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TOPEX/POSEIDON

stability condition Qs(r) ≡ σR(r)κ(r)/3.36G(r) > 1 and the single unstable wavelength in the√Qs(r) = 1 stellar disk λ (r) = (2π × 3.36/ 0.948)G (r)/κ2(r) can be derived from a dispersion relation for axisymmetric perturbations in a differentially rotating stellar disk with the local radial velocity dispersion

σR(r).

TOPEX/POSEIDON A cooperative project between the U.S. and France to develop and operate a satellite dedicated to observing the Earth’s oceans. Since its launch in 1992, this satellite has used an advanced radar altimeter to measure sea surface height over 90% of the world’s ice-free oceans. By determining the orbit of the spacecraft to within a few centimeters, the project has produced global maps of ocean topography significantly more accurate than any previous satellite altimeter. A second goal of the project was the production of accurate global tide maps. Consequently, the TOPEX/POSEIDON orbit was designed to avoid the aliasing of the solar tides into undesirable frequencies, and this repeat orbit covers the globe every 10 days. See also satellite altimetry.

Top hat detector A toroidal-geometry focusing detector for low energy ions and electrons (e.g., 100 to 30,000 eV) widely used in magnetospheric research. It gives high counting rates and uses fast electronic circuits to sort particles by their time of flight through the instrument.

topocentric system This spherical coordinate system (range, altitude, azimuth) serves to specify a direction in space relative to the local horizontal, vertical, and North, as well as the distance from the location of the observer. See altitude, azimuth, zenith, zenith angle, nadir.

topographic wave An orographic wave; a wave in moving air driven by irregularities in the surface topography of the Earth.

topography The elevation of the Earth’s surface above sea level. Topography is created by active mountain building processes and is destroyed by erosion.

topological defect See cosmic topological defect.

topology of space The set of properties of a space that can be established without using the notion of distance. Two spaces are said to be topologically equivalent if one of them can be obtained from the other by stretching, squeezing, and any other deformation that does not involve disruption or gluing points together. For example, the outer surface of an open bottle is topologically equivalent to the top surface of a coin. However, the surface of a bicycle tube is not topologically equivalent to the coin-surface. The topology of the space we live in is usually imagined to be that of the Euclidean space, i.e., infinite in every direction, with no identification of points. However, general relativity and Einstein’s equations allow more complicated topologies. The simplest (e.g., Robertson–Walker) solutions to Einstein’s equations for cosmology admit 3-spaces that are Euclidean, or 3-hyperboloidal, or 3-spherical. More complicated spaces are admitted; for example, cosmological space could be that of a three-torus, a three-dimensional analog of the bicycle tube surface, which has the property that it can be circled around in three different directions after covering only a finite distance. The attractive feature of such a space (called a “small Universe”) would be that, given a sufficiently long but finite time, all of matter existing in the universe would come into view of every observer. Whether our real universe is small is a question that is in principle decidable by (very difficult) observations.

tornado An intense cyclonic wind (windspeeds up to 450 km/h) in contact with the ground and locally associated with a thunderstorm. Most frequently occurring in summer and the early autumn in the midwestern U.S. and in Australia. Typically characterized by a funnel-shaped condensation cloud extending toward the ground, though simply a debris cloud beneath a thunderstorm is evidence of a tornado.

torque The product of a force F times the lever arm from a fulcrum, measured perpendic-

© 2001 by CRC Press LLC

transcurrent (transform) plate boundary

ular to the direction of the force.

torque τ = r × F ,

where × denotes the vector cross product. τ is a pseudovector, with direction given by the right-hand rule: right-hand fingers in direction of r, curl fingers toward F, thumb then points in direction of τ. Its magnitude is

|τ| = |r | |F| ,

where |r| is the perpendicular distance from the origin, or which is equivalent to

|τ| = |r||F| sin θ ,

where θ is the angle r makes with F.

torsion A tensor quantity expressing the fact that covariant derivatives do not commute when applied to a scalar function:

α β f − β αf = Tαβσ σ f .

