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∂Z
∂Z
∂θse
∂θsw

convergent plate boundaries

conserves energy; if the column is conditionally unstable and the humidity exceeds a specified value, the column is adjusted to moist static neutrality.

convective cloud A type of cloud that is generated by convective activities in the atmosphere. The main feature of it is its strongly vertical development. Strong vertically developed clouds are also called heap clouds.

convective heat transfer Transfer of heat by mass movement, due to free or forced convection. The latter case is also referred to as advective heat transfer.

convective instability Stratification instability caused by convective activities, i.e., the lower layer has higher moisture and becomes saturated first when being lifted, and hence cools thereafter at a rate slower than does the upper, drier portion, until the lapse rate of the whole layer becomes equal to the saturation adiabatic and any further lifting results in instability. In general, use < 0 or < 0 as the criterion of the convective instability, where θsw and θse are pseudo-wet-bulb potential temperature and pseudo-equivalent potential temperature, respectively.

convective scaling In the boundary layer, pure convective turbulence depends only on the thickness Hcon of the convectively well-mixed layer and the boundary buoyancy flux Jbo [Monin and Obukhov, 1954]. Dimensional analysis pro-

vides the scaling relations as a function of Hcon

and Jo by:

 

 

 

 

 

 

b

 

 

 

 

 

 

 

 

 

Length

Lcs Hcon

 

Time

τcs

 

H

con

/wcs

 

Velocity

 

 

o

1/3

wcs (HconJb)

 

Diffusivity

Kcs wcsHcon

 

Dissipation of turbulent

εcs Jbo

 

 

kinetic energy

 

 

If convection is driven purely by heat fluxes (i.e., Jbo = gαFth/(cpρ)), further scaling relations for temperature are as shown in the table on page 86.

convective turbulence If density increases at the top of a fluid (i.e., cooling, evaporation

of salty water at the surface, etc.) or if density decreases at the bottom of a fluid (i.e., warming from below, etc.), convective plumes (thermals for temperature) will set in and mix a progressively thicker boundary layer. Convective scaling allows the quantification of the relevant physical parameters of convection as a function of the boundary buoyancy flux Jbo and the thickness Hcon of the convectively unstable layer. See also penetrative convection.

convergent boundary Plates are destroyed or severely deformed at convergent boundaries.

Two types of convergent boundaries exist: subduction and collision. A subduction convergent boundary occurs when two plates composed of oceanic crust (thin, basalt composition) or an ocean plate and a continental plate (thick, more silicic composition) meet. At the ocean-ocean boundary, one of the oceanic plates dives down under the other plate. At an ocean-continent boundary, the oceanic plate is always subducted under the continental plate. The location where the first plate subducts under the second plate is characterized by a deep trough, called a trench. As the oceanic plate dives deeper into the Earth’s interior, the temperature rises and sediments which accumulated on the ocean floor begin to melt. This magma rises towards the surface and erupts on the overriding plate, creating the very explosive volcanos called stratovolcanos (or composite volcanos). Subduction boundaries are characterized by this explosive volcanism and earthquakes from a variety of depths (down to about 200 km). Japan is an example of an ocean-ocean subduction boundary, while the Cascade volcanos (including Mt. St. Helens) in the northwestern U.S. are an example of the ocean-continent subduction boundary. If both plates are composed of continental crust, neither plate is subducted. Instead the two plates crumple to form high mountain ranges, such as the Himalayas. This type of convergent boundary is called a collision boundary and is characterized by earthquakes but no volcanism. Convergent boundaries are believed to occur over the descending portions of convection cells within the Earth’s asthenosphere.

convergent plate boundaries

See conver-

gent boundary.

 

© 2001 by CRC Press LLC

conversion efficiency

Temperature (fluctuations)

 

 

Fth/(cpρwcs)

 

(gα)−1

b

 

 

cs

 

 

(Jo2/Hcon)1/3

 

Dissipation of temperature variance

χcs

 

Tcs2wcs/Hcon

 

(gα)−2

(Jo5

/H4 )1/3

 

 

 

 

 

 

 

 

 

b

con

4)1/3

Temperature gradient

∂ cs/∂z

Fth/(cpρKcs)

 

 

b

 

 

(gα)−1(Jo2/Hcon

conversion efficiency See energy conversion efficiency.

cooling flow In cosmology: Clusters of galaxies may contain of order 1000 visible galaxies, which contribute only 5 to 10% of the cluster mass, some baryonic gas observable in its X-ray emission, which constitutes 30% of the mass needed to bind the cluster; and an amount60% of the mass in currently unknown dark matter. In the outer rarified portions of the cluster, the baryon gas cools inefficiently, but toward the center of the cluster, the higher density leads to rapid cooling of this gas. The gas accordingly loses pressure support and falls into the center at a typical rate 100M /year. All clusters observed with cooling flows have a giant elliptical at their center, suggesting that the inflow has persisted for cosmological times (roughly one Hubble time) to form this central galaxy, further suggesting that cooling flows are generic in large clusters. However, cooling flows do not exist in interacting clusters (the result of cluster mergers), and it is a current active topic of research to understand the mechanism of disruption and the timescale for re-establishment of cooling flows.

