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equatorial anomaly

epoch An arbitrary fixed instant of time used as a chronological reference for calendars, celestial reference systems, star catalogs, or orbital motions. Prior to 1984, star catalog coordinates were commonly referred to the mean equator and equinox of the beginning of the Besselian year (see year). Thereafter, the Julian year (365.25 days) has been used.

equant A point in the Ptolemaic description of orbits about which the center of the epicycle moved at constant angular velocity as it moved along the deferent. The equant was equidistant on the opposite side of the center of deferent from the Earth. See deferent, epicycle.

equation of continuity Any of a class of equations that express the fact that some quantity (mass, charge, energy, etc.) cannot be created or destroyed. Such equations typically specify that the rate of increase of the quantity in a given region of space equals the net current of the quantity flowing into the region. Thus, the change of a property (e.g., mass) inside a volume element results from the convergence of a flux

 

across the boundaries of the volume and

C( )

 

from sources and sinks S( ) inside the volume:

∂t

+ ·

= S( ) .

C( )

 

 

 

equations of state, which give both the string energy per unit length U and its tension T (in general both are variable), and also the relation between them. The simplest example of equation of state is T = U = const, corresponding to the Goto–Nambu string.

Also conducting cosmic strings can be described by fitting analytical expressions to the numerical solutions of the classical equations of motion for the microscopic fields. The best analytical expression available for the Witten model is known as the Carter–Peter equation of state. See Carter–Peter model, conducting string, energy per unit length (cosmic string), Goto–Nambu string, tension (cosmic string), wiggle (cosmic string).

equation of state of pure water Potential density of pure water is a function of temperature only. For actual values see Chen and Millero (1986).

equation of time The hour angle of the true (observed) sun minus the hour angle of the (fictitious) mean sun of mean solar time.

equator The locus of a point traveling around the globe that is equidistant from the north and south poles forms the equator.

The most common application is the conserva-

equator, geomagnetic

(1.) The line around

the Earth, along which the vertical component

tion of mass

 

 

 

 

 

 

 

 

of the magnetic field is zero. Approximately

 

 

 

 

 

 

 

 

 

 

 

 

∂ρ

 

(ρu)

 

 

j

equidistant from both magnetic poles, but dis-

 

 

∂t = − ·

 

 

torted from that shape by non-dipole harmonics

 

 

= − ·

 

with ρ being the density and j

=

 

 

of the Earth’s magnetic field.

 

(2.) A term sometimes applied to the equa-

 

ρu the mass

current. Using the total derivative instead of the

torial surface of the magnetosphere.

partial one, this can be written as

 

 

 

 

 

 

 

 

dρ

 

 

∂ρ

 

 

 

 

equatorial anomaly

 

Although processes in

 

 

=

 

s + u · ρ = −ρ · u .

the ionospheric F region are complex, it is still

 

dt

∂t

 

 

 

 

 

 

 

 

 

 

reasonable to expect the maximum daytime ion-

 

 

 

 

 

 

 

 

 

 

ization to fall roughly near to the location of

equation of state

An equation relating the

the overhead sun.

However, in the equato-

pressure, volume, and temperature (or some

rial region, and most noticeable near equinox,

other set of thermodynamical variables) of a sub-

the daytime maximum in ionization splits form-

stance or system.

 

 

 

 

ing crests 20to 30to the north and south of

 

 

 

 

 

 

 

 

 

 

the dip equator, leaving an ionization trough

equation of state (cosmic string)

 

For an ac-

at the dip equator. This is called the equato-

curate macroscopic description of a vacuum vor-

rial anomaly. It is formed by a process analo-

tex defect as a cosmic string, one needs the string

gous to a fountain, ionization near the dip equa-

© 2001 by CRC Press LLC

equatorial bulge

tor being driven upward by the local E-region horizontal dynamo electric fields and the local horizontal magnetic field. As the ionization is lifted to higher altitudes, it encounters magnetic field lines connected to higher latitudes and falls back down, forming the crests. Generally, the anomaly is most pronounced around 1400 LT and then declines steadily until it disappears around 2000 LT. However, this behavior can change greatly with season, phase of the solar cycle, and diurnally. See equatorial electrojet, geomagnetic dip equator.

equatorial bulge The rotation of the earth causes the equatorial radius to be larger than the polar radius by about 21 km. This results in an equatorial bulge.

equatorial cold tongue A strip of cold surface water that extends like a tongue along the equator from the southeastern boundaries of the Pacific and Atlantic Oceans. The southeasterly trade winds are its direct cause, pushing the thermocline close to the surface and inducing upwelling that pumps cold thermocline water to the surface. The contrast between the warm western and cold eastern oceans in turn enhances the easterly trade winds on the equator. The surface water temperatures in the cold tongue peak in March-April and reach the minimum in July-September, despite negligible seasonal change in solar radiation at the top of the atmosphere on the equator. The water in the equatorial cold tongue is rich in nutrients and carbon dioxide, making it the largest natural source of atmospheric CO2.

equatorial convergence zone Also called intertropical convergence zone, i.e., ITCZ. Convergence zone at the tropospheric low level wind fields over tropics region, usually from 5S 10S to 5N 10N. From cloud pictures, ITCZ appears as a long cloud band and consists of many cloud clusters with west–east direction and almost surrounds the Earth. This cloud band width is about 200 to 300 km. In some regions and some times there are two cloud bands located on the south and the north sides of the equator, the so-called “double ITCZ.”