Here α is the covariant derivative along basis vector α, and Tαβσ are the components of the torsion tensor. In the formalism of general relativity, the torsion vanishes. See covariant derivative.

torsional oscillation A type of motion thought to occur in the Earth’s core, where the flow is akin to the solid body rotation of cylinders coaxial with the Earth’s rotation axis about that axis. The flow would be of this form if the density in the core were constant; however, in the real Earth, rather than the azimuthal component of velocity uφ, it should be the azimuthal component of momentum ρuφ (where ρ is the density) that is constant on these cylinders. Different cylinders rotate at different speeds, stretching any magnetic field that links cylinders, which generates a torque resisting the motion through the tension in the magnetic field. This torque on the cylinders causes an acceleration, which leads to oscillations. In the real Earth, such motions would be superimposed upon a much more slowly evolving “basic state”, likely a flow in a magnetostrophic balance. There is observational evidence of oscillatory flows at the surface of the core with the

spatial form of torsional oscillations with periods of around 75 years, although these oscillations seem to be fairly heavily damped, perhaps by resistive coupling at the core-mantle boundary. See core flow.

total electron content (TEC) The total number of free electrons in a unit area column from the ground to a height well above the level of peak ionization. The units are electrons m−2 and 1 TEC unit = 1016 electrons m−2. Typically, TEC varies from 1 to 200 TEC units. The TEC is usually measured by observing the transmissions along a slant path to a satellite. The slant TEC is then converted to a vertical TEC by using a geometric correction and assuming that the ionosphere is a thin shell about the Earth. The TEC can be used to provide estimates of Faraday rotation and time delay on transionospheric propagation paths.

total radiance mean cosine The average cosine of the polar angle of all photons; it equals the ratio of the net plane irradiance to the total scalar irradiance.

towards polarity The condition in interplanetary space when the local magnetic field lines, when followed to the sun, point toward it. See interplanetary magnetic sector, away polarity.

tracers Identifiable substances or sets of ocean properties that do not affect the density of sea water. Tracers have no impact on water movement but can be used to infer currents. In addition to the classical tracers (oxygen and nutrients), oceanographers use tracers introduced or enriched by human activity, such as carbon, cesium, chlorofluorocarbons, plutonium, strontium, and tritium.

traction A method of transporting material by pushing, rolling, or sliding that material across a surface. The forces causing traction to occur are usually the result of eolian and/or fluvial processes. Traction is the primary mode of transport for particles larger than about 2 mm in diameter.

transcurrent (transform) plate boundary

The boundary, which is a strike-slip fault or a

© 2001 by CRC Press LLC

transform boundary

shear zone, between two lithospheric plates that both move parallel with the boundary but in opposite directions.

transform boundary Represents the boundary where two plates slide past each other. This boundary is characterized by strike-slip faulting and can be a left-lateral or a right-lateral fault, depending on the movement of the plates involved. A transform boundary is characterized by shallow earthquakes but no volcanic activity. An example of a transform boundary is the San Andreas Fault which runs through California.

transform fault When two surface plates slide past each other, the fault on which this occurs is a transform fault. A transform fault is also a strike-slip fault. An accretional plate margin is made up of an orthogonal pattern of spreading centers (ocean ridges) and transform faults. The San Andreas fault is an example of a major transform fault. Transform faults are usually very active seismically.

transform push Normal force that one lithospheric plate exerts on another plate across a transform plate boundary.

transient shock Shock propagating through a medium, either as a blast wave shock or as a driven shock in front of an obstacle moving faster than the local signal speed of the medium. Transient shocks are also called traveling shocks; examples are the super-sonic bang in front of an aircraft, or the shock piling up in front of a fast coronal mass ejection or a fast magnetic cloud.

transitional depth A water depth between shallow water and deep water. The term depth, as used here, is a relative term and denotes actual depth divided by wavelength.

transition region In solar physics, the thin (some hundred kilometers) layer in the solar atmosphere at a height of a few thousand kilometers above the photosphere, where the temperature increases quickly from about 6000 K to more than 105 while the density drops by about one order of magnitude, and the collision times increase by more than four orders of mag-

nitude. Thus, below the transition region, the solar plasma basically behaves like a gas with the bulk motion of the plasma carrying around the frozen-in magnetic field, while above the transition region collisions are rare, and the magnetic field determines the particle motion. It is observed mainly in EUV emission lines between 104 and 106 K.

transition region and coronal explorer (TRACE) A NASA funded spacecraft launched in April 1998. It explores the magnetic field in the solar atmosphere by studying the 3- dimensional field structure, its temporal evolution in response to photospheric flows, the timedependent coronal fine structure, and the coronal and transition region thermal topology. TRACE has a spatial resolution of 1 arcsec (700 km).

translatory wave A wave that exhibits a net motion, as opposed to a standing wave.

