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lapse rate

lapse rate Vertical change rate of the air temperature. See adiabatic lapse rate, moist lapse rate.

Large Angle and Spectrometric Coronagraph (LASCO) A three-part coronagraph on board the SOHO spacecraft designed to provide white light images of the sun’s outer corona. LASCO consists of three successively larger occulting disks providing coronal images at 1.1 – 3 R , 1.5 – 6 R , and 3.5 – 30 R , respectively.

Large Magellanic Cloud (LMC) An irregular galaxy in the southern constellation Dorado at Right Ascension 5h20m, declination −6◦, at 55 kpc distance. The LMC has angular dimension of 650 × 550 , about 10 kpc. It has a positive radial velocity (away from us) of + 13 km/s. Both the Large Magellanic Cloud and the Small Magellanic Cloud orbit the Milky Way. On February 24, 1987 supernova 1987A, a peculiar type II supernova, occurred in the Large Magellanic Cloud, the nearest observed supernova since Kepler’s supernova. See Small Magellanic Cloud, Kepler’s supernova.

large-scale Structures in any physical system obtained by ignoring or averaging over small scale features; in oceanography, structures of water properties (such as CTD profiles) with scales larger than tens of meters (finestructure) representing the overall stratification of the natural water body.

Larissa Moon of Neptune, also designated NIV. It was first seen on Voyager photos in 1989. Its orbit has an eccentricity of 0.00138, an inclination of 0.20◦, a precession of 143◦ yr−1, and a semimajor axis of 7.36 × 104 km. Its size is 104 × 89 km, but its mass is not known. It has a geometric albedo of 0.056, and orbits Neptune once every 0.555 Earth days.

Larmor frequency The angular frequency of gyration of a charged particle in a magnetic field; in cgs units, qB/mγ c, where q and m are the charge and rest mass of the particle, B is the magnetic field strength, c is the vacuum speed of light, and γ is the Lorentz factor. Equivalent terms are gyrofrequency and (nonrelativisti-

cally) cyclotron frequency. Named after Joseph Larmor (1857–1942).

Larmor radius The radius of gyration of a charged particle in a magnetic field, equal to the Larmor frequency multiplied by the component of velocity transverse to the magnetic field. Equivalent terms are gyroradius and (nonrelativistically) cyclotron radius. See Larmor frequency.

last scattering In physical cosmology, the universe is apparently now transparent to microwave photons, which are observed as the cosmic microwave background, but was not transparent earlier. Thus, those photons underwent a last scattering. In cosmological descriptions, the temperature is approximately uniform at any given instant of cosmic time, and is given by T = Tnowanow/a where a is the cosmological length scale. In a Big Bang universe such as we inhabit, anow > a for any previous epoch. Tnow is observed to be about 2.7 K. An identical expression holds for the redshift z of previously emitted radiation (ν is the frequency = c/λ , λ is the wavelength)

ν = ν anow = νnow(1 + z) . a

At a redshift of z 1000, the temperature was around 3000 K, hot enough for thermal photons to ionize hydrogen to a plasma of protons and electrons. The free electrons strongly scattered photons (Thomson scattering). As the universal temperature dropped through 3000 K, the proton-electron plasma combined (perversely called recombination in the literature) to form neutral hydrogen, which is transparent to thermal photons with T < 3000 K. In simple physical descriptions of the universe, this was the last scattering of those photons, which are now observed as a microwave background. Although the physics is unclear, it is possible that sources of ionizing radiation (quasars, supernovae) may have been prolific enough to reionize the universe during the epoch between z 30 and z 5. In that case the last scattering occurred at the much more recent epoch of z 5. The collection of points at which the last scattering of currently observed radiation occurred is called

© 2001 by CRC Press LLC

law-of-the-wall layer

the last scattering surface. See quasar, supernova, Thomson scattering.

latent heat Latent heat of vaporization is the amount of heat per unit mass which is required to vaporize the liquid; latent heat of fusion is the equivalent definition for melting.

latitude Angular distance from the Earth’s equator, counted positive northward and negative southward. It is zero on the equator, 90◦ at the North Pole, and −90◦ at the South Pole. Geodetic latitude φ, defined as the angle of the local normal to the Earth ellipsoid with the Earth’s equatorial plane, is used for most mapping. Geocentric latitude φ for any point P is the angle between the line OP from Earth’s center O to the point, and Earth’s equatorial plane, counted positive northward and negative southward. It is useful for describing the orbits of spacecraft and other bodies near the Earth. Astronomical latitude is the angle between the local vertical (the normal to the geoid) and the Earth’s equatorial plane, and is generally within 10” arc of geodetic latitude in value. Geodetic latitude is derived from astronomical latitude by correcting for local gravity anomalies. The maximum difference between geometric and geodetic latitude is about 10’ arc, and occurs at mid-latitudes.