On average, in January, the ITCZ is located at about the equator and 15S; in April at about

4N and 5S; in July at 20N and 2S; and in November at 10N and 5S. The ITCZ has both active and inactive periods of short term variation. During the active period, it is most distant from the equator and has strong convective activity, with a series of large scale cloud clusters and frequent cyclonic vortices. During the inactive period, it is near the equator and has weakly developed clouds, which are mainly smaller scale scattered cumulus.

The ITCZ is the main region with ascending air in tropics, in which the deep cumulus convective activities are strong and frequent, especially during the active period. At times some of the cumulus can reach to the tropopause. In strong convergence regions, tropical disturbances are often created in the ICTZ. These tropical disturbances may develop into tropical cyclones in suitable environmental conditions. About 70 to 80% of tropical cyclones come from tropical disturbances developed in the ITCZ.

equatorial easterlies At the south side of the subtropical high in the high level of the troposphere, there are strong easterlies located at about 5 20N, 30 130E. The maximum speed is often located at 5 10N in the Arabian Sea region at about the 150 hPa level and is about 35 to 50 m/s. Along the Arabian Sea to the west, the equatorial easterlies move south gradually and reach the equator at North Africa. Over its entrance region (east of 90E) there is a direct meridional circulation, while over its exit region (west of 60E) there is an indirect meridional circulation. Through these meridional circulations, equatorial easterlies are connected to the southwest monsoon system at lower troposphere.

equatorial electrojet A current flowing above the Earth’s magnetic equator, inferred from magnetic disturbances on the ground. It flows on the sunlit side of Earth, from west to east.

equatorial Kelvin wave Oceanic Kelvin wave that propagates along the equator. For the first baroclinic mode in the ocean, a Kelvin wave would take about 2 months to cross the Pacific from New Guinea to South America.

© 2001 by CRC Press LLC

equilibrium tide (gravitational tide)

equatorial surface of the magnetosphere A surface with respect to which the Earth’s magnetospheric field and its trapped plasma exhibit approximate north-south symmetry. It is usually defined as a collection of the points of weakest magnetic intensity |B| on “closed” field lines which start and end on the surface of Earth. In the plasma sheet the surface is often called the “neutral sheet” and it undergoes a periodic deformation (“warping”) due to the daily and annual variation of the geomagnetic tilt angle ψ. See minimum-B surface.

equatorial undercurrent A strong narrow eastward current found in the region of strong density gradient below the ocean mixed layer and with its core close to the equator. Its vertical thickness is around 100 m and its half-width is a degree of latitude. The maximum current is typically 1 ms1. This eastward current is a major feature of the equatorial ocean circulation, particularly in the Pacific and Atlantic Oceans.

equatorial upwelling The resultant volume transport in the Ekman layer is at right angles to and to the right of the wind direction in the northern hemisphere. If the wind is easterly, water in the Ekman layer will tend to move away from the equator on both sides of the equator and will be replaced by water moving upward from below the layer. This is called equatorial upwelling. If the wind is westerly, water in the Ekman layer will tend to move toward the equator in both sides of the equator and repel the water below the layer. This is called equatorial downwelling.

equatorial waveguide An oceanic or atmospheric wave that is confined to propagate near the equator due to the vanishing of the Coriolis force at the equator. While the conditions for geostrophic balance theoretically fail at the equator, in practice any mass crossing the equator will be influenced by the Coriolis force on either side. The force turns such motion back towards the equator, thus creating a trap or a waveguide.

equatorial waves A class of equatorially trapped wave solutions first obtained by Taroh Matsuno in 1966, consisting of the Rossby, in-

ertial gravity, mixed Rossby-gravity, and Kelvin waves. The Rossby and inertial gravity waves are waves of rotating fluid, having their counterparts in off-equatorial regions. The Kelvin and mixed Rossby-gravity waves are unique to the equatorial waveguide arising from the singularity of the equator where the Coriolis parameter f = 2G sin θ vanishes. Here G is the angular velocity of the Earth’s rotation around the north pole and θ is latitude.

