isotope

ISC (International Seismological Centre)

ISC was formed in Edinburgh, Scotland in 1964 and moved to Newbury in southern England, and subsequently to Thatcham, near Newbury. ISC collects and compiles seismic observation data throughout the world, and determines hypocentral parameters (location, origin time, magnitude, fault plane solution), issuing monthly reports (Bulletin of the International Seismological Centre) with observation data. ISC also issues printed regional catalogs of earthquakes, extracting hypocentral parameters from the monthly reports, and catalogs of research papers in relation to seismology. These have become important fundamental data concerning earthquakes. For more information, refer to http://www.isc.ac.uk/.

isentropic coordinate When horizontal scales are large compared with vertical scales, it is sometimes advantageous to replace the z- coordinate with potential temperature θ to use with x and y as independent coordinates, and then the variables (x, y, θ) are known as isentropic coordinates.

island arc Ocean trenches (subduction zones) often have an arcuate structure; they form part of a circle or an arc. The line of volcanic islands associated with the subduction zone has a similar distribution; thus they form an island arc. The Aleutian islands in Alaska are an example.

isobar A line connecting points of equal pressure on a graphical representation of a physical system, or the actual physical surface of equal pressure.

isobaric coordinate	When horizontal scales
are large compared	with vertical scales, it

is sometimes advantageous to replace the z- coordinate with pressure to use with x and y as independent coordinates, and then the variables (x,y,p) are known as isobaric coordinates, or pressure coordinates. This set of coordinates is widely used in atmospheric science.

isogonic lines Lines of constant declination. See declination.

isoline A line along which some parameter is constant. For example, isobars are lines of constant pressure.

isometry A transformation of coordinates xµ → x µ = x µ(x) is said to be an isometry of space if the form of the metric g of the space does not change under the transformation

g (x ) = g(x) .

For infinitesimal transformations, one can introduce Killing vectors which represent infinitesimal isometries. See Killing vector.

isopycnal processes Processes taking place along surfaces of equal density.

isostacy The process of compensation or hydrostatic equilibrium by which the densities of elevated mountain ranges are compensated by the low density of depressed crustal roots.

An area that is isostatically compensated will show no free air gravity anomaly. There are two types of isostacy: Airy isostacy, in which variations in crustal thickness (“roots”) explain the compensation, and Pratt isostacy, which explains isostatic compensation in terms of variations in the density of materials.

isotherm A line connecting points of equal temperature on a graphical representation of a physical system, or the actual physical surface of equal temperature.

isothermal atmosphere An atmosphere in hydrostatic equilibrium in which the temperature is constant with height. In such an atmosphere the pressure and density in an ideal gas are proportional, and therefore the pressure decreases exponentially upward:

p = p0 exp (−gz/Rd Tv) ,

where Rd is the gas constant for dry air; Tv is the virtual temperature; g is the acceleration of gravity. Also called exponential atmosphere.

isotope A particular species of an element identified by the number of neutrons in the nucleus A − Z. (The number of protons in the nucleus, the atomic number Z, determines which

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isotope delta value (δ)

element is under discussion. Here A is the atomic mass number.) For instance, hydrogen (atomic number Z = 1) has two stable isotopes. In each hydrogen nucleus there is one proton (equal to the atomic number). Normal hydrogen, 1H (Z = 1, A = 1), is the isotope with no neutrons; deuterium, 2H (Z = 1, A = 2), is the isotope with one neutron. There is also an unstable isotope, tritium, 3H (Z = 1, A = 3), with two neutrons, which decays by beta decay in 12.26 years.

isotope delta value (δ) Stable isotope compositions of low-mass (light) elements such as oxygen, hydrogen, and carbon are normally reported as δ values. Delta values are reported in units of parts per thousand (per mil or ◦/◦◦) relative to a standard of known composition: δ(◦/◦◦) = (Rx/Rs −1) ×1000, where R represents the ratio of the heavy to light isotope (e.g., 18O/16O), Rx is the ratio in the sample, and Rs is the ratio in the standard, which can be rewritten, for instance, for the oxygen isotopes of water as

δ18O =
		18O/16O sample −		18O/16O standard
		18O/16O				× 1000
			standard
isotope fractionation factor (α)					The frac-

tionation associated with the equilibrium exchange reaction between two substances A and B (e.g., liquid and vapor phases of water) is: αA−B = RA/RB , where R is the ratio of the heavy isotope to the lighter isotope in compounds A and B. For the liquid-vapor system of water at 20◦C:

