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drag coefficient

the layers is small, saltier water will sink into the lower layer in the form of thin columns (or fingers, hence, “salt fingering”). Likewise, the water below the interface gains heat faster than it gains salt, resulting in penetration of fresher, colder water into the upper layer.

On the other hand, if a layer of cold, fresh water is above a layer of warm, salty water, the water just above the interface gains buoyancy from the heat transfer through the interface and tends to rise. At the same time, the water below the interface loses buoyancy and tends to sink. This fluid motion leads to the development of strata of homogeneous convective layers separated by thin regions of high vertical gradients of temperature and salinity. This phenomenon is often called layering.

The degree of double diffusion is usually expressed by the stability ratio Rρ, which is defined by

Rρ =

stability due to the stabilizing component

.

instability due to the destabilizing component

Two cases of double-diffusion occur:

Rρ

=

(α∂?/∂z)/(β∂S/∂z) > 1

 

 

for the finger regime ,

Rρ

=

(β∂S/∂z)/(α∂?/∂z) > 1

 

 

for the diffusive regime .

Double diffusion is potentially active when 1 < Rρ < (κT /κs) ≈ 70 (temperature-dependent, see Lewis number), where κT , κs are the molecular diffusivities of temperature (heat) and salt, respectively. In fact, double diffusion becomes manifest by convectively well-mixed layers, if 1 < Rρ < 4 and is most intense for Rρ −→ 1.

double probe A pair of DC antennas extended in opposite directions from a satellite. By observing the voltage difference between their ends, the component of the electric field E in that direction can be estimated.

Double probes extending 5 to 10 m are often used in low Earth orbit to observe electric fields in the auroral and polar regions of the upper atmosphere. Their readings must be corrected for the voltage due to the spacecraft motion, shadow effects, and other problems, but

because of the high ambient ion density, they tend to work well since they are much larger than the Debye length. Some have been used in more distant regions, where boom lengths of the order of 100 m are needed.

double star Roughly synonymous with binary star, but generally restricted to mean those pairs where the stars are far enough apart that they will complete their evolution without affecting each other. Also, frequently, binary stars that can be resolved into two separate points of light on the sky. See binary star.

downward (upward) irradiance diffuse at-

tenuation coefficient

The negative of the

derivative with respect to depth of the natural logarithm of the downward (upward) plane irradiance [m−1].

downward (upward) radiance mean cosine

The average cosine of the nadir (zenith) angle of all downward (upward) traveling photons; it equals the ratio of the plane irradiance to the scalar irradiance for the downward (upward) direction.

downward (upward) scalar irradiance diffuse attenuation coefficient The negative of the derivative with respect to depth of the natural logarithm of the downward (upward) scalar irradiance [m−1].

downwelling The process of accumulation and sinking of warm surface waters along a coastline. The primary downwelling regions are in the subtropical ocean waters. Downwelling may bring waters rich in oxygen to deeper layers of oceans or lakes.

draconitic month See month.

drag coefficient Coefficient linking the current velocity squared to the drag force. In natural waters, the stress τ (drag force per unit area) onto the boundary is usually parameterized by τ = ρChuh2 [Nm−2]. The index h indicates at which level above bottom (often h = 1m) the velocity uh is considered. For smooth bottom boundaries (see roughness length), Ch is typically (2.2 ± 0.6) · 10−3 and is equal to the

© 2001 by CRC Press LLC

dragging phenomenon

skin friction. If bottom irregularities are present (see rough flow) a so-called form drag adds to the skin friction. Also in this case, the same parameterization for τ is customary but with a larger value for Ch. At the surface boundary, roughness is due to viscosity at very low wind speed (W10 < 2ms−1) and due to waves at wind speed W10 > 6ms−1. Therefore, C10 has a minimum at about W10 = 3 − 5ms−1 of C10 ≈ 1 · 10−3 and increases to 10−3 outside the maximum. The index 10 on W10 refers to the standard height for wind measurements of h = 10m above water level.

dragging phenomenon See frame dragging.

dredge A machine that removes sediment from an area for deposition elsewhere. Common designs include the cutterhead dredge, which functions much like a giant drill with a hollow shaft for transporting sediment, and the clamshell dredge, which is essentially a crane with a clamshell-shaped bucket for grabbing and moving sediments.

