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brown dwarf

bright point A transient H-alpha brightening of ﬂare intensity, less than 20 millionths of the solar hemisphere in area. Such a brightening when covering a larger area becomes classiﬁed as a solar ﬂare.

brittle behavior (brittle fracture) A phenomenological term describing the nature of material failure. According to the simplest or “classical” view, brittle behavior (brittle fracture) of a solid material is a discrete event in which the failure of the solid occurs, without signiﬁcant prior deformation and without warning, at a particular stress. In general, material is described as “brittle” when fracture occurs with no preceding appreciable permanent deformation. Sometimes brittle behavior refers to failure following limited amounts of inelastic strain that are small compared with the elastic strain.

brittle-ductile transition A temperature range over which the principal failure mechanism of a rock body (such as the continental crust) under deviatoric stress changes from brittle to ductile. Brittle failure takes place at low temperatures by developing fractures or slipping along pre-existing fractures. Ductile failure takes place at higher temperatures and, observed at the macroscopic scale, by continuous deformation. The transition occurs due to the activation of diffusion or dislocation creep at elevated temperatures and is affected by the rate of ductile deformation and the pore ﬂuid pressure in the brittle region. In the Earth’s continental crust, this transition is marked by the absence of earthquakes below a certain depth where the temperature is higher than about 300 to 400◦C. In the oceanic crust and mantle, the transition occurs at higher temperatures.

brittle-plastic transition	See brittle-ductile
transition.
broad line radio galaxies	Radio galaxies

showing optical spectra very similar to, and in several cases almost indistinguishable from, those of Seyfert-1 galaxies. Broad line radio galaxies are type 1, low-luminosity, radio-loud active galactic nuclei; the radio-loud counterpart of Seyfert-1 galaxies. Differences between Seyfert-1 and Broad Line Radio galaxies en-

compass the morphology of the host galaxy (Seyfert-1 are mostly, albeit not exclusively, spirals, while broad line radio galaxies are hosted by ellipticals) and some features of the optical spectrum, like weaker singly ionized iron emission and larger internal absorption due to dust in broad line radio galaxies. See Seyfert galaxies.

broad line region The region where the broad lines of active galactic nuclei are produced. The strongest lines observed in the optical and UV spectrum are the Balmer lines of hydrogen, the hydrogen Lyman α line, the line from the three times ionized carbon at 154.9 nm, and some recombination lines from singly ionized and neutral helium. Since no forbidden lines are observed, the broad line region is most likely a relatively high density region with particle density in the range 109 to 1013 ions per cubic centimeter. The broad line region is believed to be very close to the central source of radiating energy of the active galactic nucleus. Observations of variation of broad line proﬁles and ﬂuxes suggest that the broad line regions line emitting gas is conﬁned within 1 pc in Seyfert-1 galaxies. Models of the broad line regions invoke a large number of dense emitting clouds, rapidly rotating around a central illuminating source. Alternatively, it has been suggested that at least part of the emission of the broad line regions could come from the middle and outer region of the accretion disk suspected to be a universal constituent of the central engine of active galactic nuclei.

brown dwarf A sphere of gas with the composition of a star (that is, roughly 43 hydrogen, 41 helium, and at most a few percent of heavier elements) but with a mass low enough that the center never, as the object contracts out of interstellar gas, gets hot enough for hydrogen burning to balance the energy being lost from the surface of the sphere. Very young brown dwarfs can be as bright as low-mass stars (10−4 to 10−5 of the solar luminosity), but they fade with time until they are too cool and faint to see. The number of brown dwarfs in our galaxy is not very well known. They are probably not common enough (at least in the galactic disk) to contribute much to the dark matter, but small numbers have been observed (a) in young clusters of stars, (b) as

Brunt frequency

companions to somewhat more massive stars, and (c) in isolation in space. See dark matter, galactic disk, hydrogen burning, interstellar gas.

Brunt frequency See buoyancy frequency.

Brunt–Väisälä frequency See buoyancy frequency.

