Fraunhofer lines

where M is the mass of the central body, and v is the velocity of the body in its orbit. For a 650-km altitude orbit around the Earth, this contribution is of order 6.6 arcsec/year.

Proposed space experiments would measure the orbital dragging (LAGEOS-III experiment) and the gyroscope precession (Gravity Probe B, GPB).

In strong field situations, as in close orbit around (but still outside) a rotating black hole dragging is so strong that no observer can remain at rest with respect to distant stars.

Fraunhofer lines Absorption lines in the solar spectrum (first observed by Fraunhofer in 1814).

free-air correction A correction made to gravity survey data that removes the effect of the elevation difference between the observation point and a reference level such as mean sealevel. It is one of several steps taken to reduce the data to a common reference level. The free-air correction accounts only for the different distances of the two elevations from the center of the earth, ignoring the mass between the two elevations. The commonly used formula for free-air correction for elevation difference h is 'g = 2h gh/R, where gh is the measured gravity value, and R is the average radius of the Earth.

free-air gravity anomaly The difference between the measured gravity field and the reference field for a spheroidal Earth; the correction to the value of the gravitational acceleration (g) which includes the height of the measuring instrument above the geoid. It is called “free air” because no masses between the instrument and the geoid are included in the correction. Inclusion of the excess gravitational pull due to masses between the measuring instrument and the geoid gives rise to the Bouguer anomaly.

free atmosphere The atmosphere above the level frictionally coupled to the surface, usually taken as about 500 m.

free bodies A physical body in which there are no forces applied. Such a body will maintain a uniform motion (until a force acts upon

it) according to the first law of Newtonian Mechanics.

free-bound continuum emission Radiation produced when the interaction of a free electron with an ion results in the capture of the electron onto the ion (e.g., recombination emission). The most energetic spectral lines of importance in solar physics belong to the Lyman series of Fe XXVI. The continuum edge for this series lies at 9.2 keV, so that all radiation above this energy must be in the form of continua, both free-bound and free-free. As the energy increases, the contribution of the free-bound emission to the total emission falls off relative to the free-free emission.

free convection Flow of a fluid driven purely by buoyancy. In the case of thermal free convection, the necessary condition for its onset is that the vertical thermal gradient must be greater than the adiabatic gradient. Whether free convection actually occurs depends on geometrical constraints. Parts of the Earth’s mantle and core are believed to be freely convecting, but little is known about the patterns of convection.

free-free continuum emission Radiation produced when the interaction of a free electron with an ion leaves the electron free (e.g., bremsstrahlung).

free oscillations When a great earthquake occurs the entire Earth vibrates. These vibrations are known as free oscillations.

freeze A meteorological condition in which the temperature at ground level falls below 0◦C.

F region The F region is the part of the ionosphere existing between approximately 160 and 500 km above the surface of the Earth. During daytime, at middle and low latitudes the F region may form into two layers, called the F1 and F2 layers. The F1 layer exists from about 160 to 250 km above the surface of the Earth. Though fairly regular in its characteristics, it is not observable everywhere or on all days. The F1 layer has approximately 5 × 105 e/cm3 (free electrons per cubic centimeter) at noontime and minimum sunspot activity, and in-

© 2001 by CRC Press LLC

friction slope

creases to roughly 2 × 106 e/cm3 during maximum sunspot activity. The density falls off to below 104 e/cm3 at night. The F1 layer merges into the F2 layer at night. The F2 layer exists from about 250 to 400 km above the surface of the Earth. The F2 layer is the principal reflecting layer for HF communications during both day and night. The longest distance for one-hop F2 propagation is usually around 4000 km. The F2 layer has about 106 e/cm3 and is thus usually the most densely ionized ionospheric layer. However, variations are usually large, irregular, and particularly pronounced during ionospheric storms. During some ionospheric storms, the F region ionization can reduce sufficiently so that the F2 region peak electron density is less than the F1 region peak density. See ionosphere, ionogram, ionospheric storm, spread F, traveling ionospheric disturbance, winter anomaly.

frequency of optimum traffic (FOT)	See
Optimum Working Frequency (OWF).

Fresnel reflectance The fraction of radiant energy in a narrow beam that is reflected from a surface at which there is an index of refraction mismatch.

