Файловый архив студентов. Файловый архив студентов.
1261 вуз, 4612 предмет.
/ Регистрация
FAQ Обратная связь Вопросы и предложения
Добавил:
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Сумский государственный университет
Предмет:
Английский язык
Файл:
Dictionary of Geophysics, Astrophysic, and Astronomy.pdf
Скачиваний:
122
Добавлен:
10.08.2013
Размер:
5.66 Mб
Скачать
☆
►Содержание►

Kolmogorov spectrum

the length scale is expressed by

LK = η = ν3 1/4 rad m−1

3

where ν is the viscosity of the fluid and 3 is the rate at which energy is dissipated by the smallest turbulent eddies (see dissipation rate). Values for η are of the order of millimeters in the ocean and in the atmosphere. This implies that for scales shorter than the Kolmogorov scale LK, the turbulent kinetic energy is converted into heat by molecular viscosity ν. LK is often referred to as the size of the smallest possible eddies to exist in a fluid for a given level of dissipation and viscosity.

Kolmogorov spectrum The spectrum of the turbulent kinetic energy follows in the inertial subrange (scales smaller than the energycontaining range of eddies; larger than the Kolmogorov scale) the characteristic so-called −5/3-law: φ(k) = 1.56ε2/3k−5/3 (see inertial subrange). The name of the spectrum is due to Kolmogorov (1941).

Kolmogorov wavenumber Defines the wave numbers at which the turbulent kinetic energy

is converted into heat by molecular viscosity ν, i.e., kK = (ε/ν3)1/4 [rad m−1] or kK = (2π)−1(ε/ν3)1/4 [cycle m−1]. See Kolmogorov

scale.

Kp index A 3-hourly planetary geomagnetic index of activity generated in Göttingen, Germany, based on the K indices from 12 Magnetic Observatories distributed around the world. The Kp index is calculated by combining these indices using local weightings. The Kp index is often presented as a Bartels musical diagram, a presentation that emphasises the 27-day recurrent nature of much geomagnetic activity. See geomagnetic indices.

KREEP Unusual lunar (and martian) rocks, with unusual amounts of “incompatible elements”: K-potassium, Rare Earth Elements, and P-phosphorous, representing the chemical

remnant of a magma ocean (caused by impact or volcanism).

Kruskal extension (1960) The maximal analytic extension of the Schwarzschild space-time by the introduction of a coordinate system in which the coordinate velocity of light is constant. See maximal extension of a space-time.

krypton (Kr) From the Greek kryptos or “hidden.” A gaseous element, atomic number 36, one of the noble gasses, discovered by William Ramsay and M.W. Travers in 1898. Its naturally occurring atomic weight is 83.80. Natural krypton is found in the atmosphere at about 1 ppm. Its naturally occurring isotopes are 78Kr, 80Kr, 82Kr, 83Kr, 84Kr, 86Kr. 84Kr is naturally most abundant.

K star Star of spectral type K. Arcturus and Aldebaran are K stars.

Kuiper belt Region beyond about 35 AU and extending to roughly 100 AU, in the ecliptic, that is the source of most short-period comets. Originally suspected on theoretical grounds in the early 1950s, it was not until 1992 that the first Kuiper belt objects were observed. The belt is roughly planar, and it is believed that interactions between Kuiper belt objects and the giant planets cause belt objects to occasionally cross the orbit of Neptune. Objects that have a gravitational encounter with that planet will either be ejected from the solar system, or perturbed into the region of the planets. The Centaur class of asteroids, which orbit the sun in the region between Jupiter and Neptune, as well as the planet Pluto/Charon, are believed to have originated in the Kuiper belt. Unlike the Oort cloud comets, Kuiper belt objects are thought to have been formed in situ.

Kuiper belt object, trans-Neptunian object, Edgeworth–Kuiper object A minor body that resides in the Kuiper belt. Sizes can range up to a few hundred kilometers.

Kuroshio See Japan current.

© 2001 by CRC Press LLC

Lagrangian

L

lagoon A shallow, sheltered bay that lies between a reef and an island, or between a barrier island and the mainland.

Lagrange points Five locations within a three-body system where a small object will always maintain a fixed orientation with respect to the two larger masses though the entire system rotates about the center of mass. If the largest mass in the system is indicated by M1 and the second largest mass is M2, the five Lagrange points are as follows: in a straight line with M1 and M2 and just outside the orbit of M2 (usually called the L1 point); in a straight line with M1 and M2 and just inside the orbit of M2 (L2); in a straight line with M1 and M2 and located in M2’s orbit 180◦ away from M2 (i.e., on the other side of M1) (L3); and 60◦ ahead and behind M2 within M2’s orbit (L4 and L5). In the sun-Jupiter system, the Trojan asteroids are found at the L4 and L5 locations. In the Earth-sun system, the Lagrangian points L1 and L2 are both on the sunEarth line, about 236 RE (≈ 0.01 AU) sunward and anti-sunward of Earth, respectively. The other points are far from Earth and therefore too much affected by other planets to be of much use, e.g., L3 on the Earth-sun line but on the far side of the sun. However, L1 (or its vicinity) is a prime choice for observing the solar wind before it reaches Earth, and L2 is similarly useful for studying the distant tail of the magnetosphere. Spacecraft have visited both regions — ISEE-3, WIND, SOHO and ACE that of L1, ISEE-3 and GEOTAIL that of L2. Neither equilibrium is stable, and for this and other reasons spacecraft using those locations require on-board propulsion.