B star Star of spectral type B. Rigel and Spica are examples of B stars.

bulkhead A man-made wall, typically vertical, which holds back or protects sediment from the impact of water. May be held in place by driven piles or with anchors placed in the sediment behind the wall. Bulkheads are commonly made of treated wood or steel.

bulk modulus For a density ρ and a pressure P , the quantity ρdP/dρ is called the bulk modulus. The reciprocal of compressibility. Two versions of this parameter are used. One has the temperature constant during the pressure change and is usually designated the isothermal bulk modulus, KT . The other has the entropy constant during the pressure change and is called the adiabatic bulk modulus.

bulk parameters (1.) Quantities derived from spatial or temporal average values of other quantities. For example, non-dimensional scaling numbers, such as the Reynolds number or the Froude number, are often deﬁned in terms of average values of velocity and length. These average values are sometimes also referred to as “characteristic scales” of the ﬂow.

(2.) Quantities that are computed from spatial or temporal averages of ﬁeld data. The data that constitute the bulk parameter are often sampled with a number of different instruments. It must be assumed that the data are statistically homogeneous and isotropic in the sampling interval.

buoyancy The upward force on a body equal to the weight of the ﬂuid displaced by the body.

Fbuoy = ρV g

where ρ is the density, V is the volume of the ﬂuid, and g is the acceleration of gravity.

buoyancy ﬂux Turbulence in a stratiﬁed ﬂuid affects the stratiﬁcation. The buoyancy ﬂux Jb [W kg−1] quantiﬁes (in differential form) the rate of change of the potential energy of the stratiﬁcation. It is deﬁned by Jb = gρ−1 < w ρ >= gρ−1Fρ, where g is the gravitational acceleration, ρ density, ρ density ﬂuctuations, w vertical velocity ﬂuctuations, and Fρ the vertical density (mass) ﬂux [kgm−2s−1]. Three principal cases can be distinguished:

(1)In a stable water column, the buoyancy ﬂux Jb expresses the rate at which turbulent kinetic energy (source of Jb) is turned over to increase the potential energy of the water column by work against stratiﬁcation: Jb = −KρN2,

where Kρ is the turbulent diapycnal diffusivity and N2 is stability. This process is accompanied by dissipation of turbulent kinetic energy ( ). For the relation between Jb and , see mixing efﬁciency.

(2)In an unstable water column (see convective turbulence), potential energy (source of Jb) is released, which fuels kinetic energy into turbulence. If the source of the density change ∂ρ/∂t is at the surface or bottom of the mixed boundary layer, the boundary buoyancy ﬂux is

deﬁned by, Jbo = ρ−1hmixg∂ρ/∂t, where hmix is the thickness of the mixed boundary layer.

(3) Under the conditional instability of double diffusion, the water column releases potential energy (source of Jb) from the water column to turbulent kinetic energy at a rate Jb, which is given by the so-called double-diffusive ﬂux laws (Turner, 1974; McDougall and Taylor, 1984).

buoyancy frequency A measure of the degree of stability in the water column, deﬁned by

N2 = −g ∂ρ

ρ∂z

where g is the constant of gravity, ρ is the density, and z is the vertical coordinate (positive upwards). When N2 is positive, the medium is stable, and N represents the frequency of oscillation of a water parcel in purely vertical motion. When N2 is negative, the medium is unstable. In the large vertical gradient regions of the upper ocean, N typically ranges from 3 to 7 cycles per hour. In the deep ocean, N is between 0.5 and 1 cycles per hour. Also called the stability fre-

Butcher–Oemler effect

quency, the Brunt–Väisäla frequency, the Brunt frequency, and Väisälä frequency.

buoyancy Reynolds number The nondimensional ratio ReB = /(νN2) expresses the intensity of turbulence, quantiﬁed by the dissipation of turbulent kinetic energy , relative to the turbulence-suppressing effect of stability N2 and viscosity ν. If ReB > 20−30, turbulence is considered as actively mixing despite the stratiﬁcation (Rohr and Van Atta, 1987), but as long as ReB < 200 turbulence is not expected to be isotropic (Gargett et al.; 1984).

buoyancy scale Largest overturning length scale allowed by the ambient stratiﬁcation. In stratiﬁed turbulent ﬂows away from boundaries, the size of the largest overturns or eddies is limited by the work required to overcome buoyancy forces. The buoyancy scale can be estimated from

1/2

LN = 2π N3

where N is the buoyancy frequency and is the dissipation rate of turbulent kinetic energy.

buoyancy scaling In the interior of stratiﬁed natural water bodies, internal wave shear is usually the dominant source of turbulence. Because turbulence is limited by the presence of stratiﬁcation, it depends on both the stability N2 of the water column and the dissipation of turbulent kinetic energy . Dimensional analysis provides the relations for buoyancy scaling as a function of N and .

