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ν1/4q1/2

beams, ion

−1/4 the nondimensional vertical wavenumber, ν the kinematic viscosity of water, χT the dissipation rate of temperature variance, and the dissipation rate of turbulent kinetic energy; LB is the Batchelor scale (Batchelor, 1959). The constancy of the turbulence parameter q, usually taken as q = 3.4 (Dillon and Caldwell, 1980), is subject to debate. The Batchelor spectrum of salt follows the same function with the molecular diffusivity κS of salt (instead of κT ) and the dissipation rate of salt variance χS (instead of χT ). For small k, the spectrum φT (kz) drops as k−1 (viscousconvective subrange), and for k larger than the

Batchelor wavenumber kB , φT (kz) rolls off at a much steeper rate (viscous-diffusive subrange). These two subranges are commonly referred to as Batchelor spectrum.

Batchelor wavenumber The inverse of the Batchelor scale, expressing the wavenumber kB , above which scalar ﬂuctuations (such as those of temperature or salt) become eradicated by the smoothing effect of molecular diffusion (i.e., Batchelor spectrum drops off sharply above kB ). Two deﬁnitions are common: kB = (ε/νκ2)1/4 [rad m−1], or kB = (2π)−1(ε/νκ2)1/4 [cycles m−1]. κ is the molecular diffusivity of the scalar (κ = κT for temperature or κ = κS for salt).

batholith Large igneous body where molten rocks have solidiﬁed at depth in the ocean. A typical batholith has a thickness of a few kilometers and horizontal dimension of tens to hundreds of kilometers.

bathymetry Measure of the depth of the sea ﬂoor below sea level.

b-boundary (or bundle boundary) In relativity, assorted boundary points of the spacetime manifold deﬁned by equivalence classes of curves in the orthogonal frame bundle of the space-time (B. Schmidt). The goal of this work is to evade the difﬁculties of setting up a topology on a manifold with an indeﬁnite metric by using the positive-deﬁnite measure on the frame bundle. Examples of cosmological space-times have been found which show that the notion of the b-boundary is not suitable for deﬁning the

boundary of a space-time, due to topological problems.

beach cusps Periodic (in space), transient, cuspate features which commonly appear in beach planforms. Wavelengths typically range from 1 to 50 meters, with amplitudes less than a wavelength.

beachface The relatively planar portion of a beach in the vicinity of the still water line. Subject to swash by wave action; therefore, alternately wet and dry.

beach mining The process of removing sand for some human activity, often industrial.

beach morphology	The study of the shape
and form of a beach or coastal area.
beach nourishment	The process of placing

sand on an eroding beach to advance the shoreline seaward. Sand is typically transported by hydraulic dredge via a pipeline, delivered by a split-hull barge, or transferred overland by truck. Typical project sand volumes are 10,000 to 10 million m3.

beach proﬁle A cross-shore slice through a beach, illustrating how bathymetry varies in the shore-normal direction.

beach ridge A linear ridge of sand that appears behind the modern beach and indicates a prograding beach. Multiple beach ridges are often visible. Referred to as “Cheniers” in Texas and Louisiana.

beam attenuation coefﬁcient The limit of the ratio of the spectral absorptance plus spectral scatterance to the distance of photon travel as that distance becomes vanishingly small [m−1]; equal to the sum of the absorption and scattering coefﬁcients.

beams, ion Beam-like upwards ﬂow of ions, usually O+ (singly ionized oxygen), observed above the atmosphere during polar auroras. First seen in 1976 by the S3-3 satellite, ion beams are believed to be accelerated by the same parallel electric ﬁeld that accel-

beam spread function

erates auroral electrons downwards, possibly a quasi-neutral electric ﬁeld associated with upwards Birkeland currents. See conics.

beam spread function The irradiance distribution on the inner surface of a sphere as generated by an initially collimated, narrow beam and normalized to the beam power [m−2]; numerically equals the point spread function.

beam transmissometer An instrument for measuring the fraction of a collimated beam lost by absorption and scattering per unit distance of photon travel; measures the beam attenuation coefﬁcient.

Beaufort wind scale A descriptive table of wind speeds developed by Admiral Sir Francis Beaufort in 1806. For practical use, in particular at sea, wind speeds are described by the states of the sea surface and the wave height H . The original scale considers 12 grades from calm to hurricane; in 1956, grade 12 was divided into grades from 12 to 17. The wind velocity is related to the Beaufort Force approximated by v = B1.5, where v is the wind speed measured at 10 m height and B is the Beaufort Force. See tables on pages 39 and 40.

bed load A term used in the study of sediment transport by moving ﬂuids. Bed load denotes the fraction of sediment transported very close to the bed, such as the particles that bounce along the bed. The remainder of the sediment is suspended in the water column and is referred to as suspended load and wash load.