Of the Lagrangian points of the Earth-moon system, the two points L4 and L5, on the moon’s orbit but 60◦ on either side of the moon, have received some attention as possible sites of space colonies in the far future. Their equilibria are stable.

Lagrangian In particle mechanics, a function L = L(xi, dxj /dt, t) of the coordinate(s) of the particle xi, the associated velocity(ies) dxj /dt, and the parameter t, typically time, such that the equations of motion can be written:

d ∂L

∂L

0 .

 

 

 

 

 

 

dt ∂ ∂x∂ti −

∂xi =

 

In this equation (Lagrange’s equation) the partial derivatives are taken as if the coordinates xi and the velocities dxj /dt were independent.

The explicit d/dt acting on

∂L

 

differentiates

i

 

 

∂(

∂x

)

 

∂t

 

 

 

 

xi and dxi /dt. For a simple Lagrangian with conservative potential V ,

1

m

dxi/dt

2

xj

,

L = T − V =

 

 

− V

2

one obtains the usual Newtonian equation

 

 

d

dxi

= −

∂V

 

 

 

 

 

m

 

 

 

.

 

 

dt

dt

∂xi

 

 

Importantly, if the kinetic energy term T and the potential V in the Lagrangian are rewritten in terms of new coordinates (e.g., spherical), the equations applied to this new form are again the correct equations, expressed in the new coordinate system.

A Lagrangian of the form L = L(xi, dxj /dt, t) will produce a resulting equation that is second order in time, as in Newton’s equations. If the Lagrangian contains higher derivatives of the coordinates, then Lagrange’s equation must be modified. For instance, if L contains the accel-

eration,

aj = d2xj , dt2

so that

L = L xi, dxj /dt, d2xk/dt2, t ,

the equation of motion becomes

 

d2

 

∂L

 

 

d

 

∂L

 

 

∂L

 

0 ,

−dt

2

 

d2xi

+ dt

∂

∂xi

−

 

i

=

 

 

 

 

∂ dt2

∂t

∂x

 

 

which will in general produce an equation of motion containing third time derivatives. The presence of higher derivatives in the Lagrangian produces higher order derivatives in the equation of

© 2001 by CRC Press LLC

Lagrangian coordinates

motion, which generalize the terms given above and appear with alternating sign.

The Lagrangian arises in consideration of extremizing the action of a system, and a development from this point of view clarifies many of the properties of the Lagrangian. See action, variational principle.

Lagrangian coordinates In hydrodynamics, physical parameters such as pressure, fluid velocity, and density can be expressed as functions of individual flowing particles and time. In this case the physical parameters are said to be represented in Lagrangian Coordinates (see also Eulerian Coordinates). Named after Joseph Louis Lagrange (1736–1813).

Lagrangian coordinates In fluid mechanics, a coordinate system fixed to the fluid, so that the coordinates of a particular packet of fluid are unchanged in time. In such a frame some of the fluid behavior is easier to compute. However, transforming back to a lab frame may become difficult to impossible, particularly in complicated flows. See Eulerian coordinates.

Lagrangian representation Description of a phenomenon relative to the moving water parcel. Floats, neutral buoys, and deliberately introduced tracers are typical applications to measure currents in the Lagrangian frame. See Eu- lerian representation.

Lagrangian velocity That velocity that would be measured by tracking a dyed particle in a fluid. See also Eulerian velocity.

Laing–Garrington effect (1988) The higher degree of polarization of the radio lobe associated to the jet, with respect to that associated to the counter-jet, observed in quasars, and to a lower level in radio galaxies. The Laing– Garrington effect is straightforwardly explained assuming that the there is no strong intrinsic difference between jet and counter-jet, and that the different surface brightness of the jet and counter-jet is due to relativistic beaming. Then the radio emission coming from the counter-jet is more distant from the observer. The source is expected to be embedded in a tenuous hot thermal medium which depolarizes intrinsically

polarized radiation because of Faraday rotation. Radiation from the counter-jet then travels a longer path through the plasma and emerges less polarized.

Lambertian surface A surface whose radiance, reflectance, or emittance is proportional to the cosine of the polar angle such that the reflected or emitted radiance is equal in all directions over the hemisphere.

Lambert’s law The radiant intensity (flux per unit solid angle) emitted in any direction from a unit radiating surface varies as the cosine of the angle between the normal to the surface and the direction of the radiation.