transmission coefficient In essentially 1- dimensional wave motion, a (complex) dimensionless parameter giving the ratio of the transmitted wave (amplitude and phase) at some barrier, to the incident wave. In some contexts, the term is used to mean the absolute value (modulus) of this quantity. For instance, in water wave descriptions, the meaning is the ratio of a transmitted wave height to the corresponding incident wave height. Used to describe the effectiveness of a coastal structure, such as a breakwater for reduction of wave height.

transmissivity (T ) A measure of the ability of a saturated aquifer of thickness b and hy-

draulic conductivity K to transmit water:

 

2T =

Kb, with units of square meters per day [L

/T].

transonic string model

See elastic

string

model.

 

 

 

transparency The degree of lack of absorption of a wavelength of interest as light traverses the atmosphere from the source to an Earthbased detector, or as light traverses any semitransparent medium.

transpiration The process whereby plants give off water vapor through their leaves back

© 2001 by CRC Press LLC

trench

to the atmosphere, via absorption of soil water by plant roots and translocation through the vascular system to stomata in the leaves, where evaporation takes place.

transverse Doppler shift A shift arising because of the Doppler effect when a photon is emitted from a source moving perpendicularly to the line of sight. The transverse shift is not present in the classical Doppler effect (where a frequency shift is possible only if there is a nonzero component of the velocity along the direction of emission of the photon). It is a purely special relativistic effect that arises because of time dilatation, i.e., because the observer in a different frame measures a different time interval than an observer co-moving with the source.

transverse wave Wave propagation in which the associated local forces or motions are perpendicular to the direction of the wave. In materials supporting shear (such as elastic metals or rock), mechanical waves (called shear waves) can propagate with transverse modes. In electromagnetism, propagating fields (e.g., light, X-rays, radio waves) are transverse in that they propagate magnetic and electric fields that are perpendicular to the direction of propagation. Gravitational radiation in general relativ- ity induces relative motions between test particles that are perpendicular to the direction of propagation. Hence, gravitational radiation as described by general relativity is a transverse wave.

trapped surface A C2 space-like twosurface T , such that the two families of null geodesics orthogonal to T are converging at T . A closed trapped surface is a compact trapped surface without boundary. See apparent horizon, future/past event horizon.

traveling ionospheric disturbance (TID)

Traveling ionospheric disturbances, or TIDs, are readily observed on ionograms and in a variety of observations from other systems depending on reflections from the ionosphere. The TID is due to an atmospheric gravity wave traveling in the neutral atmosphere. The wave moves the neutral atmosphere, which in turn moves the ionization. TIDs can be relatively large-scale

structures in the F region, with horizontal wavelengths of the order of 100 to 1000 km traveling with speeds between 50 m s−1 and 1000 m s−1, and have periods of minutes to more than 1 h. Some, often the faster large scale TIDs, are associated with magnetic storms and originate in the auroral zone. These may travel great distances. Others appear to be more localized, possibly originating in the troposphere or lower E region. TIDs appear as a rippled electron density surface to a radio wave and can cause focusing and defocusing if the TID wavelength is greater than the beamwidth. Thus, TIDs can give rise to fading in radio systems and misleading angle of arrival measurements. See F region.

travel time curve A plot of the arrival time of a seismic phase as a function of distance of the receiver from the source. A single graph may contain many such curves representing the arrival of different seismic phases. The distance between the seismic station and the source is commonly quoted in terms of the angle subtended by the two from the center of the Earth, 5. Not all phases will be observed at all 5, because in some places within the Earth wave velocity decreases with depth, causing rays to refract around a shadow zone, and some waves may be entirely blocked. The Earth’s outer core causes both of these effects, blocking the passage of S waves, because the fluid outer core is unable to support shear waves on seismic timescales, and causing P waves to refract around a shadow zone because the P wave velocity is much reduced. If the wave speed within a depth range strongly increases with depth (as in the transition zone), then the resulting refraction patterns may cause a triplication, i.e., a phase may be observed at a particular 5 at three different times corresponding to the arrival of waves at three different takeoff angles that are refracted to arrive at the same site.

trench Generally refers to trenches on the sea floor. These are deep valleys also known as subduction zones. The oceanic lithosphere bends and descends into the interior of the Earth at ocean trenches.

Also, the bathymetric low at a subduction zone, related to the flexure of the subducting plate.

© 2001 by CRC Press LLC

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