Beer’s law Radiation traveling in a certain direction in a scattering or absorbing medium is exponentially attenuated.

Belinda Moon of Uranus also designated UXIV. Discovered by Voyager 2 in 1986, it is a small, irregular body, approximately 34 km in radius. Its orbit has an eccentricity of 0, an inclination of 0◦, a precession of 129◦ yr−1, and a semimajor axis of 7.53 × 104 km. 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 0.624 Earth days.

Benard cell When a gas or plasma is heated uniformly from below, convection takes place in vertical cells, the Benard cells. The motion is upward in the center of the cell and downward at the cell boundaries. In laboratory experiments, the pattern of convection cells is regular and long-lived. Natural Benard cells can be observed in the terrestrial atmosphere under calm conditions or as granulation at the top of the solar convection zone.

Benioff zone In a subduction zone the oceanic lithosphere descends into the mantle at velocities of about 10 cm per year. The upper boundary of the descending plate is a fault zone between the plate and overlying crustal and mantle wedge. The earthquakes on this fault deﬁne the Benioff zone. The zone has a typical dip of 30◦ to 45◦ and extends to depths of 670 km. The existence of these dipping zones of seismicity was one of the major arguments for plate tectonics.

benthic The portion of the marine environment inhabited by marine organisms that live in or on the bottom of the ocean.

benthos Bottom-dwelling marine organisms.

Bergen school Meteorology. A school of analysis founded in 1918 by the Norwegian physicist Vihelm Bjerknes (1862–1951), his son Jacob Bjerknes (1897–1975), Halvor Solberg (1895– ), and Tor Bergeron (1891– ). V. Bjerknes began his career as a physicist. In the late 1890s, he turned his attention to the dynamics of atmosphere and oceans. The “circulation theorems” he developed during this period provided a theoretical basis for the basic concepts in the general circulation. During World War I, Bjerknes, as founding director of the Geophysical Institute at Bergen, was successful in convincing the Norwegian government to install a dense network of surface stations which provided data for investigating the surface wind ﬁeld. These studies led to the concept of fronts and ultimately to models of the life cycle of frontal cyclones. In 1919, J. Bjerknes introduced the concept of warm, cold, and occluded fronts, and correctly explained their relationship to extratropical cyclones. By 1926, in collaboration with Solberg

beta-effect

Classic Beaufort Scale

		Wind speed
B◦	Name	[knots]	[m/s]	Sea surface characteristics	H [m]
0	Calm	< 1	0.0–0.2	Sea like a mirror	0
1	Light air	2	0.9	Ripples	0.1–0.2
2	Light breeze	5	2.5	Small wavelets	0.3–0.5
3	Gentle breeze	9	4.4	Large wavelets, crests	0.6–1.0
				begin to break
4	Moderate breeze	13	6.7	Small waves, white horses	1.5
5	Fresh breeze	18	9.3	Moderate waves, becoming	2.0
				longer
6	Strong breeze	24	12.3	White foam crests	3.5
7	Moderate gale	30	15.5	Sea heaps up; white foam	5.0
				from breaking waves blown
				in streaks
8	Fresh gale	37	19	Moderately high waves, greater
				length; edges of crests break
				into spindrift
9	Strong gale	44	22.6	High waves, sea begins to roll	9.5
10	Whole gale	52	26.5	Sea-surface white from great	12
				patches of foam blown in dense
				streaks
11	Storm	60	30.6	Exceptionally high waves; sea	15
				covered by patches of foam;
				visibility reduced
12	Hurricane	68	34.8	Air ﬁlled with foam and spray;
				visibility greatly reduced

and others, he had described the structure and life cycle of extratropical cyclones. Bergeron also made important contributions to the understanding of occluded fronts and the formation of precipitation.

Bergeron, Tor (1891– ) See Bergen school.

berm A nearly horizontal ledge, ridge, or shelf of sediment which lies behind the beach face at a beach. More than one berm will sometimes be evident within the backshore region.

