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fault scarp

Fata Morgana A complex mirage made up of multiple images as of cliffs and buildings, distorted and magnified, which occasionally gives the impression of elaborate castles floating in the air. A Fata Morgana can only occur where there are alternating warm and cold layers of air near the ground or surface of water. Named after the effect seen in the Straits of Medina, and attributed to the sorcery of King Arthur’s halfsister, Morgan Le Fay.

fathom A nautical unit of depth, equal to 6 ft. It is also sometimes used for horizontal measure; a related unit is the cable, equal to 100 fathoms. Also, a nautical mile is approximately 1000 fathoms. See nautical mile.

fault A seismic fracture across which lateral motion occurs. In some cases a fracture is simply a crack in rocks where slip has occurred. Major faults may be broad zones of granulated rock (fault gouge) accommodating lateral motions of 1000 km or more. Faults can be classified as thrust faults, normal faults, or strike-slip faults.

fault constitutive law A representation of fault mechanical properties using relations among stress, strain rate, and displacement on fault planes. A variety of constitutive laws have been proposed such as the slip weakening model which represents the relation between shear stress and slip, and the rateand statedependent friction law which represents the relation between friction and slip accompanied by changes in slip rate. These are empirical laws derived from laboratory experiments of rock friction. There are two modes for friction: stable sliding and unstable sliding. It is thought that aseismic slips such as fault creep and slow earthquakes correspond to the former, while usual earthquakes correspond to the latter. Numerical simulations are being carried out to tackle problems of earthquake cycle and seismic nucleation process of large earthquakes, using the fault constitutive laws.

fault gouge The granulated material on a fault that has been generated during the many earthquakes that have occurred on the fault.

fault parameter Parameter that characterizes faulting. As a geometrical quantity, there is the strike of a fault plane, dip angle and slip direction, while as quantities which represent fault size, there is fault area (length times width) and the amount of slip. Furthermore, rupture velocity, rise time, and slip rate are physical parameters which represent source processes. From these fault parameters, seismic moment and stress drop can be calculated. These fault parameters can be obtained from radiation patterns of seismic waves, waveforms, and aftershock distributions.

fault plane solution An earthquake is generated by the relative motion of rocks across a fault. The movement has to be parallel to the fault plane, i.e., a vector representing the motion of one side with respect to the other will lie on the fault plane, and therefore there will be a plane normal to this vector (termed the “auxiliary plane”) that will be perpendicular to the fault plane. For the simplest type of earthquake

— simple movement along a flat fault plane, known as a “double-couple” earthquake — the pattern of radiation is divided into four lobes separated by the fault and auxiliary planes. The reason for this is that these planes divide the rock into areas in which the released stress is compressive or extensional, and thereby directions in which the first motions of the propagated radiation are compressions or rarefactions. With sufficient seismic data from around the world, it is possible to reconstruct the pattern of radiation for these first motions, and so to pick out the fault and auxiliary planes. This is known as the fault plane solution. Without other information it is difficult to tell which plane is the fault plane and which is the auxiliary plane, but local observations of the fault where the earthquake occurred or knowledge of the tectonic setting can help to determine this. The fault plane solution is invaluable in discriminating between different types of fault (e.g., thrust faults and transcurrent faults).

fault scarp When there is vertical movement on a fault during an earthquake, one side of the fault is elevated relative to the other. This is a fault scarp.

© 2001 by CRC Press LLC

F corona

F corona The Fraunhofer, or F, solar corona is generated by the diffraction of photospheric radiation by slow moving dust in the interplanetary medium. The contribution of the F corona to the total coronal white light emission becomes increasingly important beyond 2R . The Fraunhofer lines are clearly visible in the spectrum of this near-sun enhanced zodiacal light.

feeder beach A sacrificial beach; a region of placed sand intended to be eroded to benefit an adjoining area.

feldspar Metal aluminosilicate rocks with approximate specific gravity in the range of 2.5 to 2.76. The principal types are KAlSi3O8 (orthoclase), NaAlSi3O8 (albite), CaAl2Si2O8 (anorthite).