D region The midand low-latitude D region is the portion of the ionosphere formed below 90 km above the surface of the Earth. It lies below the E region. Above 70 km the D layer is mainly due to ionization of the trace constituent NO by solar Lyman-α radiation, while at lower altitudes ionization by galactic cosmic rays is important. The D region has a marked diurnal variation, with daytime maxima just after local noon (typically 108 to 109 electrons m−3), and disappears at night. The ionization is highest in summer. In winter, on some days the D-region ionization can increase above normal levels. This winter anomaly is thought to be due to meteorological effects on the lower ionosphere together with post (geomagnetic) storm particle precipitation. The D region is responsible for MF and most HF radio wave absorption. The nature of the D region depends on collisions between free electrons in the layer and the atmosphere. Collisions are relatively more important in the lower ionosphere than in the higher layers. Absorption results from radio waves passing through the D region and losing energy to the local atmosphere as a result of these collisions. At LF/VLF/ELF the ionization in the

D region may be high enough to reflect the radio waves. At high latitudes particle precipitation can strongly enhance D-region ionization leading to increased absorption. See ionosphere, ionospheric absorption, polar cap absorption.

drift The gradual motion by ions and electrons undergoing guiding center motion. It is generally defined as the net motion, perpendicular to the magnetic field, of the guiding center itself.

drift, curvature The guiding center drift vc associated with the curvature of magnetic field lines. For a particle of mass m and charge e, with velocities in m/sec and the velocity component v|| along the magnetic field B, the

non-relativistic curvature drift velocity is vc = 2 v||2[B × (B · B)/B3] where is in m−1 and is the gyration frequency. In a field of

B nT (nanotesla), for protons = 0.096 B, for electrons = 176 B.

drift, electric The guiding center drift u imposed on a charged particle in a magnetic field B by an electric field E. In MKS units, given E in V/m, B in Tesla, u = E × B/B2 m/sec. Unlike other drifts, u acts equally on positive and negative charges, and therefore does not produce an electric current, but rather a bulk flow of the plasma: convection in the Earth’s magnetosphere, for instance, is generally viewed as associated with electric drifts.

Intuitively, the electric drift can be viewed as an effect of the voltage drop across the circular orbit of guiding-center motion in a magnetic field. Positive ions accelerate in the direction of E, and being fastest at the part of the circle furthest in that direction, their motion there curves less than at the opposite end of the circle. That causes their guiding centers to move sideways, in a direction perpendicular to both E and B. Negative electrons are accelerated in the opposite direction, but since they also circle the guiding center in the opposite sense, their drift velocity u is the same.

drift, gradient The guiding center drift vg associated with the gradient of the magnetic field intensity B. For a particle of mass m and charge e and with velocity component v perpendicular

© 2001 by CRC Press LLC

duality in elastic string models

to the magnetic field, the non-relativistic gradient drift velocity is vg = v 2(B × B)/B2, where distances are in meters and where in a field of B nT (nanotesla), for protons = 0.096 B, for electrons = 176 B.

drift, magnetization The guiding center drift implied by the magnetization current.

driftmeter An instrument for measuring the bulk flow of plasma in space; by ascribing this flow to electric guiding center drift, two components of the ambient electric field E can be deduced. Driftmeters generally consist of two matched plasma detectors observing diametrically opposed directions: any bulk motion is expressed as a difference in the observed plasma flux. Driftmeters are widely used in research satellites as an alternative to double probes.

drift, polarization The guiding center drift implied by the polarization current.

driven shock Shock building in front of an object moving with a speed higher than the local sound speed. Examples are the shock in front of a super-sonic aircraft or the shock in front of a coronal mass ejection. Since driven shocks are connected to a moving obstacle, they are also traveling shocks.

drizzle Rain in the form of very small drops (less than .5 mm) that fall slowly to the earth. Typically formed in thin stratus cloud layers, so that the drops have little time to enlarge as they fall.

drumlins Streamlined hills of unconsolidated, unsorted material deposited by a glacier. They are parallel to the direction of movement of the glacier. Drumlins are often 25 to 50 m high and about 1 km in length. They can be formed by ice erosion of an earlier glacial deposit or by shaping of the accumulated debris under an active glacier.

drunkards walk Descriptive term for the zig-zag motion of a particle in spatial diffusion.

dry-adiabatic lapse

When dry or unsat-

urated air ascends or

descends adiabatically,

the temperature change is given by the dryadiabatic lapse rate. In static equilibrium con-

ditions,

γd = −dT = Ag dz Cp

where γd is dry-adiabatic lapse rate, A is mechanical equivalent of heat, g is gravitational acceleration, Cp is specific heat at constant pressure of dry air. At standard conditions the dryadiabatic lapse rate is 9.8◦ C/km.

dry freeze A weather event in which the temperature drops below freezing, thus killing vegetation, but the humidity is so low that no hoarfrost forms.

duality in elastic string models A cosmic string may carry a current that can be either timelike or spacelike. Such a string is then called an elastic string, and would in fact be the relativistic analog of an ordinary violin-like string. In order to model the presence of a current in the string core, a single parameter is required, called the state parameter w, whose sign reflects the nature of the current: w > 0 for a spacelike current, and w < 0 for a timelike current. This parameter w is interpretable as the square of the gradient (with respect to the string worldsheet internal coordinates) of the phase of a current carrier field. Given the state parameter, the string motion is governed by a Lagrangian function L(w) whose integrated form over the string worldsheet provides the action. Defining K = −2dL/dw, it can be shown that the square χ of the current is given by

χ = Kw2 .

