DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

Prandtl number
grasses with few trees except along riverbanks.
Prairies covered much of central United States
and Canada prior to the development of farming
and fire control methods in these areas in the late
19th century.
Prandtl number A dimensionless number
(Pr) given by the ratio of the kinematic viscosity
to the diffusivity. It expresses the ratio of the
diffusivity of momentum to that of temperature
through a fluid.
Pr = ν
χ
where ν is kinematic viscosity, χ is heat diffusivity
coefficient, χ = K
, in which, K, ρ,
ρCp
and Cp are thermal conductivity, density, and
specific heat at constant pressure, respectively.
For air, Pr ≈ 1.4. Pr is strongly temperaturedependent.
The turbulent Prandtl number is defined
analogously by Prt = νt/χt where νt
is turbulent viscosity and χt is turbulent diffusivity.
For very intense turbulence Prt → 1,
whereas for very weak turbulence (laminar),
Prt→Pr.
Prasad–Sommerfield limit A limiting case
of parameters describing (magnetic) monopoles
so that they have mass equal to a minimum
value called the Bogomol’nyi bound. For this
set of parameters, for some theoretical models
also including a scalar field (called a Higgs
field) it becomes possible analytically to solve
the field equations, to find that the force between
two equal (magnetically repelling) monopoles
exactly vanishes because this force gets compensated
by the long-range Higgs field attractive
interaction. See Bogomol’nyi bound, cosmic
topological defect, monopole, t’Hooft–
Polyakov monopole.
Pratt compensation In Pratt compensation,
the densityρP varies above a depth of compensation
W in order to balance the mass of elevated
topography.
Pratt isostasy An idealized mechanism of
isostatic equilibrium proposed by J.H. Pratt in
1854, in which the crust consists of vertical rock
columns of different densities with a common
compensation depth independently floating on
© 2001 by CRC Press LLC
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a fluid mantle. A column of lower density has a
higher surface elevation. See Airy isostasy.
precession The slow, conical movement of
the rotation axis of a rotating body. In the
case of solar system objects (planets), precession
is caused by the gravitational torques of
other nearby objects. The Earth’s orbit around
the sun defines a plane (the plane of the ecliptic)
and the Earth’s axis of rotation is at an angle of
66.5 ◦ to this plane. The Earth’s “obliquity” is
the angle between the rotation axis and a normal
to this plane, i.e., 23.5 ◦ . The Earth’s rotation
creates a bulge around the equator, which itself
defines a plane at 23.5 ◦ to the ecliptic. Both
the sun and the moon exert a tidal couple on
the Earth’s bulge, which results in the forced
precession both of the Earth’s rotational axis
and of the material orientation of the Earth itself.
This is analogous to the precession of a
rapidly spinning gyroscope pivoted at one end
in a gravitational field: The material orientation
of the gyroscope’s symmetry axis rotates
so as to form a cone, while the axis of rotation
of the gyroscope (which lies very close to the
symmetry axis) follows. Similarly, the Earth’s
pole swivels around the normal to the ecliptic
so as to describe cones. The period of this precession
is 25,730 years. Superimposed on the
simple rotation of the Earth’s pole are irregularities
termed nutations, as well as the Chandler
wobble and a longer term variation in the obliquity
to the ecliptic. A notable effect of precession
is the changing of the North Star (today the
north celestial pole is near the star Polaris, but
around 2000 BC it was near the star Thuban) as
the Earth’s rotation axis points toward different
locations in space.
precession of the equinoxes Slow shift in
the celestial coordinates of astronomical objects
because of the precession of the Earth’s
pole direction. Celestial positions in published
ephemerides are typically correct at the epoch
2000.0 (i.e., correct for noon UT, January 1,
2000), and correction tables and formulae correct
the coordinates to any particular epoch.
(Older tables give coordinates correct at the
epoch 1950.) See precession.