ω effect

Ocean water is a vast source or sink of heat, dissolved gases, and dissolved minerals. Its currents transport of these quantities worldwide and the total terrestrial climate and biosphere depend on these ocean processes. The tremendous heat capacity of the oceans contributes strongly to the stability of the Earth’s temperature.

ocean color A generic term referring to the spectral dependence of the radiance leaving a water body.

ocean color sensor Any instrument for sensing of ocean color, usually from aircraft or satellites.

oceanic optics See optical oceanography.

Ockham’s razor See Occam’s razor.

offshore A region extending from the seaward edge of the surf zone to the edge of the continental shelf. Also used to denote a direction or relative position.

Olbers paradox A paradox stated in 1826 by the German astronomer Heinrich Wilhelm Matthäus Olbers that shows the inconsistency of Newtonian cosmology. According to this paradox, in an infinite unchanging Newtonian universe filled with stars at a constant number density, the combined radiant energy from all stars should make the night sky bright. Indeed, if the absolute luminosity of a typical star is L and the number density of stars in the universe is a constant n, then the total radiant energy at any point is given by

E = 0	∞	4πr2 4πr2ndr = Ln 0	∞ dr .
		L

The integral diverges and gives an infinite quantity.

Olbers attempted to solve the paradox by assuming that light from distant stars gets absorbed by interstellar matter. This does not in fact solve the problem, since in an unchanging universe a state of thermal equilibrium will eventually be achieved, and the absorbing matter will radiate exactly the same amount of energy as it absorbs.

Solution of Olbers paradox is possible in the framework of relativistic cosmology, according to which the universe is neither infinite in size nor unchanging. It is now known that the universe undergoes a cosmological expansion, due to which the light from distant stars and galaxies is shifted towards smaller frequencies, thus greatly reducing the radiated energy reaching a distant observer.

oligotrophic water Water with low phytoplankton biomass, typical in many open ocean

regions; chlorophyll a concentration is below 0.5 mg m−3.

Olympus Mons A young, shield volcano in the Tharsis Province of Mars that stands 25 km above the plains, and measures over 700 km across, and is considered to have formed by successive eruptions of low-viscosity lavas. The volcano has a volume 50 to 100 times that of the largest volcano on Earth, Mauna Loa. A basal scarp exists around Olympus Mons, which is up to 6 km high in places. The shield has a complex summit caldera 80 km in diameter, which consists of several coalesced collapse craters with wrinkle ridges on their floors.

The enormous height of the shield volcano has been attributed to the absence of plate tectonics on Mars. In this way, Olympus Mons may have developed by continuous and prolonged eruption from a point source vent over a thermal anomaly in the mantle, to result in one volcano of enormous height, compared with comparatively small volcanoes (e.g., the Hawaiian Emperor chain) strung along segments of moving crust on Earth.

omega bands Ribbons of aurora in a meandering pattern across the sky, which gives their segments a shape like the Greek capital letter omega ( ).

ω effect This a mechanism by which some simple fluid motions — those of differential rotation — can generate magnetic field, and hence contribute to the maintenance of a dynamo. Differential rotation occurs in a fluid rotating axisymmetrically about an axis, but where the rotation rate varies within the fluid. Magnetic flux in a highly conducting fluid behaves as if

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One-form, 1-form

attached to the fluid itself (apart from the effects of magnetic diffusion, which are related to the resistivity of the fluid). Therefore, the magnetic field is stretched parallel to the shear in the fluid associated with the differential rotation. For nearly spherical situations, such as the dynamo in the Earth’s core, it is useful to consider a poloidal/toroidal decomposition of the magnetic field, in which case it can be seen that the ω effect is particularly efficient at generating toroidal field from poloidal field, although not the reverse. To maintain a dynamo, poloidal field must also be generated (from either poloidal or toroidal field), which can be accomplished through the α effect, and Earth-like dynamos are often described as αω dynamos (although it should be noted that this term may be used to imply a type of mean-field dynamo simulation). Some astrophysical dynamos are thought not to rely upon the ω effect, and are often called α2 dynamos. See α effect.

One-form, 1-form A covariant vector. The paradigm is the gradient df of a function f , which defines a geometrical structure, namely the collection of level surfaces of the function, which show how rapidly the function varies. In a coordinate system {xα}, the gradients of the coordinate functions are 1-forms dxβ , and the collection of these gradients {dxβ } is a basis for 1-forms.