Fermat’s principle A ray of light or other radiation follows the path that requires the least time to travel from one point to another, including reflections and refractions that may occur. The similar statement holds for sound expressed in terms of ray acoustics.

fermion An elementary particle with internal angular momentum (spin) equal to an odd multiple of 21 h¯ where h¯ is Planck’s reduced constant, h¯ = 1.054571596x1034Js. Fermions obey the exclusion principle; their wavefunction is antisymmetric under interchange of particle position. Electrons, neutrinos, protons, and neutrons are fermions.

fermionic zero mode In field theory, the mass of fermions (spin 1/2 particles) is proportional to the value of a field (the Higgs field) to which they couple. A topological defect is a region of space inside which the Higgs field has a vanishing value. As a result, such fermions have effectively vanishing masses inside the core of the defect, and can travel at the velocity of light. Such fermions are called zero modes. Such string behavior may be very important in the early development of structure in the universe. See Higgs mechanism, Witten conducting string, Yukawa coupling.

Ferrel cell Eddy-driven midlatitude zonal mean circulation cell in the atmosphere. See Hadley circulation.

fertile mantle Mantle rock that includes a basaltic component.

fetch A linear distance across a body of water over which the wind speed and direction may be assumed to be reasonably constant.

FG Sagittae star Member of a very small class of variable stars which has just experienced the last flash of helium burning on the asymptotic giant branch. This causes the star to change its color and brightness very quickly. In addition, the last hydrogen is likely to be lost from the surface and carbon mixed into the visible atmosphere. FG Sagittae stars probably evolve to R Coronae Borealis stars.

fibril A linear pattern in the Hα chromosphere of the sun occurring near strong sunspots and plage or in filament channels. Fibrils are similar in appearance to spicules except that they are bent over and extend along the solar surface at a height of about 4000 km rather than protruding radially outwards. They have lengths typically 15000 km with a thickness of 2000 km and exhibit axial proper motions 20 to 30 kms1.

Fickian flux (Fick’s law) The statement that the flux J of a diffusing substance is proportional to the concentration gradient, i.e., J = −D( xC) where D is called the diffusion coefficient. Often written in 1-dimensional form: JC = −DC∂C/∂x. While the first Fickian law is well suited for molecular diffusivities DC, it is in fact often invoked as the first-order closure scheme for turbulent fluxes. The turbulent flux for this so-called eddy-formulation is Ji = −Ki∂C/∂xi, where Ki is the turbulent diffusivity in direction i. This first-order closure scheme collapses if the eddies get very large and the local gradients are too small (non-local diffusion, see Stull, 1988).

Fick’s second law The rate of change of a property C is given by the divergence of all the fluxes (JC) and all sinks and sources C)

© 2001 by CRC Press LLC

field ordering

of C. The conservation equation ∂C/∂t = −div(JC)+λC is often referred to as the second Fickian law.

field A mathematical construct that represents physical interactions as spread through space and time. Any quantity that can be defined at every point of (a region of) space (or spacetime) can be defined to be a field. Classical examples include the electromagnetic and the gravitational field.

field capacity (θf c) The maximum amount of water in the unsaturated zone of the soil that can be held against the pull of gravity.

field line motion A theoretical formalism that helps visualize the effects of electric fields and varying magnetic fields on the plasma they permeate. In a magnetic field B, it ascribes to each point a velocity v that satisfies B/∂t

× (v × B) = 0.

If the field is embedded in a highly conducting fluid (e.g., the molten metal in the Earth’s core) or in a collision-free plasma (such as is found in space around Earth), the bulk flow velocity v of the fluid or plasma in general comes close to satisfying the MHD condition E = −v × B, where E is the ambient electric field. By Maxwell’s equations, the curl of this is the equation defining field line motion; hence, the fluid or plasma moves with the field lines.

In a collisionless plasma the MHD condition is related to the electric drift of the plasma. In all such cases, two particles of the fluid or plasma which initially share the same field line continue doing so as time advances. It should, however, be noted that this is only the motion perpendicular to field lines: in addition, the fluid or plasma may also slide along field lines.

