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diurnal

smoothing effect of molecular thermal diffusivity κT . In natural waters, χ is mostly estimated by proﬁlers that measure the temperature ﬂuctuations T at a high rate (at least such, as to resolve the structures to the Batchelor scale). If small-scale turbulence is isotropic, the rate of dissipation of temperature variance χ[K2s−1] is estimated from the temperature gradient spectra by χ = 6κT < (∂T /∂z)2 >, where z is the proﬁling direction. The vertical turbulent diffusivity κvt can be estimated by the relation κvt = χ[2(∂T /∂z)2]−1, a procedure often referred to as Osborn–Cox method (Osborn and Cox, 1972). See Cox number.

dissipation of turbulent kinetic energy

The rate at which turbulent kinetic energy #[W kg−1] is transformed to heat by internal fric-

tion caused by viscosity ν. Dissipation is given by # = 2ν ij [0.5 · (∂ui/∂xj + ∂uj /∂xi)]2

(see strain rate). In natural waters, # is mostly estimated by proﬁlers that measure one velocity component u in the direction perpendicular to the motion of the measuring proﬁler (direction z). For isotropic small-scale turbulence, the above nine terms in the summation collapse to the simple form # = 7.5ν < (∂u /∂z)2 > (<> indicates the average over a length scale, chosen typically 0.5 to several meters). An alternative estimate can be determined by the inertial dissipation method.

dissipation proﬁler Instrument for the measurement of oceanic turbulence levels. It is equipped with fast sampling airfoil probes and thermistors to resolve velocity and temperature ﬂuctuations in the dissipation range. Generally, these instruments are designed to either fall or rise vertically in the water in order to produce a proﬁle of the turbulent activity in the water column. For certain applications, the instruments are towed horizontally.

dissipation range The range of length scales or wavenumbers at which velocity ﬂuctuations in turbulent ﬂows are damped out (dissipated) by molecular viscosity. See Kolmogorov scale, turbulent cascade.

dissipation rate Rate at which turbulent kinetic energy (TKE) is removed from turbu-

lent ﬂows at length scales deﬁned by the Kolmogorov scale. The dissipation rate enters the turbulent kinetic energy equation as the term

# = 2νeij eij

where ν is the viscosity and eij is the ﬂuctuating strain rate tensor deﬁned by

		1
eij ≡	2			∂xj	+	∂xi

where ui and xi are the velocity and position, respectively, for the spatial directions i = 1, 2, 3. In oceanic turbulence studies, # can be estimated from measurements of velocity gradients. Under the assumption of isotropic and steady turbulence, # is estimated from

# =	2	ν	∂x1			2
	15			∂u2

where x1 is the direction along which the measurement device measures the perpendicular turbulent velocity ﬂuctuations u2. See also airfoil probe.

dissolved organic matter		See colored dis-
solved organic matter.
distance indicator	See standard candle.

distance modulus The distance to an object can be derived by comparing its apparent magnitude (m) and absolute magnitude M, where M is deﬁned to be the ﬂux of the star at a standard distance of (10pc2). Using the standard deﬁnition for magnitude, we have

L/4πR2

m − M = −2.5 log

L/4π(10pc2)

where R is the distance to the star and L is the star’s intrinsic brightness (luminosity). This reduces to

m − M = 5 log(R) − 5 .

diurnal Due to the daily variation of the solar radiation received at the Earth’s surface, meteorological quantities, such as temperature, pressure, atmospheric pollution, wind speed and direction, etc. have daily variations. Diurnal variation is a periodic variation and does not contain

diurnal motion

the non-periodic variation caused by synoptic situations (such as advection processes). The strength of diurnal variation is related to location, stronger in continental areas and weaker in maritime areas, e.g., the strongest diurnal variation region is the Tibetan Plateau. The diurnal range in equatorial areas exceeds the annual variation in average temperature. More strictly, diurnal pertains to occurrences during the day, as opposed to nocturnal occurrences; diel occurrences are those that happen once per day.

diurnal motion Apparent motion of objects on the celestial sphere due to the rotation of Earth from west to east, which causes objects to appear to rise in the east and set in the west daily.

divergence Branching off or moving in different directions. Also denotes a mathematical operation; the divergence of a vector u is denoted by · u.

divergence law for irradiance	See Ger-
shun’s law.

divergence theorem Also called Gauss’ theorem:

	· d	A	=	·
B	n	A		B dV

with V being a volume enclosed by surface A and n is a unit normal to A. Used, for instance, to convert between integral and differential forms of Maxwell’s equations.