If f is the Earth ellipsoid flattening factor (A −C)/A (see Earth ellipsoid), then for points on the ellipsoid, the geodetic and geocentric latitudes are related by:

tan φ = (1 − f )2 tan (φ) .

For points at a height h, this equation must be replaced by the following: The cylindrical coordinates (ρ, Z) of such a point can be found from:

ρ = h + A/ 1 − 2f − f 2 sin2 φ cos φ

Z = h + A (1 − f )2 / 1 − sf − f 2 sin2 φ sin φ .

The geocentric latitude is then

φ = tan−1 (Z/ρ) .

The inverse of the transformation can be obtained analytically by solving a quartic equation, but the inversion is usually done iteratively.

lattice preferred orientation (LPO) The geometric and spatial relationship of the crystals making up polycrystalline aggregates, in which substantial portions of the crystals are oriented dominantly with one particular crystallographic orientation. Lattice preferred orientation in general results from plastic deformation, controlled by dislocation glide.

Laurasia Prior to the opening of the North Atlantic Ocean, North America and Europe were attached and formed the continent Laurasia.

lava Material that is molten on the surface of a planetary body. (When the molten material is still underground, it is usually called magma.) The composition of the lava depends on the body — terrestrial lava flows are usually composed of silicate minerals, while those on Jupiter’s moon of Io are primarily composed of sulfur and lava flows on icy bodies are composed of volatile elements such as water and ammonia. The features formed by lava depend on various characteristics of the volcanism which produces the lava, including eruption rates, viscosity of the material, and gas content. Low viscosity lavas produced with high eruption rates often give rise to flood lavas (also often called flood basalts on the terrestrial planets) while slightly lower eruption rates give rise to shield volcanos. More viscous lavas will produce shorter flows and more explosive features, such as the composite volcanos and pyroclastic deposits.

law of equal areas Kepler’s second law of planetary motion: The line joining the sun and a planet sweeps out equal areas in equal times (even though the speed of the planet and its distance from the sun both vary). This is now recognized as a consequence of the conservation of the angular momentum of the planetary motion.

law-of-the-wall layer Boundary layer zone where the logarithmic velocity profile applies; i.e., ∂u/∂z = (u /κ) ln(z/z0), where u is friction velocity, κ is von Kàrmàn constant (0.41 ± 0.01), z is depth, and z0 is roughness length. In natural waters law-of-the-wall layer is typically found in the bottom boundary layer, as well as

© 2001 by CRC Press LLC

law-of-the-wall scaling

in the surface layer below the wave-affected surface layer. See law-of-the-wall scaling.

law-of-the-wall scaling In a law-of-the-wall boundary layer zone, where the logarithmic velocity profile applies, a layer’s turbulence depends on the surface stress τ0 (or equivalent u = (τ0/ρ)1/2) and on depth z. Dimensional analysis provides the law-of-the-wall scaling relations (often simply called wall-layer scaling) given by the table.

laws of black hole physics Classical black hole solutions of general relativity (see Schwarzschild metric, Reissner–Nordströ m metric, Kerr–Newman metric) obey four laws which are analogous to the laws of thermodynamics:

1.Zeroth law: The surface gravity κ is constant on the horizon.

2.First law: The variation of the ADM mass M is given by the Smarr formula

δM =

κ

8 π δA + 6 δJ + 8 δQ ,

where A is the area of the horizon, J is the angular momentum of the black hole, 6 is the angular velocity at the horizon, Q is the charge of the black hole, and 8 is the electric potential at the horizon.

3. Second law: No physical process can decrease the area A of the horizon,

δA ≥ 0 .

4. Third law: The state corresponding to vanishing surface gravity κ = 0 cannot be reached in a finite time.

From the zeroth and third law, one notices a similarity between the surface gravity κ/2 π and the temperature of a classical thermodynamical system. The ADM mass M behaves like the total energy (first law) and the area A/4 as an entropy (second law). The analogy was further substantiated by the discovery due to S. Hawking that a black hole in a vacuum emits radiation via quantum processes with a Planckian spectrum at the temperature κ/2 π. See ADM mass, black hole, Kerr–Newman met- ric, Reissner–Nordströ mmetric, Schwarzschild metric, surface gravity.