Field line motion helps intuitive understanding of plasma motions. In limiting cases where the motion dominates the magnetic field — e.g., the solar wind which is known to move (more or less) radially — field line motion provides a shortcut to calculating the magnetic field B, given the sources of B on the sun. On the other hand, if B completely dominates the plasma (e.g., where it is very rarefied), if we know the way B changes (i.e., B/∂t), the observed field

line structure can help derive the bulk flow velocity v.

field of view The angular size of the full image formed in an optical instrument; the angular separation of two points that lie at the edges of the optical field.

field ordering In condensed matter physics, when the temperature of a ferromagnet goes below the critical point, Tc, a non-zero magnetiza-

tion develops. The rotational symmetry pre-

M

viously possessed by the system is then broken due to the presence of a preferred direction, the

one fixed by . The value of , zero for the

M M high-temperature phase and non-zero for temperatures below Tc, plays the role of the order parameter of the phase transition.

In cosmological transitions, the role of the order parameter is played by the vacuum expectation value of the Higgs field (here denoted φ). Standard topological defects (like monopoles, walls, strings) involve regions in space where this order parameter remains in the high-temperature symmetric phase (vanishing φ). In this case the field potential energy (the false vacuum trapped inside the defect) is the main source of the energy associated with the defects.

There are, however, other types of defects where the bulk of energy is concentrated not as potential energy but in spatial gradients. Cosmic textures are one example of this. They have the property that the broken-symmetry phase vacuum manifold M of the order parameter φ has the same dimension as space (equal to three, for cosmological applications), and this allows φ to always stay on M, regardless of the location considered. Hence, possessing no potential energy, all the relevant dynamics comes from the ordering of this field φ, that is from the tendency to minimize its gradients.

Texture knots will shrink (instability to collapse) as explained by the Derrick theorem. This will result in the ordering field becoming increasingly tightly wound in the vacuum manifold. Then the spatial gradients (kinetic energy terms) in the configuration will eventually become so high as to be able to exceed the energy of the symmetric state and unwind the knot.

© 2001 by CRC Press LLC

figure of the Earth

See cosmic topological defect, Derrick theorem, spontaneous symmetry breaking.

figure of the Earth The shape of the Earth. To a first approximation it is an oblate spheroid with a polar radius of 6357 km and an equator radius of 6378 km.

filament A structure in the corona consisting of cool ( 7000 K), dense ( 1012 cm3)

plasma supported by magnetic fields and seen as dark lines threaded over the solar disk. When seen in emission at the solar limb, a filament appears as a protuberance: a bright arc of matter extending high above the photosphere, spanning latitudes of up to some 10. Their density is about a factor of ten higher than the ambient density (therefore the arc is bright when seen above the solar limb), and the filament can extend up to about 100 times the scale height in the corona. Filaments are aligned along the separation of opposing magnetic field patches in the photosphere. Their existence therefore is related to solar activity with only a few filaments observed during solar minimum and a much larger number during solar maximum. Filaments can have very long lifetimes, lasting 2 to 3 solar rotations in some cases. They are found, preferentially, in two latitude belts on the sun; in a strip at high latitudes known as the polar crown and in active mid-latitudes. Typical magnetic fields are 5 to 10 G in quiescent filaments and may be as high as 200 G in active region filaments fields.

The cold end dense matter of the filament/protuberance is held against gravity by magnetic tension in the anchoring magnetic field lines. Two configurations can be distinguished by comparing the photospheric magnetic field pattern with that of the filament:

1.Kippenhahn–Schlüter configuration, also called normal configuration: the magnetic field inside the filament has the same direction as the photospheric field below it.

2.Raadu–Kuperus configuration, also called inverse configuration: the magnetic field inside the filament is directed opposite to the one in the photosphere. This is possible only because the anchoring field lines have a neutral point below the filament. In particular, in large and highrising filaments, which tend to give rise to coronal mass ejections, the Raadu–Kuperus configu-

ration seems to be the dominant one. This is attributed to the X-point below the filament where reconnection is likely to occur, leading to the expulsion of the filament (coronal mass ejection) and the generation of electromagnetic emission due to the accelerated electrons (the flare). See coronal mass ejection, reconnection.

filament channel A broad pattern of fibrils in the chromosphere, marking where a filament may soon form or where a filament recently disappeared.