equilibrium In mechanics, a configuration in which the total force on a system vanishes, so if placed in such a configuration the system remains in it.

equilibrium beach profile A theoretical beach profile shape that results if wave conditions and water level are held constant for an indefinite period. It has a monotonic, concaveup shape.

equilibrium range High-wavenumber part of the turbulent kinetic energy spectrum that includes the inertial subrange and the dissipation range. The turbulence at these wavenumbers is nearly isotropic and the shape of the spectrum at these wavenumbers does not depend on the amount of kinetic energy present at larger scales or the size of these energy containing scales. Kinetic energy is merely transferred by inertial forces through the inertial subrange until the energy is dissipated into heat at the Kolmogorov microscale.

equilibrium space-times Stationary electrovacuum space-times describing the external fields of an arbitrary array of electrically charged, massive sources. Equilibrium is achieved by the balance of gravitational and electromagnetic forces. The static equilibrium space-times were found by S.D. Majumdar and A. Papapetrou (1947). See Israel–Wilson– Perjés space-times.

equilibrium tide (gravitational tide) A hypothetical ocean tide that responds instantly to tide producing forces, forming an equilibrium surface. The effects of friction, inertia, and the irregular distribution of land mass are ignored.

© 2001 by CRC Press LLC

equilibrium vapor pressure

equilibrium vapor pressure The vapor pressure in an equilibrium state system with two or more phases of water. If the system consists of vapor and pure water (ice), the equilibrium vapor pressure is the water (ice) surface saturated vapor pressure, and it is a function of temperature only. If the system consists of vapor and waterdrop or solution, due to curvature effects or solution effects, the equilibrium vapor pressure will be higher (vapor-waterdrop system) or lower (vapor-solution system) than the equilibrium vapor pressure in vapor-water system.

equinox Dates on which the day and night are of equal length. Dates on which the sun is at (one of two) locations of the intersection of the ecliptic and the celestial equator. Because the Earth poles are inclined by 2327 to its orbital plane, Northern and Southern hemispheres typically receive different daily periods of sunlight. At the equinoxes the location of the planet in its orbit is such that the sun strikes “broadside,” equally illuminating the two hemispheres. See autumnal equinox, vernal equinox.

equivalence principle A principle expressing the universality of gravitational interactions. It can be expressed in various degrees of “strength”.

Weak equivalence principle: The motion of any freely falling test particle is independent of its composition or structure. (Here “test particle” means that the particle’s gravitational binding and gravitational field are negligible.)

Medium strong equivalence principle: Near every event in spacetime, in a sufficiently small neighborhood, in every freely falling reference frame all nongravitational phenomena are exactly as they are in the absence of gravity.

Strong equivalence principle: Near every event in spacetime, in a sufficiently small neighborhood, in every freely falling reference frame all phenomena (including gravitational ones) are exactly as they are in the absence of external gravitational sources.

Various candidate descriptions of gravity obey one or the other of these laws. General relativity, which is very well verified in terms of large scale phenomena, obeys the strong equivalence principle. See Eötvös experiment.

Eratosthenes Mathematician, astronomer, geographer, and poet (third century BC). Measured the circumference of the Earth with considerable accuracy ( 15% above actual value) by determining astronomically the difference in latitude between the cities of Syene (now Aswan) and Alexandria, Egypt. He also compiled a star catalog and measured the obliquity of the ecliptic.

E region The portion of the ionosphere formed between approximately 95 and 130 km above the surface of the Earth. It lies between the D and F regions. The E region is directly controlled by the sun’s ionizing radiation and the amount of ionization present in the E region is directly related to the amount of radiation present. Thus, the E region has a maximum in ionization at local noon ( 1011 electrons m3), disappears shortly after sunset at E-region heights, and forms again at E-layer sunrise. It has a readily predicted behavior globally, diurnally, and seasonally that can be described by the sun’s solar zenith angle. There is also a small solar cycle variation in the daytime electron densities. At night, a small amount of ionization is found at E-region heights and is thought to be due to solar radiation scattered around from the daylight hemisphere together with a contribution due to cosmic rays. See ionosphere, sporadic E, spread E.

erg A cgs unit of energy equal to work done by a force of 1 dyne acting over a distance of 1 cm. 1 erg = 107J; 107 erg s1 1 Watt.

ergodic motion In mechanics, motion such that the trajectory of any given initial condition passes through every point of the surface in phase space having the same total energy as the initial condition.

ergoregion In general relativity, in spinning black hole spacetimes (Kerr black holes) the region in which particle kinematics allows rotational energy to be extracted from the black hole into energy of orbits that can reach infinity. See Kerr black hole.

ergs A large region covered by sand-sized (1/16 to 2 mm in diameter) material. Ergs are

© 2001 by CRC Press LLC

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