wind shear

Wind speed in km/h:

TWC =Ts − ((Ts − T ) (.474266

√

+ .2392 V −.01261 V )) .

In every case Ts is the skin temperature, TS = 91.4◦F or 33◦C; the effective wind chill factor gives a result in the same units.

Note that these formulae are inapplicable below very low wind speeds (equivalently 4 mph, 1.78816 m/s, 6.437 km/sec, 3.476 knots). Below this speed the wind chill temperature is taken to be the same as the actual temperature (although the formula will actually give temperatures above the measured temperature for winds below this lower limit).

Also notice that above about 40 mph of windspeed, there is little additional wind chill effect.

wind-driven circulation The circulation that is driven by the wind stress forcing in the ocean or lake.

wind evaporation-sea surface temperature feedback An ocean-atmospheric interaction mechanism that causes equatorial asymmetries in the climate system. The most notable examples of its effect are the northward departure of the Pacific and Atlantic intertropical convergence zone and the north-south seesaw oscillation in the tropical Atlantic climate. Suppose that there are a pair of sea surface temperature (SST) anomalies, positive to the north and negative to the south of the equator. The lower atmosphere responds with anomalous southerly winds blowing across the equator. The induced Coriolis force generates westerly (easterly) wind anomalies to the north (south) of the equator. Superimposed on easterly trade winds in the basic state, these zonal wind anomalies weaken (enhance) the trade winds and surface evaporation, raising (lowering) SST to the north (south) of the equator and amplifying the initial SST anomalies.

winding number In solid state physics and in cosmology, topological defects may appear when, during a phase transition, the symmetry of the full Hamiltonian is not respected by the vacuum of the theory. Then, for example, in the case of a Higgs field self-potential with the form

of a paraboloid at high temperatures, but which turns into a potential with “Mexican hat” shape at low temperatures, the initial U(1) (change of phase) symmetry is not present after the potential changes shape; in this latter case, the complex field, attempting to minimize its energy, will choose one particular location at the bottom of the potential, in so doing breaking the symmetry present before. Further, the particular potential location chosen may be a function of position.

Now, it may well happen that when we follow a closed path in physical space, the Higgs field also performs a complete circle around the minima of its potential. It is in this case that its phase will develop a non-trivial winding of 2π, signaling the presence of the vortex line. The

field solution far away from the string will then take the form φ |φ|einθ with n = 1 and θ

the azimuthal angle. More generally, the field may also wrap around the bottom of its potential n times during just one closed path in physical space. Thus n, the winding number, can exceed unity. In the cosmic string example described above, for example, n always takes integer values and is directly related to the magnetic flux quantization of vortex lines.

Other topological defects produced during the breakdown of continuous symmetries will also carry a winding number; examples are magnetic monopoles and cosmic textures. In the texture case, in particular, the defect configuration can be characterized by a non-integer (fractional, for example) winding number. See cosmic texture, cosmic topological defect, cosmic string, homotopy group, monopole, Nielsen– Olesen vortex.

wind rose A polar histogram that shows the directional distribution of winds for a site. Generally also scaled to indicate wind speeds as well.

wind scale A system similar to the Beaufort scale, used in the U.S. to describe the speed of winds. See Beaufort wind scale.

wind shear The spatial variation of wind velocity (speed and/or direction) in a predetermined direction. Generally can be divided as the horizontal wind shear and vertical wind

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winter anomaly

			Scale
	Wind Condition	Speed (MPH)	Number
	Light	Less than 1	0
		1–3	1
		4–7	2
	Gentle	8–12	3
	Moderate	13–18	4
	Fresh	19–24	5
	Strong	25–31	6
		32–38	7
	Gale	39–46	8
		47–54	9
	Whole gale	55–63	10
		64–75	11
	Hurricane	Above 75	12

shear. Also it can be divided as the cyclonic wind shear and anti-cyclonic wind shear.

winter anomaly In ionospheric physics, the F region peak electron densities in the winter hemisphere at middle latitudes are usually enhanced above the summer peak electron densities. Often, the equinoctial electron densities are enhanced above both solstices. However, it is still more common to refer to this as a winter anomaly. The phenomenon is most evident during daytime solar maximum. The exact cause of the anomaly has been attributed to a number of sources, more recently to changes in atmospheric chemistry associated with upper atmosphere winds. See F region.