filter layer In civil or coastal engineering, denotes a layer of material (typically stone, gravel, or sand, possibly combined with a geotextile fabric) intended to prevent migration of fine material into or out of a structure. May also be employed to reduce settlement. As an example, breakwaters are often built with a filter layer in the base to help prevent scouring and settlement.

finestructure In atmospheric dynamics, structures with scales from tens of meters to decimeters, covering the processes of internal waves and intrusions. Finestructure processes are intermediary between the large-scale (overall stratification) structures and the small-scale (turbulence).

fine structure constant Dimensionless constant relating to strength of electromagnetic interactions:

α = e2/ (4π 0hc¯ ) = 7.297352533(27)×103 .

fingering See double diffusion.

finger regime The double-diffusive regime, where temperature stabilizes and salinity destabilizes (i.e., warmer and saltier water is on top of cooler and fresher water). In this case, the non-dimensional stability ratio is defined as

Rρ = (α∂ /∂z)/(β∂S/∂z). The term “finger” refers to the saltier finger-like plumes driving the double-diffusive convection. Classical locations of the finger regime are under the Mediterranean Outflow, in the East North-Atlantic and the C-SALT field east of Barbados.

© 2001 by CRC Press LLC

first order phase transitions

finite amplitude wave A wave of finite amplitude. In oceanography, a wave of finite height. All waves are finite amplitude, but the simplest water wave theory (linear wave theory) assumes waves of infinitesimal wave height. A variety of finite amplitude (higher order) wave theories are available for water and other wave phenomena.

finite difference A method of approximating functions by specifying values on a specified grid of points, and approximating derivatives by taking algebraic differences of the values on the points. For instance, the expression

[f (x + δ) f (x δ)]/(2δ)

is an approximation of the first partial derivative with respect to the coordinate x, where the points along the x axis are separated by distance δ.

finite element method A numerical method used to solve partial differential equations. In the finite element method, the spatial domain is divided into a set of non-overlapping elements. Neighboring elements share nodal points along their common boundaries. By approximation, an unknown variable inside an element is interpolated from values at the nodal points of the element using a set of interpolation functions. A numerical solution subject to given initial and boundary conditions is obtained by solving for all nodal values in the domain.

fireball An aerial display associated with a meteor that reaches a brightness greater than that of the full moon. Applied often to any bright meteor.

firehose instability Instability of a thermally anisotropic collisionless plasma, associated with an excess of pressure parallel to the magnetic field. The nonrelativistic condition for instability is (cgs units)

4π

1 + B2 P P $ < 0 ,

where B is the mean magnetic field strength, P and P are, respectively, the pressures transverse and parallel to the mean magnetic field, and

$= 1 ρα ('Vα)2 .

ρα

ρα is the mass density of charge species α and 'Vα is its relative velocity of streaming relative to the plasma.

$ is effectively an enhancement of P due to intraspecies streaming.

first fundamental form The metric g on a space or spacetime M. (Perhaps as induced from a higher dimensional space N if Mis embedded in N.)

first integral A quantity that is constant for a particular motion (depending on the initial conditions) because the differential equations describing a system allow a partial analytic integration.

first law of thermodynamics The conservation of energy:

dQ = dU + pdV

where dQ is an amount of heat input, dU is a change in the internal energy of the system, and pdV is the work done.

first order phase transitions For firstorder transitions in cosmology, which may for instance lead to cosmic defects (strings, monopoles, domain walls . . . ) at very high energies the symmetry breaking potential has φ = 0 as the only vacuum state, i.e., the only minimum of the potential. When the temperature goes down to below the critical temperature Tc, a set of different minima develops, a potential barrier separating the old (false) and the lower energy new (true) vacua. Provided the barrier at this small temperature is high enough, compared to the thermal energy present in the system, the field φ will remain trapped in the false vacuum state even for small (< Tc) temperatures.

Classically, this is the complete picture. However, quantum tunneling effects can liberate the field from the old vacuum state, at least in some regions of space: there is a probability per unit time and volume in space that at a point x a bubble of true vacuum will nucleate. The result is the formation of bubbles of true vacuum with the value of the Higgs field in each bubble being independent of the value of the field in all other bubbles. This leads to the formation of domains (the bubbles) where

© 2001 by CRC Press LLC

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