	Length	Lbs ( N−3)1/2
	Time	τbs N−1
	Velocity	wbs ( N−1)1/2
	Diffusivity	Kbs N−2
	Buoyancy ﬂux	Jbs
buoyancy subrange		Range of the energy

spectra, which is affected by buoyancy forces and where subsequently turbulence is expected to be anisotropic (see buoyancy Reynolds num- ber). The relevant parameters to quantify turbulence in the buoyancy subrange are dissipation of turbulent kinetic energy and stability N2. See buoyancy scaling.

Bureau International des Poids et Mesures (BIPM) International bureau of weights and measures in Sevres, France, charged mainly with the production of International Atomic Time.

Burgers vector (b) The dislocation displacement vector deﬁned by the procedure ﬁrst suggested by Frank (1951). When a dislocation line or loop is deﬁned as the boundary between a slipped area and an unslipped area on a slip plane, it can be characterized by a unit vector expressing the amount and direction of slip caused by its propagation on the slip plane. This unit vector, which corresponds to unit motion of dislocations, is called Burgers Vector (b). Burgers vector must correspond to one of the unit vectors for a given crystal structure.

burst In solar physics, a transient enhancement of the solar radio emission, usually associated with an active region or ﬂare. In cosmic ray physics, a sudden ﬂux of cosmic rays with a common origin.

bursty bulk ﬂows In the Earth’s magnetosphere, intervals of rapid ion ﬂows observed in the plasma sheet, lasting typically 10 min. Extreme velocity peaks within these intervals reach many hundreds of kilometers per second, last for a fraction of a minute, and are termed ﬂow bursts. Flows closer to Earth than 25 RE tend to be directed earthward; more distant ones are usually tailward.

Butcher–Oemler effect The increase in the fraction of blue galaxies in distant clusters of galaxies. H. Butcher and A. Oemler, in papers published in 1978 and 1984, discussed an excess of galaxies with color index B-V signiﬁcantly bluer than that of normal elliptical and S0 galaxies. This excess of blue galaxies was found in clusters of galaxies at redshift near 0.4: Butcher and Oemler discovered that 20% of galaxies in clusters at redshift larger than 0.2 were blue galaxies, while blue galaxies accounted for only 3% of all galaxies in nearby clusters. Blue color suggests strong star formation. The detection of a large number of blue galaxies indicates that signiﬁcant galactic evolution is still occurring at

butterﬂy diagram

a very recent epoch, about .9 of the present age of the universe.

butterﬂy diagram A diagram showing the behavior of the observed latitude of a sunspot with time during the course of several solar cycles. The latitudinal drift of the sunspot emergence as the cycle proceeds (from high latitudes to the solar equator) resembles a butterﬂy’s wings. The physical cause of this behavior is thought to be due to the generation of magnetic ﬁeld by the solar dynamo.

Buys Ballots Law In the Northern hemisphere, if one stands with one’s back to the wind, the low pressure is to the left, and the high is to the right. The rule is opposite in the Southern hemisphere and arises because of the Coriolis force from the Earth’s rotation. This is useful because bad weather is typically associated with low pressure regions.

b-value One of the coefﬁcients of the Guttenberg–Richter relation relating the frequency of occurrence to the magnitude of earthquakes.

Byerlee’s law A laboratory experimental result of static rock friction obtained by U.S. geophysicist J.D. Byerlee in 1978. The experiments show that, statistically, regardless of rock type, temperature, and conﬁning pressure, the relation between normal stress σn and shear stress τ on the ﬂat frictional surface between two rock specimens is:

τ	=	0.85σn	(σn ≤ 200 MPa)
τ	=	50 + 0.6σn	(σn > 200 MPa) .

Assuming that the top part of the Earth’s lithosphere is pervasively fractured by faults of random orientations, Byerlee’s law is frequently used to deﬁne the brittle strength of the lithosphere. Shear stresses along major geological faults have been inferred to be much lower than Byerlee’s law predictions.

bypass As used in the study of coastal geomorphology, the process by which sediment moves from one side of a tidal inlet to the other. Artiﬁcial bypassing schemes have also been used to transport sediment across a stabilized inlet or past a harbor entrance.