Bernoulli equation For steady ﬂow of a frictionless, incompressible ﬂuid along a smooth line of ﬂow known as a streamline, the total mechanical energy per unit weight is a constant that is the sum of the velocity head (u2/2g), the elevation head (z), and the pressure head (p/ρg): u2/2g + z + p/ρg = constant, where u is the velocity, g is the acceleration of gravity, z is the elevation above some arbitrary datum, p is the ﬂuid pressure, and ρ is the ﬂuid density. The

Bernoulli equation expresses all terms in the units of energy per unit weight or joules/newton, which reduces to meters. The Bernoulli equation therefore has the advantage of having all units in dimensions of length. The sum of these three factors is the hydraulic head h.

Besselian year

See year.

beta decay Nuclear transition mediated by the weak force, in which the nuclear charge changes by one, either Z → Z+1, A → A with the emission of an electron plus an antineutrino; or Z → Z − 1, A → A with the emission of a positron plus a neutrino. The paradigm is the

free decay of the neutron: n → p + e− + ν¯.

beta-effect (β-effect) A combined effect of the rotation and curvature of the Earth which tends to produce ocean currents on the western boundaries of basins with speeds exceeding

Beta Lyrae systems

Beaufort Wind Scale Limits of Wind Speed at 10 m

Force	Knots	m/sec	km/hr	mi/hr	Description of wind
0	<1	0-0.2	<1	<1	Calm
1	1-3	0.3-1.5	1-5	1-3	Light air
2	4-6	1.6-3.3	6-11	4-7	Light breeze
3	7-10	3.4-5.4	12-19	8-12	Gentle breeze
4	11-16	5.5-7.9	20-28	13-18	Moderate breeze
5	17-21	8.0-10.7	29-38	19-24	Fresh breeze
6	22-27	10.8-13.8 39-49		25-31	Strong breeze
7	28-33	13.9-17.1 50-61		32-38	Moderate gale
8	34-40	17.2-20.7 62-74		39-46	Fresh gale
9	41-47	20.8-24.4 75-88		47-54	Strong gale
10	48-55	24.5-28.4 89-102		55-63	Whole gale
11	56-63	28.5-32.6 103-117		64-72	Storm
12	64-71	32.7-36.9 118-133		73-82	Hurricane
13	72-80	37.0-41.4 134-149		83-92	Hurricane
14	81-89	41.5-46.1 150-166		93-103	Hurricane
15	90-99	46.2-50.9 167-183		104-114	Hurricane
16	100-108 51.0-56.0 184-201			115-125	Hurricane
17	109-118	56.1-61.2	202-220	126-136	Hurricane

those in the rest of the ocean basin. See betaplane approximation.

Beta Lyrae systems Binary stars in which the more massive star has recently ﬁlled its Roche Lobe so that material has begun ﬂowing down onto the companion star (in a stream or accretion disk). This occurs very rapidly (on the Kelvin–Helmholtz time scale) until the ratio of masses has been reversed. The companion is often completely hidden by the disk, so that one sees eclipses of the mass donor by something that itself emits very little light. It is not absolutely certain that Beta Lyrae itself is actually a

Beta Lyrae system. See Roche lobe.

beta-plane approximation (Rossby et al., 1939) The effects of the Earth’s sphericity are retained in the Cartesian metric by approximating the Coriolis parameter, f, with the linear function of y, which is the latidinal coordinate and is measured positive northward from the reference latitude. This approximation is called the

β-plane approximation.

Bianca Moon of Uranus also designated UVIII. Discovered by Voyager 2 in 1986, it is a small, irregular body, approximately 22 km in radius. Its orbit has an eccentricity of 0.001, an inclination of 0◦, a precession of 299◦ yr−1, and

a semimajor axis of 5.92×104 km. 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 0.435 Earth days.

Bianchi classiﬁcation A classiﬁcation of three-parametric symmetries into inequivalent classes.

For three-dimensional spaces, the number of distinct classes is ﬁnite, and the complete list of all classes is called the Bianchi classiﬁcation (after the Italian mathematician Luigi Bianchi). The total number of Bianchi’s classes is 9, although some of the classes are themselves collections labeled by free parameters. This classiﬁcation is useful in constructing mathematical

models of the universe.
biased vacuum states (domain wall)	Do-

main walls are formed whenever a discrete symmetry is broken, and their existence is a consequence of the presence of degenerate potential minima in the broken phase. Domain walls in the universe would importantly alter standard cosmology. They are, however, produced in some particle physics theories, which are therefore highly constrained.

It is conceivable that the Higgs potential may be modiﬁed somehow, so that the above mentioned equivalent minima acquire different val-