winter solstice The point that lies on the ecliptic midway between the vernal and autumnal equinoxes and at which the sun, in its apparent annual motion, is at its greatest angular distance south of the celestial equator. On the day of the winter solstice, which occurs on about December 21, the length of night time darkness is at its maximum in the northern hemisphere. After the winter solstice, the length of daylight time in the northern hemisphere will increase until the summer solstice. Because of complex interactions with heat reservoirs in the atmosphere, soil, and oceans, the northern hemisphere temperature continues to decrease for a period of time after the winter solstice. In the southern hemisphere, the winter solstice (about Decem-

ber 21) is the beginning of summer, the day of the year with the longest period of sunlight.

Witten conducting string Extensions of the simplest grand unified models with the formation of cosmic strings in general involve extra degrees of freedom which are coupled to the vortex-forming Higgs field. These may be, for example, other microscopic fields that could be responsible for the generation of currents, bound to the core of the vortices, and that may play a fundamental role in the dynamics of the defects.

The Witten-type bosonic superconductivity model is one in which the fundamental Lagrangian is invariant under the action of a U(1)× U(1) symmetry group. The first U(1) is spontaneously broken through the usual Higgs mechanism in which the Higgs field acquires a nonvanishing vacuum expectation value. Hence, at an energy scale m we are left with a network of ordinary cosmic strings with tension and energy per unit length T U m2, as dictated by the Kibble mechanism. The Higgs field is coupled not only with its associated gauge vector field but also with a second charged scalar boson, the current carrier field, which in turn obeys a quartic potential. A second phase transition breaks the second U(1) gauge (or global, in the case of neutral currents) group and, at an energy scale

(in general < ), the generation of a m m m

current-carrying condensate in the vortex makes the tension no longer constant, but dependent on the magnitude of the current, with the general feature that T ≤ m2 ≤ U, breaking, therefore, the degeneracy of the Goto–Nambu strings.

The fact that the absolute value of the current carrier field is nonvanishing in the string results in that either electromagnetism (in the case that the associated gauge vector is the electromagnetic potential) or the global U(1) is spontaneously broken in the core, with the resulting Goldstone bosons carrying charge up and down the string. Once generated, these currents are not affected by any resistance mechanism in the string core (unlike what would be the case for ordinary conducting wires) and hence are persistent.

Thus these strings are endowed with some superconducting properties, although the fact of being defined inside a core no bigger than the Higgs Compton wavelength (of order the

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WWSSN (World-Wide Standardized Seismograph Network)

electromagnetic penetration depth) complicates somewhat the interpretation (e.g., the Meissner effect) in usual condensed matter terms. See Abelian Higgs model, conducting string, Nielsen–Olesen vortex, spontaneous symmetry breaking, winding number.

wolf number An historic term for the sunspot number.

work In Newtonian mechanics, the product of an applied force and the displacement in the direction of the force.

work W = F · d = |F ||d| sin θ ,

where θ is the angle between the force and the displacement.

Work has units of Joules: 1 Joule = 1 Newton·meter, or of ergs: 1 erg = 1 dyne·cm.

worldsheet charge	See electric regime
(string).
worldsheet geometry	See fundamental ten-
sors of a worldsheet.

wormhole A connection between two locations in space-time. This involves a curvature of space-time which acts as a bridge between two distant points that may lie in the same region or in different regions and which are otherwise inaccessible to each other. There is currently no evidence of their existence. See curved spacetime, Einstein–Roser bridge.

wrinkle ridges Features that occur in the northern plains of Mars, probably of volcanic origin. They are classically described as consisting of a rise, a broad arch, and an associated narrow sinuous ridge. They may be segmented to form an “en echelon” arrangement. Detailed analysis shows that almost all wrinkle ridges mark a regional elevation offset and so are asymmetrical. Dimensions are ≈10 km wide, ≈100 m high, with a regional elevation offset range between ≈10 to 1000 m where detectable.

W Ursa Majoris (W UMa) See contact binary.

