DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

eter) andζ is the vertical component of relative
vorticity; and H is the layer thickness.
In a stratified fluid, the potential vorticity is
defined by
Q=
ω+ 2
ρ
·∇
where ω is relative vorticity, is the Earth’s rotation,
ρ is density, and is a conserved quantity.
This form is called Ertel potential vorticity
(Ertel, 1942). If is potential temperature, this
is also called isentropic potential vorticity.
potentiometric surface (or piezometric surface)
Water will rise to the potentiometric
surface in a well or piezometer penetrating a
confined aquifer. The elevation of the potentiometric
surface above an arbitrary datum is the
sum of the pressure head and the elevation head,
or the hydraulic head h in Darcy’s law. The
water table is the potentiometric surface in an
unconfined aquifer.
power The rate of doing work, energy per
unit time. In mechanics, power P= F· v. The
units of power are erg/sec, or Joule/sec. Note
that 1 Joule/sec ≡ 1 Watt.
power-law fluid A viscous fluid in which
the rate of shear strain is proportional to the
power of shear stress. The flow law is often
generalized to be ˙εij =Cσ n−1 σ ′ ij , where ˙εij
is the rate of strain, σ ′ ij is deviatoric stress,
σ=(σ ′ ijσ ′ ij/2) 1/2 is an invariant of σ ′ ij , and
C is a quantity independent of strain rate and
stress. An effective viscosity can be defined as
µe =(2Cσ n−1 ) −1 , such that the flow law takes
the form of the Newtonian fluid σ ′ ij= 2µe˙εij .
A solid such as a rock deforms like a power law
fluid as a result of dislocation creep at high temperatures
and stresses.
Poynting–Robertson effect A drag force
arising on particles orbiting the sun, because solar
radiation striking the leading surface is blueshifted
compared to that striking the following
surface. Thus, the particles receive a component
of momentum from the radiation pressure which
is opposite to the direction of motion. This drag
force causes interplanetary dust particles to spiral
inward towards the sun, removing such parti-
© 2001 by CRC Press LLC
prairie
cles from the solar system. For 10 micron-sized
dust particles at the Earth’s orbit, the Poynting–
Robertson effect will cause these particles to spiral
into the sun on a time scale of only 1 million
years. The presence of interplanetary dust particles
even today thus indicates that such material
is continuously being resupplied by comets and
collisions among asteroids. In very accurately
tracked satellites (e.g., LAGEOS) the Poynting–
Robertson effect is important in long-term accurate
modeling of the orbit.
pprocess Thesetofnuclearreactionsresponsible
for producing the rare nuclides of the heavy
elementswithprotontoneutronratiohigherthan
the ratio in the most tightly bound nuclides of
each element. It acts on products of the s process
and r process either by adding protons or
(more likely) removing neutrons, and probably
occurs in supernovae and their environs. No element
has a p-process nuclide as its most abundant
isotope, and so we know nothing about the
abundance of p-process products outside the solar
system.
pp-waves (1923) In general relativity, a particular
description of gravitational waves in a
matter-free space, described by the metric
ds 2 = 2 dudv − 2 dζd¯ζ + 2H (u, ζ, ¯ζ)du 2
discovered by Brinkmann. The Weyl conformal
curvature is Petrov type N, and the principal null
direction is covariantly constant.
H = f(ζ,u)+ ¯
f ¯ζ,u .
Here ζ is a complex stereographic spherical coordinate.
In another representation
ds 2 = 2H(x,y,z)dt 2 − dx 2 − dy 2 − 2 dzdt
where the function H(x,y,z) satisfies the ellip-
tic equation
∂ 2
∂2
+
∂x2 ∂y2
H = 0 .
The normals of the wave fronts are covariantly
constant vectors, hence the waves are planefronted.
See Petrov types, Weyl tensor.
prairie An extensive level or rolling grassland
consisting of rich soil and a variety of
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