DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

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 Eulerian
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
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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’slaw Theradiantintensity(fluxper
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
whereσ andε 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 =
G =
vE
(1 +v)(1 − 2v)
E
2(1 +v) .
and
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.