Coordinated Universal Time (UTC)

Starting in 1972, Greenwich Mean Solar Time was split into Coordinated Universal Time (UTC), the basis of civil timekeeping ever since, and Universal Time (UT1), which is a measure of Earth’s rotation. UTC advances in step with International Atomic Time (TAI), except that at leap seconds it is adjusted to remain within 0.9 s of UT1. Therefore, to compute the true elapsed seconds between any two events defined in UTC since 1972, a table of leap seconds is required. For example, because the leap seconds totaled 24 during all of 1989, and 29 during all of 1995 (five seconds having been inserted during the interim), when calculating the time interval between any date and time in 1989 and 1995, it is necessary to add 5 seconds to what would be calculated

on the basis of equal 24 hour days, each hour having 60 minutes comprised of 60 seconds. In other words, on five distinct occasions between January 1, 1989, and December 31, 1995, there was an hour whose final minute had 61 seconds.

coordinate singularity A location in a space (or spacetime, in relativity) where description of physical fields is impossible because the coordinates do not correctly map to (a region of) a rectangular coordinate chart. An example is the origin in spherical coordinates, where angular directions have no meaning. In general relativity, the situation is more difficult because the metric itself can change, and recognizing a coordinate singularity as such requires subtlety: A coordinate singularity is a singularity which is removable by (singular) transformation to a frame in which all components of physical objects remain bounded. In general relativity, the surface of a spherical black hole, the surface r = 2M (where r is defined so that 4πr2 measures the area of a sphere) is a singularity in the original coordinates used to describe it. (See Schwarzschild black hole.) A transformation found by Kruskal and Szekeres removes the coordinate singularity and shows that all geometrical measurable quantities are finite.

coordinate system A way of assigning a set of labels to each point in a space (or, by extension, to each event in spacetime). Since common experience suggests that space is 3- dimensional, one assigns three independent functions, (e.g., x, y, z) to label points in space. The x = 0 surface, for instance, consists of all those points in space where the function x (as a function of position) vanishes. For purposes of physical description, the coordinate functions are taken to be continuous functions of the space points. In spacetime, one introduces a fourth coordinate, time. In Newtonian physics, time is a universal function, known and measurable by any observer. In special and in general relativity, time is a function of the motion of the observer

© 2001 by CRC Press LLC

core

(at least), and different observers use different space and time coordinate functions. Although the notation {x, y, z} suggests rectangular coordinates, the constant x− surfaces can in fact be curved, for instance, if x is really the radius from the origin in a spherical coordinate system. In general, the coordinate functions can lead to curved constant-coordinate surfaces (curvilinear coordinates). Then the four spacetime coordinates form a set of functions, say φα(P ) where φα, α = 0, 1, 2, 3 correspond to the time and the three spatial coordinate functions; P represents a point in spacetime.

A coordinate system is closely related to a reference frame. For instance, one can align basis vectors (which constitute the frame) along the intersection of constant-coordinate surfaces, with some rule for assigning length or magnitude of the basis vectors.

coordinate time Time defined relative to an inertial (in particular, nonrotating) reference frame, whose relationship with time measured on the surface of the Earth can be calculated using relativity (not to be confused with “coordinated time” like Coordinated Universal Time). General uses are “Geocentric Coordinate Time” (TCG) and “Barycentric Coordinate Time” (TCB), the latter referring to the solar system barycenter.

coordinate transformation in special relativity The transformation of space-time coordinates between two reference systems that are moving uniformly with respect to each other. Classically, any physical system is composed of particles, and a full description of the system is obtained if all the positions of each particle are known for any given time. The position of each particle is represented by a trio of numbers whose value depends on the location of the reference system. Thus if two observers used two different systems of reference, then a coordinate transformation is needed in order to compare the observations. Classically time is considered to be an absolute variable; that is its value is the same regardless of the reference system. Thus, classical coordinate transformations transform an arbitrary trio of spatial coordinates at any given time. Special relativity states that the velocity of light is constant for two reference sys-

tems that are moving at constant velocities with respect to each other. In order for this to hold time can no longer be an absolute variable, and its value must depend on the reference system. The universal character of the speed of light plus the assumption that space is homogeneous and isotropic leads to the Lorentz transformation of space-time coordinates. The Lorentz transformations transform an arbitrary foursome of coordinates (three spatial coordinates plus time) from one system of reference to another that is moving uniformly with respect to the first.