© 2001 by CRC Press LLC

276

layering See double diffusion.

leader spot A sunspot or sunspot group lying on the western side of an active region complex, i.e., leading in the direction of solar rotation. The largest spots tend to form in the side of the bipolar group that is preceding in the direction of solar rotation. The growth of the longitudinal extent of an active region as it develops is achieved primarily through the rapid forward motion of the preceding spot.

leap second A second inserted in Universal Time at the end of June 30 or December 31 when, in the judgment of the Bureau International des Poids et Mesures, its addition is necessary to resynchronize International Atomic Time with Universal Time, specifically UT1. The latter is determined by the Earth’s rotation, which is generally slowed down by oceanic and atmospheric tidal friction. Leap seconds have been added since June 30, 1972.

leap year A year in the Julian and Gregorian calendars in which an extra day is inserted (February 29) to resynchronize the calendar with sidereal time.

Leda Moon of Jupiter, also designated JXIII. Discovered by C. Kowal in 1974, its orbit has an eccentricity of 0.148, an inclination of 26.07◦, and a semimajor axis of 1.109 × 107 km. Its radius is roughly 8 km, its mass 5.7 × 1015 kg, and its density 2.7 g cm−3. Its geometric albedo has not been well determined. It orbits Jupiter once every 238.7 Earth days.

lee wave The atmospheric wave that is generated in the lee of isolated hills. Typical values of the wavelengths observed in the atmosphere are 10 to 20 km.

left-lateral strike-slip fault The horizontal motion on this strike-slip fault is such that an observer on one side of the fault sees the other side moving to the left.

Lemaître, Georges (July 17, 1894 – June 20, 1966). Belgian priest, mathematician, physicist, and astrophysicist. He is most famous for his rediscovery of one of the cosmological models

Lewis number

Law-of-the-Wall Scaling Relations

Length

LLs z

Time

τLs zu −1

Velocity

wLs u

Dissipation of turbulent kinetic energy

εLs u 3(κz)−1

Temperature (fluctuations)

:Ls Fth/(ρcpu )

found by Friedmann (see Friedmann–Lemaître cosmological models) and several contributions to relativistic cosmology based on these models. His other achievements include the theory of “primaeval atom” — an overall vision of the origin and evolution of the universe (now replaced by the more detailed and better confirmed observationally Big Bang theory), several papers on physics of cosmic rays (which he interpreted as remnants of what is now called the Big Bang), mathematical physics, celestial mechanics, and automated computing (even before electronic computers were invented).

Lemaître–Tolman cosmological model Inhomogeneous cosmological model first described in 1933 by G. Lemaître, but now commonly called the Tolman model. See Tolman model.

length of day The length of day has decreased with geological time. The rotational period of the Earth has slowed due to tidal dissipation.

lens A transparent solid through which light can pass, and which has engineered-in properties to deflect or focus the light. See gravitational lens.

Lense–Thirring precession The dragging of space and time by a rotating mass, most evident in cases of rapidly rotating compact objects, such as Kerr black holes. Predicted using the equations of general relativity by J. Lense and H. Thirring in 1918, the effect has been presumably detected by the extremely tiny effects on satellites orbiting Earth, and around distant, rotating objects with very intense gravitational field, such as neutron stars and black holes. The Lense–Thirring effect gives rise to a precessional motion if an object is not orbiting in the equatorial plane of the massive body.

In the vicinity of a rotating black hole, within the ergosphere, the dragging is strong enough to force all matter to orbit in the equatorial plane of the black hole. See accretion disk, Kerr black hole.

lepton A fundamental spin 1/2 fermion that does not participate in strong interactions. The electrically charged leptons are the electron, the muon, the tau, and their antiparticles. Electrically neutral leptons are called neutrinos and have very small (or zero) mass. The neutrinos are observed to have only one helicity state (left-handed). Their antiparticles have positive helicity.

leveling (survey) A geodetic measurement to obtain height difference between two points. The height difference between the two points can be obtained by erecting leveling rods at two distant points from several to tens of several meters, and then by reading scales of the leveling rods using a level that is placed horizontally at the intermediate distance between the two points. Repeating this operation, height difference between substantially distant two points can be measured. Height above the sea at a point can be obtained from control points whose height above the sea has already been determined (bench marks) or from height difference between the point and tide gage stations. This kind of leveling is referred to as direct leveling, whereas trigonometric leveling and barometric leveling are called indirect leveling.

Lewis number The non-dimensional ratio LC = DC/DT, where DC is molecular diffusivity of substance C and DT is molecular diffusivity of heat, expresses the ratio of the rate of transfer of molecules of C to that of heat. LC in water is strongly temperature-dependent and of the order of 0.01. The turbulent Lewis num-

© 2001 by CRC Press LLC

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