Lamé constants Two moduli of elasticity, λ and G, that appear in the following form of Hooke’s law:

σij = λεkkδij + 2Gεij

where σ and ε are stress and strain, respectively. Parameter G is also called the shear modulus or rigidity. The Lamé constants are related to Young’s modulus E and Poisson’s ratio v as

λ

=

 

 

 

 

 

vE

 

 

 

and

 

 

 

 

 

 

 

 

 

(1

+

v)(1

−

2v)

 

 

 

 

 

 

 

 

 

 

G

=

 

 

E

 

 

.

 

 

 

 

 

 

 

 

 

 

 

2(1

+

v)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

laminar flow A smooth, regular flow in which fluid particles follow straight paths that are parallel to channel or pipe walls. In laminar flow, disturbances or turbulent motion are damped by viscous forces. Laminar flow is empirically defined as flow with a low Reynolds number.

Landau damping and instability In a collisionless plasma, damping or instability associated with the n = 0 resonance; the damping of a space charge wave by electrons which move at the wave phase speed and are accelerated by the wave. Landau damping is of importance in space physics and astrophysics as a process for the dissipation of magnetoacoustic waves. See magnetoacoustic wave, resonant damping and instability.

© 2001 by CRC Press LLC

Laplace equation

Langacker–Pi mechanism In cosmology, a mechanism that can reduce the number of magnetic monopoles arising from an early phase transition, through a later phase transition that creates cosmic strings linking monopoleantimonopole pairs. Because the cosmic strings are under tension, they pull together the pairs, enhancing the monopole-antimonopole annihilation probability and reducing the monopole density to consistency with cosmological observations.

Langmuir circulation Wind-induced sets of horizontal helical vortices in the surface waters of oceans and lakes. The counter-rotating vortex pairs appear in series of parallel sets, which form tube-like structures. These structures are aligned within a few degrees of the wind direction, and they are visible at the surface as streaks or lines. These streaks form at the convergence zones of the counter-rotating vortices, where debris or foam floating on the water surface is collected into long, narrow bands. Appearance of the phenomenon requires a certain threshold speed of about 3 ms−1. The horizontal spacing between vortex pairs can range from 1 m up to hundreds of meters, and smaller, more irregular structures can coexist among larger, widely spaced structures. The vortex cells penetrate vertically down to the first significant density gradient (seasonal pycnocline), and their aspect ratio is generally assumed to be about L/2D, where L is the horizontal spacing of the vortex pairs and D is their penetration depth. Typical spacing is of order tens of meters.

The generation of Langmuir cells is explained by the widely excepted CL2 model, developed by Craik and Leibovich. This model assumes a horizontally uniform current U(z) and a cross-stream irregularity u(x, y, z), where a right-handed coordinated system is considered with the x-direction pointing down-stream. The irregularity produces vertical vorticity ωz = −∂u/∂y and a horizontal vortex-force component −Usωzey directed towards the plane of maximum u, where Us = Us(z) is the Stokes drift and ey is the unit vector in the y-direction. The vortex-force causes an acceleration towards the plane of maximum u, where, in order to satisfy continuity, the water must sink. Hence, surface water is transported downward at the

streaks and upwelling occurs in between. If U decreases with depth and if shear stresses are ignored, conservation of x-momentum along the convergence plane requires that, as the water sinks, u must increase. Thus, the initial current irregularity is amplified, which then further amplifies the convergence. The vertical vorticity is rotated towards the horizontal by the Stokes drift, which results in even increased convergence and amplification of the velocity anomaly. Eventually, the vorticity is rotated completely into the horizontal and forms a set of helical vortices.

Langmuir waves Fundamental electromechanical plasma oscillations at the plasma frequency. Also called plasma oscillations or space-charge waves. Langmuir waves are dispersionless in a cold plasma and do not propagate in a stationary plasma. They are important for solar physics since the Langmuir oscillations are readily converted into electromagnetic radiation.

La Niña The 1 to 3 year part of the Southern Oscillation when there are anomalously cold sea surface temperatures in the central and east-

ern Pacific. See El Ni~ o, Southern Oscillation n

Index.

Laplace equation The equation

2φ = 0 .

This equation describes the Newtonian gravitational potential, the electrostatic potential, the temperature field and a number of other phenomena (all in the absence of sources). For instance, in groundwater flow through homogeneous regions under steady-state conditions there is no change in the hydraulic head h with time, and groundwater flow can be described by combining Darcy’s law with conservation of mass to obtain the Laplace equation:

∂2h + ∂2h + ∂2h = 0 . ∂x2 ∂y2 ∂z2

Flow nets are graphical solutions to the Laplace equation.

© 2001 by CRC Press LLC

273

Соседние файлы в предмете Английский язык
Помощь Обратная связь Вопросы и предложения Пользовательское соглашение Политика конфиденциальности