Copernicus, Nicholas Astronomer (1473– 1543). Proposed that the sun, rather than the Earth, was the center of the solar system.

coplanarity theorem In magnetohydrodynamics, the coplanarity theorem

n · (Bd × Bu) = 0

states that the shock normal n and the magnetic fields Bu and Bd in the upstream and downstream medium all lie in the same plane. The coplanarity theorem is a consequence of the jump conditions for the electromagnetic field at the shock as described by the Rankine–Hugoniot equations. See Rankine–Hugoniot relations.

Cordelia Moon of Uranus also designated UV. Discovered by Voyager 2 in 1986, it is a small, irregular, body, approximately 13 km in radius. Its orbit has an eccentricity of 0, an inclination of 0.1◦, a precession of 550◦ yr−1, and a semimajor axis of 4.98 × 104 km. It is the inner shepherding satellite for Uranus’ epsilon ring. Its surface is very dark, with a geometric albedo of less than 0.1. Its mass has not been measured. It orbits Uranus once every 0.335 Earth days.

cordillera An extensive chain of parallel mountains or mountain ranges, especially the principal mountain chain of a continent. The term was originally used to describe the parallel chains of mountains in South America (las Cordilleras de los Andes).

core Differentiated central volume of the Earth and (some) other planets. Cores vary in composition, size, and physical state among the different solar system bodies. In geophysics,

© 2001 by CRC Press LLC

core collapse

the Earth has a core with a radius of 3480 km, compared to the Earth’s radius of approximately 6370 km. The core is much denser than the mantle above and is composed primarily of iron with some other alloying elements; most of the terrestrial planets are believed to have cores composed of iron, based on their high densities. Although most of the terrestrial planets are believed to have only one core of either solid or liquid iron, the Earth (due to its large size) has two cores, an inner solid iron core with a radius approximately 600 km and an outer liquid iron core. The Earth’s core formed early in the evolution of the Earth as a large fraction of heavy iron gravitationally segregated from the silicic components. Latent heat of fusion released in the freezing of the Earth’s liquid core supplies the energy to drive mantle convection and to support plate tectonics. The cores of the lower-density Jovian planets are believed to be composed of rock and/or ice. The presence or absence of a core is best determined from seismology, although the moment of inertia of the planet also provides information on how centrally condensed the body is. In astronomy, “core” is used to describe the central flat density region of some star clusters and galaxies. It is also used to describe the central homogeneous region of a chemically differentiated star.

core collapse The beginning of the end for massive stars, which have built up cores of iron from silicon burning, when the mass of the core reaches the Chandrasekhar limit. The collapse happens in a few seconds (after millions of years of evolution of the star) and releases a total energy of about 1053 ergs, the gravitational binding energy of the neutron star left behind. Much of this is radiated in neutrinos (and perhaps gravitational radiation), about 1% appears as kinetic energy of the expanding supernova remnant, some is radiated as visible light (so that we see a supernova of type II), and some is stored in the rotation and magnetic field of the neutron star or pulsar left behind at the center. The total available is GM2/R where M and R are the mass and radius of the neutron star. Core collapse may sometimes continue on past the neutron star stage and leave a black hole.

core convection It is generally understood that the Earth’s magnetic field arises predominantly from electrical instabilities associated with the flow of conducting fluid in the Earth’s core. The common viewpoint is that the energy source for the motions that generate the field is convection in the Earth’s core associated with heat loss from the core to the mantle. If there is radioactive heating of the core from isotopes such as potassium 40, then it is possible that the temperature of the core might stay roughly constant with time, but it is usually thought that there is little radioactivity in the core and the heat loss from the core is associated with the overall secular cooling of the planet as a whole and increase in size of the solid inner core. Convection arises when density decreases with depth, either because fluid cooled near the core-mantle boundary becomes more dense than underlying fluid, or because as the core cools, the inner core freezes out, excluding light elements and releasing latent heat and hence generating buoyant fluid at the inner core boundary. This latter case may lead to “compositional convection” related to the chemical makeup of the buoyant fluid rather than its temperature (i.e., “thermal convection”), which is energetically favorable for maintaining magnetic field but can have the seemingly perverse effect of transporting heat against a thermal gradient.

core-dominated quasars High luminosity, radio-loud active nuclei whose radio morphology is characterized by a luminous core which dominates the source emission. Mapped at milliarcsecond resolution, the core becomes partly resolved into a one-sided jet. Many coredominated radio quasars exhibit radio knots with superluminal motion, indicative of ejection of plasma at a velocity very close to the speed of light. The quasars 3C 273 and 3C 120 (whose name means that they were identified as radio sources 273 and 120 in the third Cambridge radio survey) are two of the brightest quasars in the sky and prototypical core-dominated superluminal sources. In the framework of the unification schemes of active galactic nuclei, coreand lobe-dominated quasars are basically the same objects: core-dominated objects are observed with the radio axis oriented at a small angle with respect to the line of sight, while the

© 2001 by CRC Press LLC

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