WWSSN (World-Wide Standardized Seismograph Network) In 1960, three-compo- nent Press–Ewing type seismographs and shortperiod Benioff type seismographs with identical properties were deployed at about 120 stations throughout the world by U.S. Coast and Geodetic Survey (USCGS), mainly aiming at detection of underground nuclear tests. This world-wide seismograph network is called WWSSN. Seismic waveforms recorded by the seismograph network have contributed substantially to research on the source process of large earthquakes and structure of the Earth’s interior using surface waves. In the 1970s, digital recording type seismograph networks began to be deployed. To date, there are IDA, SRO, DWWSSN, RSTN, and GEOSCOPE as seismograph networks deployed. Recently, principal observation stations of WWSSN have been moved to IRIS (Incorporated Research Institutions for Seismology).

© 2001 by CRC Press LLC

X-ray source

X

xenoliths Rocks carried to the surface of the Earth in volcanic eruptions. These rocks originate both from the deep crust and from the mantle. They are a primary source of information on the composition of these regions. Diamonds are carried from the interior of the Earth in Kimberlitic eruptions and are one class of xenoliths.

xenon Rare noble gas, Xe, atomic number 54, naturally occurring atomic weight 131.29. Melting point 161.4 K, boiling point 165.1 K. Naturally occurring isotopes include those with atomic weights 124, 126, 128, 129 (the most abundant), 130, 131, 132, 134, 136. Xenon is present in the atmosphere at about 50 ppb and in the Martian atmosphere at 80 ppb.

X-ray The part of the electromagnetic spectrum whose radiation has energies in the approximate range from 1 to 150 keV. Typically used to observe the solar corona and, in particular, solar flares.

X-ray binary A binary star in which one component is a neutron star or black hole and the other is a main sequence star or red giant. Material is transferred from the latter to the former through Roche lobe overflow or a stellar wind, sometimes via an accretion disk. The accreting gas gets very hot, liberating gravitational potential energy of up to 1020 ergs per gram (about 10% of mc2). In the case of a neutron star accretor, there can be variability associated with the neutron star’s rotation period and with explosive nuclear reactions on the surface. Variability in the black hole systems is associated with changes in accretion rate and disk structure. Either kind of accretor can occur with either high mass (stellar wind) or low mass (Roche lobe overflow) donor. Most of the 10 or so known black hole systems have black hole masses of 5 to 10 solar masses. Most of the neutron star masses are 1.5 to 2.0 solar masses, permitting

a clean separation of the classes. Luminosities can reach 105 solar luminosities.

X-ray bright point X-ray bright points are small, compact, short-lived solar X-ray brightenings that are most easily seen in coronal holes.

X-ray burst A temporary enhancement of the X-ray emission of the sun. The time-intensity profile of soft X-ray bursts is similar to that of the Hα profile of an associated flare.

X-ray burster An irregular X-ray source, believed to occur when matter from an evolved large companion star accretes onto the surface of a neutron star in a binary system. Hydrogen accumulates on the surface, and when the density is high enough, explosively burns (at very high temperature) on the surface. This is similar to a nova in mechanism, but the energy associated with the burster is much higher because the gravitational field of the neutron star is so much stronger than that of a white dwarf.

X-ray flare classification Rank of a flare based on its X-ray energy output. Flares are classified by the order of magnitude of the peak burst intensity (I) measured at the Earth in the 1 to 8 Å band as follows:

Class (Wm−2)

BI < 10−6

C10−6 ≤ I ≤ 10−5 M 10−5 ≤ I ≤ 10−4

X

I ≥ 10−4

X-ray source In astrophysics, any detectable emitter of X-radiation (for instance the sun). In terms of frequency of occurrence and intrinsic brightness, X-ray binaries and the X-ray background are the major detectable examples. It is believed that all strong X-ray sources involve accretion onto a compact object, as onto a neutron star or onto a black hole, from a normal star in a X-ray binary. The background X-ray flux is believed to be made up principally from sources such as active galactic nuclei and/or quasars, which are powered by accretion from a disk onto a supermassive black hole.

© 2001 by CRC Press LLC

X-ray stars

X-ray stars Stars whose X-ray emission is strong enough to be detected from Earth. This is rather rare and generally associated with youth or rapid rotation (see stellar activity, coronae) or presence of a companion (see RS Canum Venaticorum stars). The first to be discov-

ered was Capella (with an energetic corona). Brighter X-ray sources are associated with mass transfer to white dwarfs, neutron stars, or black holes from companions and are called X-ray binaries.

© 2001 by CRC Press LLC