Fresnel zone Any one of the array of concentric surfaces in space between transmitter and receiver over which the increase in distance over the straight line path is equal to some integer multiple of one-half wavelength. A simplification allowing approximate calculation of diffraction.

fretted channels One channel type considered to indicate fluvial activity on Mars. Fretted channels are a channel type affecting much of the fretted terrain, thus straddling the highland– lowland boundary of Mars. Their formation is restricted to two latitude belts centered on 40◦N and 45◦S and spanning ≈ 25◦ wide. They are most extensive between longitude 280◦W to 350◦W. They extend from far in the uplands down to the lowland plains and represent broad, flat-floored channels, in which flow lines are a common feature. See fretted terrain.

fretted terrain Part of the highland–lowland boundary region of Mars, lying along a great

circle having a pole at ≈ 145◦W and 55◦N. The terrain also exists around the high-standing terrain retained in the northern lowland plains. It is characterized by flat-topped outliers of cratered uplands, termed plateaux, mesas, buttes, and knobs depending on their size. The differences in size are thought to reflect different extents of fracturing and subsequent modification, whereby greater fracturing and modification created the smaller landforms.

Plateaux, mesas, and buttes are generally considered to have formed during creation of the relief difference. Alternatively, it has been proposed that they represent flat-topped table mountains that formed due to the interaction of basaltic lava and ground water at low eruption rates. The final form of the fretted terrain has also been accounted for as representing the shorelines of a sea and by scarp retreat owing to mass wasting and sublimation of volatiles, or ground-water sapping.

friction The process whereby motion of one object past another is impeded, or the force producing this impediment. Friction is caused by microscopic interference between moving surfaces, and/or by microscopic fusion between the surfaces, which must be broken to continue motion. Friction is dissipative, producing heat from ordered kinetic energy. The frictional shear stress on a surface Sf is a fraction of the normal stress on the surface Sn so that

Sf = f Sn

where f is the coefficient of friction. This is known as Amontons’s law and f has a typical value of 0.6 for common surfaces in contact, and in geophysical processes. Friction controls the behavior of geophysical faults.

friction factor A coefficient that indicates the resistance to a flow or movement. Generally empirical and dimensionless (e.g., Darcy– Weisbach friction factor).

friction slope Energy loss, expressed as head (energy loss per unit weight of fluid) per unit length of flow. Appears in the Manning Equation.

© 2001 by CRC Press LLC

friction velocity

friction velocity In geophysical fluid dynamics, the ratio

u =		ρ			,
			τ

often used to express the shear stress τ at the boundary as a parameter that has the dimensions of velocity. It represents the turbulent velocity in the boundary layer, which is forced by the surface shear stress. See law-of-the-wall layer.

Friedmann, Aleksandr Aleksandrovich

(July 16, 1888–September 16, 1925) Russian mathematician/physicist/meteorologist/aviation pioneer who was the first man to derive realistic cosmological models from Einstein’s relativity theory (in 1922 and 1924). His models, later refined by Lemaître and others, still are the backbone of modern cosmology.

Friedmann–Lemaître cosmological models

The cosmological models that incorporate the cosmological principle and in which the cosmic matter is a dust. (For models with the same geometrical properties, but with more general kinds of matter, see Robertson–Walker cosmological models.) Because of the assumed homogeneity and isotropy, all scalar quantities in these models, like matter-density or expansion, are independent of position in the space at any given time, and depend only on time. All the components of the metric depend on just one unknown function of one variable (time) that is determined by one of the 10 Einstein’s equations — the only one that is not fulfilled identically with such a high symmetry. The only quantity that may be calculated from these models and (in principle) directly compared with observations is the timeevolution of the average matter-density in the universe. However, these models have played a profound role in cosmology through theoretical considerations that they inspired. The most important of these were: cosmical synthesis of elements in the hot early phase of the evolution, the emission of the microwave background radiation, theoretical investigation of conditions under which singularities exist or do not exist in spacetime, and observational tests of homogeneity and isotropy of the universe that led to important advances in the knowledge about the large-scale matter-distribution. The Friedmann–Lemaître models come in the

same three varieties as the Robertson–Walker cosmological models. When the cosmological constant F is equal to zero, the sign of the spatial curvature k determines the future evolution of a Friedmann–Lemaître model. With

k≤ 0, the model will go on expanding forever, with the rate of expansion constantly decelerated (asymptotically to zero velocity when

k= 0). With k > 0, the model will stop expanding at a definite moment and will afterward

collapse until it reaches the final singularity. In the Friedmann–Lemaître models with F = 0, the sign of k is the same as the sign of (ρ¯ − ρ0),

where ρ0 is called the critical density. See expansion of the universe. With F = 0, this sim-

ple connection between the sign of k and the sign of (ρ¯ − ρ0) (and so with the longevity of the model) no longer exists. The Friedmann– Lemaître models are named after their first discoverer, A.A. Friedmann (who derived the k > 0 model in 1922 and the k < 0 model in 1924), and G. Lemaître (who rediscovered the k > 0 model in 1927 and discussed it in connection with the observed redshift in the light coming from other galaxies).

