DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

space-time in general relativity with no cosmological
term is the Schwarzschild space-time.
Since the latter is static, this also rules out
monopole gravitational waves. Further, the
empty space-time inside a spherically symmetric
source must be flat. Generalizations with the
inclusion of a Maxwell field and cosmological
constant have been given. See Schwarzschild
solution.
Bjerknes See Bergen school.
Bjerknes circulation theorem The rate of
circulation change is due to either the baroclinicity
or the change in the enclosed area projected
in the equatorial plane:
DC
Dt =−
dp
ρ
− 2DAe
Dt
whereC is the relative circulation,p is the pressure,
ρ is the density, is the Earth’s rotation
rate and Ae is the enclosed area projection in
the equatorial plane. D is the absolute derivative
along the flow. In a barotropic fluid, the
relative circulation for a closed chain of fluid
particles will be changed if either the horizontal
area enclosed by the loop changes or the latitude
changes.
Bjerknes feedback An ocean-atmospheric
interaction mechanism first proposed by Jacob
Bjerknes in 1969 to explain the El Nino/
Southern Oscillation phenomenon. Normally
the easterly trade winds maintain a tilt of equatorial
thermocline, shallow in the east and deep
in the west. The equatorial upwelling induced
by the trades brings cold upper thermocline water
to the surface in the eastern equatorial Pacific.
A slight relaxation in the trades weakens
equatorial upwelling and depresses the thermocline
in the east, both acting to warm the eastern
Pacific. The warming in the east shifts the center
of active atmospheric convection eastward
and relaxes the easterly trades on the equator
even more. This constitutes a positive feedback
among the trade winds, thermocline depth, upwelling,
and sea surface temperature.
black aurora Name given to structured dark
patches appearing on the background of bright
aurora. Their origin is uncertain.
© 2001 by CRC Press LLC
black frost
black-body radiation The radiation from a
hypothetical thermal radiating body with perfect
emissivity. Practical black body sources consist
of a heated cavity with a small exit aperture.
Because radiation interacts repeatedly with the
walls of the cavity before emerging, the emerging
radiation is closely black body.
The spectral distribution of black-body radiation
is given by Planck’s formula:
dω
dλ = 2πc2h λ5
1
exphc/(λkT)
−1
(Joules per second per wavelength interval and
per unit area of the emitter) in which h =
6.62608 ×10 −27 erg sec is Planck’s constant and
k= 1.3807 × 10 −16 erg/K is Boltzmann’s constant;
this was the first understood instance of
a quantum phenomenon. At long wavelengths
the spectral distribution is approximately
dω
dλ
∼ 2πckT ,
λ4 which corresponds to earlier classical descriptions
by Wien and others. The peak of the distribution
obeys:
This is Wien’s law.
λPlanckT =.2898 cm K .
blackbody temperature The temperature
at which the radiation distribution from an object
can be characterized by Planck’s blackbody
equation. The distribution of radiation
from most hot, compact astronomical objects is
closely approximated by a blackbody temperature,
yet not exactly. The energy spectrum of
the sun, for example, has an energy distribution
that is closely but not exactly described by
a blackbody having a temperature TB = 6300
K. The effective temperature of the sun, which
takes into account the sun’s surface area and total
output power, is Teff = 5800 K. See effective
temperature, excitation temperature, color
temperature.
black frost Temperatures falling below
freezing in air dry enough that white hoar frost
does not form. Or, the blackening of vegetation
due to water freezing within and disrupting their
cells. See hoarfrost.