divergent boundary In tectonics, two plates move apart from each other at a divergent boundary. Magma moves up from the Earth’s asthenosphere at the divergent boundary. The magma rises to the surface, where it cools and solidiﬁes as the volcanic rock basalt. Continued magma ascent forces the newly formed basaltic crust to move to the sides as the process repeats. Thus, divergent boundaries are areas where new crust is formed and where the plates move apart. Divergent boundaries are characterized by volcanism (quiet eruptions with very ﬂuid lavas) and shallow earthquakes. Divergent boundaries are believed to occur over the uprising portions of convection cells within the Earth’s astheno-

sphere. The Mid-Atlantic Rift and the East African Rift Valley are examples of divergent boundaries.

divergent plate boundary	See divergent
boundary, seaﬂoor spreading.

diversity reception Often, a radio circuit will have many different possible paths between the transmitter and receiver. There may be differences in the quality of the service on these paths and the quality may vary in time, space, and frequency. Diversity methods seek to exploit these differences. In the simplest form, signals on two different paths may be received and the maximum signal selected. More complex diversity systems may make use of redundancy between signals collected from several paths. See ionospheric radio propagation path.

divided bar The name of an apparatus used to measure thermal conductivities of disk-shaped rock samples. Two metal, usually brass, heads with circular cross-sections are maintained at different constant temperatures. Rock samples with known and unknown thermal conductivities are sandwiched in between. The heat ﬂux q through the axis (z) of the system is determined from the measured temperature gradient dT /dz across the rock sample of known thermal conductivity λk from Fourier’s law of heat conduction. The thermal conductivity of the other sample is then given by this heat ﬂux and the measured temperature gradient across it. See conductive heat transfer.

D-layer The D-layer is the lowest ionospheric layer at heights between 60 and 85 km. In contrast to the other ionospheric layers, it is still inside the mesosphere. Ionization is primarily due to energetic particles of solar and galactic origin and some UV lines which penetrate deep into the atmosphere, such as the Lyman-α-line. The main constituent is NO, which results from a combination of atomar oxygen O and molecular nitrogen N2. The layer can be described very well by a Chapman proﬁle. Due to the high densities, free electrons are rare and ion clusters and negative ions form instead. Polar cap absoptions (PCAs) and sudden ionospheric disturbances (SID) strongly modify this layer.

Doppler beaming

dog days The time period (July 3 through August 11) during the northern summer when Sirius is high in the daytime sky, supposedly adding to the summer sun’s heat.

doldrums The equatorial zone, characterized by high temperatures with small seasonal and diurnal change (and heavy rainfall) and light winds, so that sailing ships have difﬁculty sailing through the region.

domain of dependence Let S be an achronal set. The future/past domain of dependence

D±(S) of S is the set of points x such that an arbitrary past/future endless trip containing x intersects S. The domain of dependence of S is

D(S) = D+(S) ∩ D−(S). See achronal set, causality relations.

domain of outer communication The region outside of all black hole surfaces (horizons). The region of spacetime that is visible from inﬁnity.

domain wall Cosmological topological defects arising in phase transitions for which a discrete symmetry is spontaneously broken: the phase transition G → H induces a discrete family of equivalent vacuum states and domains having a different value for the Higgs ﬁeld responsible for the symmetry breaking will form, separated by a correlation length. At the intersections between these domains, the Higgs ﬁeld will, by continuity, not be able to lie in the true vacuum (the minimum of the potential), and thus the region (a wall) will contain an enormous amount of energy. Any theory predicting such walls contradicts observational cosmology as, for instance, they would contribute to the total energy density of the universe as well as to the anisotropies of the cosmic microwave background at a level well over that observed. See cosmic topological defect, homotopy group, spontaneous symmetry breaking.

dominant energy condition For all futuredirected time-like vectors ξa, the vector −Tbaξb is a future-directed time-like or null vector. Here Tba is the stress tensor of the matter. This condition expresses the requirement that the speed of energy ﬂow is less than the speed of light.

Doodson number A set of six integers in the notation d1d2d3.d4d5d6 deﬁned by A.T. Doodson in 1921 to uniquely classify tide components. In this scheme, the tidal band is decomposed into integer multiples of six astronomical functions: τ, the mean lunar time; s, the mean longitude of the moon; h, the mean longitude of the sun; p, the mean longitude of the lunar perigee; N , the negative mean longitude of the ascending lunar mode; and ps, the mean longitude of the solar perigee. Thus, for each component j, the tidal frequency, ωj , and phase, βj , are decomposed as:

ωj + βj =

d1τ + (d2 − 5) s + (d3 − 5) h +

(d4 − 5) p + (d5 − 5) N + (d6 − 5) ps

The ﬁrst digit, d1 deﬁnes the tidal species and is always equal to the order of the spherical harmonic component of the tide potential from which it originates. Long-period tides have d1 = 0, diurnal tides have d1 = 1, and semidiurnal tides have d1 = 2. The combination of the ﬁrst two digits d1d2 deﬁnes the tidal group number, and the ﬁrst three digits d1d2d3 deﬁne the tidal constituent number. For example, the largest semi-diurnal tide, M2, has a Doodson number of 255.555, while the largest diurnal tide, K1, has a Doodson number of 165.555.