fringe (interference) In interferometry, electromagnetic radiation traversing different paths is compared. If the radiation is coherent, interference will be observed. Classically the detection area had sufficient transverse extent that geometric factors varied the path lengths, and some parts of the field exhibited bright fringes while other parts exhibited dark fringes.

front In meteorology, a surface of discontinuity between two different and adjacent air masses which have different temperature and density. Through the front region, the horizontal cyclonic shear is very strong, and the gradients of temperature and moisture are very large. Fronts can have lengths from hundreds to thousands of kilometers. The width of a front is about tens of kilometers. As the height increases, the front tilts to the cold air side, with warm air above cold air. In a frontal region, temperature advection, vorticity advection and thermal wind vorticity advection are very strong leading to the development of complicated weather systems, increasingly with the strength of the front. Different types of fronts

© 2001 by CRC Press LLC

“frozen-in” magnetic field

are distinguished according to the nature of the air masses separated by the front, the direction of the front’s advance, and stage of development. The term was first devised by Professor V. Bjerknes and his colleagues in Norway during World War I.

frontogenesis Processes that generate fronts which mostly occur in association with the developing baroclinic waves, which in turn are concentrated in the time-mean jet streams.

frost point The temperature to which air must be cooled at constant pressure and constant mixing ratio to reach saturation with respect to a plane ice surface.

Froude number A non-dimensional scaling number that describes dynamic similarity in flows with a free surface, where gravity forces must be taken into consideration (e.g., problems dealing with ship motion or open-channel flows). The Froude number is defined by

U Fr ≡ √

gl

where g is the constant of gravity, U is the characteristic velocity, and l is the characteristic length scale of the flow. Even away from a free surface, gravity can be an important role in density stratified fluids. For a continuously stratified fluid with buoyancy frequency N, it is possible to define an internal Froude number

F ri ≡ U .

Nl

However, in flows where buoyancy effects are important, it is more common to use the Richardson number Ri = 1/Fri2.

frozen field approximation If the turbulent structure changes slowly compared to the time scale of the advective (“mean”) flow, the turbulence passing past sensors can be regarded as “frozen” during a short observation interval. Taylor’s (1938) frozen field approximation implies practically that turbulence measurements as a function of time translate to their corresponding measurements in space, by applying k = ω/u, where k is wave number [rad m−1], ω

is measurement frequency [rad s−1], and u is advective velocity [m s−1]. The spectra transform by φ(k)dk = uφ(ω)dω from the frequency to the wavenumber domain.

frozen flux If the conductivity of a fluid threaded by magnetic flux is sufficiently high that diffusion of magnetic field within the fluid may be neglected, then magnetic field lines behave as if they are frozen to the fluid, i.e., they deform in exactly the same way as an imaginary line within the fluid that moves with the fluid. Magnetic forces are still at work: forces such as magnetic tension are still communicated to the fluid. With the diffusion term neglected, the induction equation of magnetohydrodynamics is:

∂B = × (u × B) . ∂t

By integrating magnetic flux over a patch that deforms with the fluid and using the above equation, it can be shown that the flux through the patch does not vary in time. Frozen flux helps to explain how helical fluid motions may stretch new loops into the magnetic field, but for Earthlike dynamos some diffusion is required for the dynamo process to work. The process of calculating flows at the surface of the core from models of the magnetic field and its time variation generally require a frozen flux assumption, or similar assumptions concerning the role of diffusion. See core flow.

“frozen-in” magnetic field A property of magnetic fields in fluids of infinite electrical conductivity, often loosely summarized by a statement to the effect that magnetic flux tubes move with the fluid, or are “frozen in” to the fluid. An equivalent statement is that any set of mass points threaded by a single common magnetic field line at time t = 0 will be threaded by a single common field line at all subsequent times t.

It is a quite general consequence of Maxwell’s equations that for any closed contour C that comoves with a fluid, the rate of change of magnetic flux G contained within C is (cgs units)

dt	=	E + c V×B	· dx ,
dG		1

© 2001 by CRC Press LLC