DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

Eulerian
Represents Newton’s 2nd Law for an inviscid
fluid.
Eulerian A term used to denote a description
of fluid behavior which involves description of
fluid flow parameters (particularly velocity) at
fixed points in space. The alternative is a Lagrangian
description, which essentially involves
describing the behavior of selected fluid particles
as they move through space.
Eulerian coordinates In hydrodynamics,
physical parameters such as pressure, fluid velocity,
and density can be expressed as functions
of positions in space and time; thus, a coordinate
system fixed to an external reference frame, in
which physical phenomena, for instance hydrodynamical
flow, move through the hydrodynamical
grid. Named after Leonhard Euler (1707–
1783). See Lagrangian coordinates.
Eulerian representation Description of a
phenomenon relative to a framework fixed in
space. Measurements in moorings are typical
applications of Eulerian-type observations. See
Lagrangian representation.
Eulerian velocity Velocity measured from
a fixed point or set of points (i.e., by a moored
current meter). See also Lagrangian velocity.
Euler, Leonhard Mathematician (1707–
1783). Made contributions in the areas of algebra,
theory of equations, trigonometry, analytic
geometry, calculus, calculus of variations, number
theory, and complex numbers. He also made
contributions to astronomy, mechanics, optics,
and acoustics.
Euler pole Euler’s theorem states that a
movement on a sphere may be represented as
a rotation about an axis. This holds not only for
the movement of a point on a sphere but also the
movement of a continuous undeformable patch
on a sphere. This turns out to be important for
the theory of plate tectonics, which models the
surface of the planet as a set of rigid plates in relative
motion. Therefore, an axis may be found
for each plate relative to some given reference
frame. These axes are known as Euler poles.
In particular, by considering the motion of one
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plate relative to another plate, one may find the
pole of relative rotation. If two plates meet at
a mid-ocean ridge, then the ridge will often be
fractured by transform faults oriented perpendicular
to a line running toward the pole of rotation
between the two plates. Because velocity
about the pole depends on distance from the
pole, the velocity between adjoining plates will
vary along the boundary between the plates unless
the boundary happens to lie on a cylinder
centered on the pole. This means that, for example,
subduction may be much faster at one end
of a trench than the other.
Euler potentials Two scalar functions of position
(α,β) used for describing a magnetic field
B and satisfying B =∇α × ∇β. Their use is
equivalent to that of a vector potential A = α∇β
(of no particular gauge, non-covariant) and is
useful because the points of any magnetic field
line share the same value of α and β. As long
as the field inside Earth is excluded, (α,β)inthe
Earth’s vicinity are usually unique to one field
line (not valid in more general geometries) and
this allows using them in mapping field lines
and as variables in the theory of plasma convection
by electric fields in the magnetosphere.
Field line motion can also be described by Euler
potentials. In toroidal geometries, (α,β) are
generally multiply valued.
euphotic depth In oceanography, the depth
to which significant phytoplankton photosynthesis
can take place; typically taken to be the
depth at which photosynthetically available radiation
falls to 1% of its value just below the
surface [m].
euphotic zone In oceanography, the water
layer in which significant phytoplankton photosynthesis
can take place; typically taken to be the
layer down to which photosynthetically available
radiation falls to 1% of its value just below
the sea surface.
euphotic zone midpoint In oceanography,
the layer at which photosynthetically available
radiation falls to 10% of its value just below the
sea surface.