Define O(χ):

O = L + Kχ

Depending on the particular regime (electric or magnetic) one considers, the two functions O and L may play the roles of energy per unit length or tension so that the knowledge of either of them together with the duality transformation is equivalent to the equation of state. The equivalence between both formalisms [either in terms of L(w) or in terms of O(χ)] can also be understood as interchanging the roles of the

© 2001 by CRC Press LLC

ductile behavior

variables of space and time along the string. It was used to reproduce the basic features of the Witten conducting string in the Carter–Peter model. See Carter–Peter model, cosmic string, cosmic topological defect, current carrier (cosmic string), elastic string model, electric regime (cosmic string), energy per unit length (cosmic string), equation of state (cosmic string), tension (cosmic string).

ductile behavior The phenomenological macroscopic nature of solid material deformation. In general ductile behavior refers to the capability for substantial change of shape without gross fracturing. The deformation processes that may enter into ductile behavior can be distinguished as cataclastic flow, crystal plasticity, and diffusion flow/grain-sliding. Which combination of processes will be involved in forming ductile behavior depends greatly on the properties of the material itself and the deformation conditions such as pressure, temperature, and strain rate.

dune Any deposit of sand-sized (1/16 to 2 mm in diameter) windblown material. Dunes are common on bodies with an atmosphere, having been seen on Earth, Mars, and Venus. Dunes typically form in areas with a prevailing wind direction and an abundant source of sand. Dunes often migrate, as wind blows the sand from one deposit into another area to build up a new deposit. Vegetation and other obstructions cause dunes to stabilize and cease their migration. There are three primary classes of dunes:

(1) longitudinal dunes, which are oriented parallel to the prevailing wind direction; (2) transverse dunes, which are oriented perpendicular to the wind direction; and (3) parabolic dunes, which are U-shaped with the dune pointing in the downwind direction. Many subclasses of dunes occur, depending on differences in wind, sand supply, and vegetation.

dusk The part of morning or evening twilight between complete darkness and civil twilight. See twilight, civil twilight, nautical twilight, astronomical twilight.

dust In astrophysics, grains formed in the envelopes of cool stars, and blown outward via

stellar winds and radiation pressure, or formed in supernova explosions. Interstellar dust has typical radii of order a 1 µm to 10 µm and an exponential size distribution n(a) aδ, where n is the number density. The exponent δ is of order 3.5. Dust plays a substantial part in star forming regions and in the foundation of planetary systems in accretion onto young stars, since the dust has a strong influence on radiative effects.

In geophysics, aerosols (or potential aerosols) of order 1 µm in size which have a large effect in the atmospheric energy balance, as well as have dramatic effects on local climate.

In relativity, a continuous medium having a well-defined mass-density and velocity, but whose pressure is equal to zero. It follows from Einstein’s equations that each point of dust moves on a geodesic. Dust is an approximate model of the matter distribution in the universe at the current stage of its evolution (in the early phase of the evolution, pressure cannot be neglected).

dust storm Wind and elevated suspended dust that visibly reduces atmospheric transparency.

dust storm (Mars) In southern summer of Mars, global dust storms break out sometimes in mid-latitudes of the southern hemisphere. They were photographically observed in 1956, 1971, 1973, and 1977. The dust is wafted on the easterlies, and encircles Mars along a latitude line. At the same time the Hadley cell carries the dust to the northern hemisphere. After about two weeks the whole of Mars, except polar regions, is obscured by the dust. Although albedo features become visible after a month or so, it takes a Martian year for the atmosphere to return to the clear state of before the dust storm. Global dust storms have not yet been observed in the northern summer when Mars is near aphelion. Local dust storms break out in all seasons in both hemispheres, especially in low latitudes and near polar caps. Dust clouds seem to be yellowish to visual observers. However, the true color is reddish: dust clouds are bright in red, but not identified in blue. Some observers report that dust clouds in their initial state, in a day or

© 2001 by CRC Press LLC

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