DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

special relativity, such a vector has zero length
even though its components are non-zero. In
psuedo-Reimannian geometry, an element ℓ of
a linear space with metricg such thatg(ℓ,ℓ) ≡
gabℓ a ℓ b = 0.
numerical cosmology (computational cosmology)
The technique, and a collection
of models of the universe obtained by solving
Einstein’s equations numerically. Because
they proceed in terms of discretization, these
models are approximate, but well-formulated
models show a convergence as the discretization
is refined. For reasonable resolution in
3-dimensional simulations, large computers are
required.
numerical model A set of discretized mathematical
equations, solved on a computer, which
represent the behavior of a physical system.
numerical relativity The study and solutions
of the differential equations of general relativity
by discretization of the equations and the computational
solution of the resulting finite algebraic
problem. In many cases without overall
symmetry, analytic methods fail and numerical
relativity is the only method to elucidate and understandgenericsolutionsforspacetimesingeneral
relativity. Computational simulation has
become a real research tool, for instance, the
critical behavior and naked singularity found by
Choptuik. Similarly, the naked singularity that
may exist in some circumstances at the center of
the Lemaître–Tolman cosmological model was
first identified in numerical calculations. Numerical
investigations have amassed considerable
knowledge about problems too complicated
for analytical treatment: collisions of rotating
black holes, emission of gravitational waves
by rotating nonsymmetric bodies or by binary
systems, collapse of a binary system to a single
body, etc. See binary black holes, critical
© 2001 by CRC Press LLC
nutation
phenomena in gravitational collapse, gravitational
wave.
Nusselt number A dimensionless number
quantifying the efficiency of heat transfer in a
convecting system. It is the ratio of total heat
flux to the conductive heat flux. For example,
the conductive heat flux across a uniform layer
of thickness h with differential temperature T
is λT /h. If the total heat flux including convective
heat transfer is q, the Nusselt number in
this case is
q
Nu =
λT /h .
nutation This is a variation of the orientation
(the obliquity) of the Earth’s axis of rotation associated
with the Earth’s forced precession. In
the theory of the rapid rotation of a rigid body,
it is used to imply an analog of the free (i.e., unforced)
precession of a body in the case where
there is also a forced precession, which causes
the body’s axis with the largest principal moment
of inertia to “nod” backwards and forwards
even as it is precessing. On Earth, this effect is
known as the Chandler wobble, and the term nutation
may also refer to motions due to the fact
that the Earth is deformable and its layers imperfectly
coupled, as well as motions caused by
time variations in the torque acting on the Earth.
This happens because the couple is produced
by the tidal interactions with the moon and sun,
which vary because the relative orientations of
the Earth, moon and sun change with time in various
different ways. There are nutations at various
periods, the largest nutation being at 18.6
years. Nutation is one of the contributors to the
Milankovich cycles which cause climatic variations.
In the case of the Earth, nutation causes
the obliquity to vary from 21 ◦ to 24 ◦ (the current
value of Earth’s obliquity is 23.5 ◦ ) over a period
of 41,000 years. See precession.
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