectively as ξa. One
can define a 2 × 2 induced metric γab on the
string worldsheet, using the spacetime metric
gµν, through
∂x
γab = gµν
µ
∂ξa ∂xν ,
∂ξb with inverse γ ab . Then the first fundamental
tensor of the worldsheet is
η µν ab ∂xµ
= γ
∂ξa ∂xν .
∂ξb The surface spanned by the string in spacetime
is curved in general. This is quantified by
the second fundamental tensor K ρ
µν which describes
how the 2-dimensional sheet is embedded
in spacetime, and is calculable by means of
the covariant derivative in spacetime ∇µ
with symmetry
K ρ
µν = ησ µ ηα ν ∇αη ρ σ ,
K ρ
µν
ρ
= Kνµ , and trace
K µ α µ
= K
α .