Doppler beaming Beaming of radiation due to the rapid, i.e., close to the speed of light, motion of an emitting source with respect to an observer. Light emitted isotropically in the rest frame of a source is observed greatly enhanced if the source is moving toward the observer: For a radiating particle moving at a velocity close to the speed of light, corresponding to a Lorentz

factor γ 1 (γ is equal to 1 (1 − (v/c)2), where v is the velocity of the radiating matter, and c is the speed of light), the observer would see most light concentrated in a narrow beacon of half-opening angle 1/γ radians, and enhanced (or “Doppler boosted”) by a factor that can be proportional to a large power (3 to 4) of γ . Doppler beaming is relevant whenever there are charges moving at a velocity close to the speed of light (for example, if v = 0.95c then γ = 3), as in the case of radio jets in radio galaxies and quasars.

Doppler broadening

Doppler broadening The broadening of a spectral line in a gas because of red and blue shifts associated with thermal motion in the gas.

Doppler dimming A means by which to determine outﬂow plasma velocities from coronagraph measurements of the solar corona, where the outﬂows are perpendicular to the line-of- sight. In the solar wind of the outer corona, Doppler dimming observed in Lyman α at 1216 Å provides a diagnostic tool for determining the outﬂow speed. At heights of interest, 4R , densities are too small for signiﬁcant coronal Lyman α emission, so the observed radiation is produced by resonance scattering of chromospheric Lyman α off the HI locally present in the corona. The intensity of the detected radiation is determined both by the chromospheric intensity and by the systematic velocity of the scattering HI . This scattering is largest when the velocity is zero and Doppler dimming occurs when the velocity, relative to the chromosphere, increases.

Doppler effect The observed frequency of the wave signal from a standard source is a function of the motion of the emitter and the detector. In Newtonian physics with a universal time t, for waves moving at a given speed vp with respect to a medium (e.g., for sound waves in air):

received frequency f = 1 ± vo/vp f

1 vs/vp

where f is the source frequency, measured at rest near the source, vs is the source speed, vo is the observer speed relative to the medium, both measured along the line joining source and observer; the upper sign is for motion reducing the relative separation. In Newtonian physics only the component along the line between the source and observer contributes to the Doppler effect.

When considering the Doppler effect of light or other electromagnetic signals, one uses the special relativistic formula. Here there is no medium, so the concept of motion relative to the medium is meaningless. The relativistic formula is:

f	=	1 − v/c cos θ f ,
		√		1 − v2/c2)
			(

where v is the velocity of relative motion of the source and observer, θ is the angle between the direction of propagation of the photon and the velocity of the observer, measured in the rest frame of the emitter. (θ = 0 corresponds to motion increasing the separation.) Notice that in relativistic systems there is a transverse Doppler shift arising from the denominator, even when there is no motion along the line between source and observer.

Doppler shift Doppler effect.

double couple A seismological model that a focal mechanism is produced by release of double-couple torques with mutually opposite direction at a hypocenter. In contrast, a model that a focal mechanism consists of a single torque is referred to as single couple. Although radiation patterns for initial motion of P-waves are the same for both models, those for S-waves become of four quadrant type for double couple, whereas they are of two quadrant type for single couple. Radiation patterns for Love wave and Rayleigh wave and their amplitude ratios are also different between the two models. At the beginning of the 1960s, a point source model equivalent to lateral faulting was theoretically proved to be double couple. The force and moment are zero for a double couple, and the amount of one of the two torques is called seismic moment.

double diffusion Mixing process resulting from differential (“double”) diffusion of salt and heat between two water masses. In the absence of mechanical stirring caused by shear currents, this type of mixing occurs in two layer situations, in which two water types of different heat and salt composition are stacked vertically. A necessary condition for double diffusion is that the gradients of temperature and salinity have the same sign. See also stability ratio.

Two scenarios are possible: in the ﬁrst, warmer and saltier water is above colder, fresher water. Since the rate of molecular diffusion for heat is about 100 times larger than that of salt, the upper water loses heat to the lower water faster than it loses salt. This results in a loss of buoyancy of the upper water in the vicinity of the interface. If the initial density difference between