	18O/16O
αliquid-vapor =	18O/16O liquid		= 1.0098
		vapor

isotropic A material whose properties are independent of direction. For instance, in hydrodynamics hydraulic properties (such as intrinsic permeability) do not depend on the direction of flow and are equal in all directions.

isotropic turbulence Very large eddies tend to be anisotropic because they contain structure that is related to the energy input. Succes-

sive interaction between the three spatial components redistributes turbulent kinetic energy successively more equally among the components, leading to increased isotropy at smaller scales. However, because of stratification, complete isotropy is seldom attained, not even at the smallest scales.

isotropy In geometry, independence of direction; a system is isotropic if there exists no preferred spatial direction at any point in the system; a space is said to be isotropic with respect to a point of view P if it looks the same in all directions when seen from P .

In relativity and cosmology, the metric of an isotropic D-dimensional space is form invariant with respect to all rotations of center P . The latter are thus generated by NI = D (D − 1)/2 Killing vectors.

If the space is isotropic with respect to all points, then it is also homogeneous and admits NO = D further Killing vectors. When the number of Killing vectors equals NI + NO = D (D + 1)/2, then the space is maximally symmetric.

In cosmology, the assumption may be made in modeling the universe that it is at some level approximately isotropic. However, after anisotropies connected with the motion of the Earth around the sun, of the sun in our galaxy and of the galaxy itself towards the Great Attractor are subtracted, the temperature of the microwave background radiation (presumably emitted at redshift z 1,000) is not quite isotropic around us showing a residual anisotropy: JT /T ≈ 10−5, where T = 2.73 K is the average temperature of the radiation and JT are differences between the values of T in different directions. This is taken as an indication of early inhomogeneity leading to inhomogeneities in matter, which grew to the observed large-scale structure. See homogeneity, Killing vector, maximally symmetric space.

Israel–Wilson–Perjés space-times (1971)

Stationary space-times describing the external fields of an arbitrary array of spinning and electrically charged bodies held in equilibrium by the balance of the gravitational and electromagnetic forces. See equilibrium space-times.

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Jeans length

J

J2 A dimensionless coefficient in the P2(cos θ) term of the Legendre polynomial expression of the gravitational potential of a planet, where θ is the colatitude (90◦-latitude). Assuming symmetry of mass distribution with respect to the rotational axis and to the equatorial plane and without considering the effect of rotation, the gravitational potential of a planet as a function of radial coordinate r and colatitude θ is

V = −

r

+ J2 r3

2 cos2

θ −

2

GM

GMa2

3

1

+

higher order terms of

1

r

where G = 6.6725985 × 10−11 m3 kg−1 s−2 is the gravitational constant, M is the total mass of the planet, and a is the equatorial radius. J2 is an important parameter in the gravitational and rotational dynamics of a planet because of its relation with the moments of inertia:

C − A J2 = Ma2

where C and A are the polar and equatorial moments of inertia, respectively, and a is the mean radius of the Earth. The value of J2 for the Earth is about 1.082626 × 10−3. Redistribution of mass in the Earth causes changes to the gravitational potential and hence J2.

Jacobian In considering the transformation between a given coordinate n−dimensional system {xi } and the new one {yi }, the elementary volume element undergoes a transformation:

dyn = J dxn ,

where J is the Jacobian, given by det|∂y/∂x|, where the matrix J (y, x) = {∂y/∂x} is constructed with elements of the form

∂yi /∂xj

for all i and j. J (y, x) is sometimes called the Jacobian matrix, and J = detJ (y, x) the Jacobian determinant.

Jacobi ellipsoid A triaxial stationary configuration of rigidly rotating fluid with meridional ellipticity exceeding 0.91267.

Jansky (Jy) A unit of spectral flux used in radio astronomy: 1Jy = 10−26W m−2Hz−1.

Janus Moon of Saturn, also designated SX. Discovered by A. Dollfus in 1966, it is now uncertain if Dollfus saw Janus or its co-orbital partner, Epimetheus. Its orbit has an eccentricity of 0.007, an inclination of 0.14◦, and a semimajor axis of 1.51×105 km. Its size is 98×96×75 km, its mass 2.01 × 1018 kg, and its density 0.68 g cm−3. It has a geometric albedo of 0.8 and orbits Saturn once every 0.695 Earth days.

Japan current An ocean current flowing northeast from the Philippines along the eastern coast of Japan.

