DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

Taylor’s hypothesis
number. Its value depends on the length scale
of the convective system, the rotation rate, and
kinematic viscosity. The Taylor number Ta is
Ta =(2ωU) 2
/ ν U
H2 2 = 4ω 2 H 4 /ν 2
whereH is depth of fluid, is rotational angular
velocity, ν is kinematic viscosity, and U is a
typical velocity. If Ta is equal or greater than
one, the rotational effects are significant. See
Taylor instability for a slightly different form
for Ta.
Taylor’s hypothesis See frozen field approximation.
Taylor state A configuration of magnetic
field in a conducting, rotating fluid so as to
obey the constraint that the azimuthal component
of the Lorentz force integrates to zero over
the surface of cylinders coaxial with the rotation
axis. This can be true for fluid in a magnetostrophic
balance, i.e., balance of magnetic,
pressure, buoyant, and coriolis forces, which
may hold for the Earth’s outer core if viscosity
and inertia are both small. Taylor’s constraint
holds for a magnetostrophic flow if it is anelastic
(i.e., ∇·(ρu) = 0 whereρ is the density and u
the flow velocity) and if the gravitational force
has no azimuthal (φ) component (or, at minimum,
ρgφ also integrates to zero on the cylinder).
The constraint may be written as:
T=s [(∇ ×B)× B] φd= 0
where s is the distance from the rotation axis,
B is the magnetic field, and denotes the axial
cylinder. Neither inertia nor viscosity are
identically zero in the Earth’s outer core, and
it has been suggested that the Taylor torque T
may be balanced by viscous forces acting on the
cylinder at the core-mantle boundary, such as in
Braginski’s Model-Z dynamo. However, even
in this case in the limit of vanishing viscosity,
the above constraint is asymptotically satisfied.
The effect of non-zero inertia is that a non-zero
Taylor torque is balanced by a term representing
acceleration, which leads to torsional oscillations.
The net result is a “basic state” satisfying
the above constraint with superimposed
torsional oscillations.
© 2001 by CRC Press LLC
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TCB See coordinate time.
TCG See coordinate time.
TDB See dynamical time.
TDT See dynamical time.
tectonics The study of the large scale movements
and deformation of a planetary crust.
Planetary crusts are affected by extensional
and compressional forces caused by regional
or global processes. The lunar maria display
compressional features in their centers and extensional
features along their edges, caused by
subsidence of the dense lava flows which comprise
the maria. Mercury is shrinking due to the
cooling and solidification of its large iron core,
which is creating compressional tectonics on its
surface. The icy moons of the outer solar system
display extensional tectonics due to the cooling
and solidification of the ice in their interiors.
Earth’s crust is in a constant state of flux due to
the influence of plate tectonics, which causes
large segments of the crust to move. There
is evidence from satellite magnetometer measurements
of former surface tectonic activity on
Mars.
tectosphere A layer of rock up to several
hundred kilometers thick at the top of the mantle
underlying some of the continents, which
has been observed by seismology to be distinct
(perhaps colder) than the rest of the upper part
of the mantle, i.e., as “continental roots”. The
tectosphere is thought to be relatively viscous
and tightly coupled to the overlying continent,
which implies that it is important for determining
how the motions of the continent are coupled
to those in the underlying mantle. There
are different ideas as to how tectosphere may be
formed, including simple cooling of relatively
immobile mantle underlying a continental plate
and the buildup of buoyant by-products of slab
subduction.
Telesto Moon of Saturn, also designated
SXIII. Discovered by Smith, Reitsema, Larson,
and Fountain in 1980, it orbits Saturn in the same
orbit as Tethys, but leading it by 60 ◦ . This is one
of the two stable Lagrange points in the Saturn–