JD See Julian date.

Jeans escape The process by which gases undergo thermal escape from an atmosphere. Although the temperature of the atmosphere may be too low for the average molecule to have escape velocity, there will be molecules at the tail of the Maxwell distribution that will have the required speed. If those molecules are at the base of the exosphere, they will be able to escape to space. This mechanism is called Jeans escape, and the resultant flux is the Jeans flux.

Jeans instability James Jeans discovered that perturbations in a self-gravitating gas are unstable. Density fluctuations grow as time passes. Matter collapses in some regions (leading to the growth of structures) and becomes rarified elsewhere. Similar results hold in an expanding cosmology, with modifications for the overall expansion. On very large scales and always outside the cosmic horizon, the evolution of the fluctuations is essentially free fall, so the structure at any time reflects the initial pattern or fluctuations. See Jeans length.

Jeans length Minimum length scale of a density perturbation that is gravitationally unstable; the critical size above which a smooth medium inevitably degenerates into a clumpy

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Jerlov water type

one because of gravitational attraction; the fluid collapses under its own weight. For scales smaller than this critical length, the fluid can build enough hydrostatic pressure to halt the collapse and perturbations oscillate as sound waves. For a perfect Newtonian fluid the Jeans length is given by:

λJ =	πv2		1/2
	s
	Gρ

where vs is the sound speed of the fluid, G the gravitational constant, and ρ the mean density. For a perturbation longer than the Jeans length collapsing in a non-expanding fluid, the density grows exponentially on a dynamical time scale τdyn = (4πGρ)−1/2. If the fluid is expanding, the background perturbation growth is like a power law with an exponent close to unity, the exact value depending on the equation of state of the fluid. The Jeans length during the conditions believed to be present at the time after the Big Bang when decoupling of ordinary matter and radiation occurred was 6 ×1017 m, or about 60 light years.

Jerlov water type A water clarity classification scheme based on the downward diffuse attenuation coefficient just below the sea surface.

jet In fluid mechanics, a compact, coherent, collimated stream of relatively fast moving fluid impinging into still fluid.

In meteorology, a shorthand for jet stream. In astrophysics, usually bipolar streams of

high velocity gas emitted from an active region. Examples include jets from star formation regions (collimated by magnetic fields) and from black hole accretion in stellar mass or in supermassive black holes, in which the collimation is accomplished by the rotation of the black hole.

jet stream Relatively strong west to east winds concentrated in a narrow stream up to 500 km across, located in a thin vertical range 10 to 15 km in altitude, with winds exceeding 90 km/h. Winds, especially in the winter, can approach 500 km/h. In North America, major cold outbreaks are associated with movement of the jet stream south. In summertime, and during

mild winter weather, the jet stream stays to the north. Its actual fluctuations range from northern Canada to over the Gulf of Mexico.

jetty A structure at a tidal inlet. Commonly built as a rubble mound structure, to keep waves and sediment out of a harbor entrance.

jog In geology, segments of dislocation line which have a component of their sense vector normal to the glide plane. Jogs are abrupt changes in direction taking the dislocation out of the glide plane. When the normal component extends over only a single interplanar spacing d, as for A and B, the jogs are unit jogs, or for brevity just jogs. If the normal component extends over more than one interplanar spacing, the jog is called superjog.

joints Fractures in the Earth’s crust across which there has been no relative motion. If relative motion has occurred, the fracture is a fault.

JONSWAP Acronym for Joint North Sea Wave Project, an experiment involving measurement of ocean wave energy spectra yielding an empirical spectrum of the same name.

Joule (J) The SI unit of energy, equal to Nm.

Joule heating The dissipation of current in a plasma in the form of heat due to the presence of a finite electrical conductivity. The efficient dissipation of currents in the corona requires the currents to be confined to small volumes because of the extremely high conductivity. The heating is given by WJ = j · E = j2/σ where E is the electric field, j is the current density, and σ is the electrical conductivity of the plasma. Joule heating is also known as Ohmic heating.

Jovian planet A planet that has characteristics similar to Jupiter, the largest planet in our solar system. There are four Jovian planets in our solar system: Jupiter, Saturn, Uranus, and Neptune. The primary characteristics of Jovian planets are large size (>48,000 km in diameter), large distance from the sun (>5 astronomical units), low densities (< 1600 kg/m3, indicating gaseous compositions of primarily hydrogen and helium), many moons, and ring systems.

© 2001 by CRC Press LLC