Oort cloud Roughly spherical region between about 3 × 104 and 5 × 104 AU that is the source of long period comets. Oort cloud comets are thought to have been formed in the region of the outer planets, and been ejected to the Oort cloud by means of gravitational interactions, mostly with Jupiter and Saturn. Since the Oort cloud comets are very weakly bound to the sun, interactions with passing stars or interstellar clouds, or even the gravitational gradient as the sun passes through the galactic mid-plane, will be sufficient to change significantly the orbits of these comets. They will then either be ejected completely from the solar system, or fall into the inner solar system, where they will appear as moving on highly eccentric orbits. The number of comets in the Oort cloud is not known, but it may be as high at 1012, and contain a substantial fraction of the mass of the solar system.

open cluster A group of several hundred to several thousand stars lying in a small region (of order 10 pc across) in the plane of the galaxy. Typically the site of active star formation, and of many young stars of closely similar ages.

open field region A region of the sun with predominantly unipolar magnetic field and where the field is regarded as “open”, i.e., not returning to an opposite polarity region on the solar surface. In open field regions, the solar corona is not in hydrostatic equilibrium but is continuously expanding outwards as the solar wind.

open magnetosphere The observed behavior of the Earth’s magnetosphere in which reconnection at the dayside magnetopause, caused by dissipation and ionic drift, allows field lines to move backward around the Earth in the solar wind.

open ocean Water seaward of the edges of the continental shelves; often, but not always, case 1 waters. See case 1 water.

open universe A model of the universe in which the space has infinite extent. If the cosmological constant is zero, such a universe will, according to the description of general relativity, expand forever.

operational MUF The operational MUF is defined as the highest frequency that would permit acceptable performance of a radio circuit between given terminals at a given time under specified conditions. The operational MUF is an anticipated performance parameter derived, possibly, from an HF prediction program. It is a frequency that could be used, and may be observed on a circuit. The operational MUF differs from the basic MUF in that it includes system parameters in its calculation. See ionospheric radio propagation path, oblique ionogram, basic MUF.

Ophelia Moon of Uranus also designated UVII. Discovered by Voyager 2 in 1986, it is a small, irregular body approximately 16 km in radius. Its orbit has an eccentricity of 0.01, an inclination of 0◦, a precession of 419◦ yr−1, and

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Optimum Working Frequency (OWF)

a semimajor axis of 5.38 × 104 km. It is the outer shepherding satellite for Uranus’ epsilon ring. Its surface is very dark, with a geometric albedo of less than 0.1. Its mass has not been measured. It orbits Uranus once every 0.376 Earth days.

ophiolites In general, the mantle of the Earth lies beneath the crust. In some cases the more dense and basic mantle rocks have been brought to the surface by mountain building processes. These are ophiolites. Important ophiolites occur in Cyprus, Yemen, and other places.

Oppenheimer–Snyder (OS) model The simplest general relativistic model of gravitational collapse. It consists of a sphere of dust (perfect fluid without pressure) in vacuum which collapses under its own weight to a point-like singularity (see Schwarzschild metric). Since there are no forces other than the self-gravity of dust, the surface of the sphere moves along a geodesic on the external Schwarzschild metric with an ADM mass given by the matching conditions with the internal Robertson–Walker comoving metric. Such mass equals the proper energy of dust only if the surface of the sphere starts collapsing from rest with infinite radius, otherwise it is either bigger or smaller than the rest mass depending on the velocity of the surface at a given radius.

The absence of internal pressure makes the OS model unrealistic for modeling the collapse of a star, but does show the qualitatively expected features. See ADM mass, black hole, comoving frame, Robertson–Walker cosmological models.

opposition Orientation of planets so that the angle planet-Earth-sun equals 180◦. For outer planets, the planets are as close to the Earth as possible in their orbits. Opposition is geometrically impossible for inner planets.

optical closure in measurement Making consistent measurements; examples include independently verifying that the sum of the absorption coefficient plus the scattering coefficient equals the beam attenuation coefficient and that the integral over all directions of the volume

scattering function equals the scattering coefficient.

optical closure in models Development of consistent analytical and/or numerical models that make predictions consistent with observations.

optical closure in scale Making the transition from small scale (e.g., single particle) data to bulk scale data in a manner consistent with observations.

optical constants The nonnegative real and imaginary parts of the refractive index; the constants often strongly depend on frequency.

optical density

See absorbance.

optical depth See optical distance.

optical distance The integral of the dimensionless product of the beam attenuation coefficient [m−1] multiplied by an infinitesimal unit of distance [m] along the direction of travel.

optical double star A pair of stars very close to each other in the sky but at different distances, so that they do not really make up a binary star system. See binary star system.

optical oceanography The subdiscipline of oceanography concerned with the propagation and interaction of radiation, typically at wavelengths between 350 and 750 nm with seawater.

Optimum Working Frequency (OWF) The frequency that is exceeded by the operational MUF, at a given time, between a specified pair of terminals via any available propagation mode, during 90% of a specified period, usually a month. The operational OWF is an anticipated performance parameter derived, possibly, from an HF prediction program. Unlike the operational MUF, the OWF is based on known statistical properties of the ionosphere and offers a safe estimate of a reliable frequency for a propagation path. When planning HF services, the OWF is often used. However, by its nature, 90% of the time it is possible to find frequencies

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orbital elements

higher than the OWF that will be better to use. Conventionally, the OWF has probably been the most important ionospheric parameter deduced for HF propagation. The OWF is also sometimes called the Frequency of Optimum Traffic (FOT). See ionospheric radio propagation path.

orbital elements Seven quantities that must be specified to specify the position of a point mass in a Newtonian orbit: the longitude of the ascending node ( ), the inclination i of the object’s orbital plane to the ecliptic (or to the plane of the sky, for extrasolar objects), the argument of the perihelion (ω), the semimajor radius of the orbit, a, the eccentricity of the orbit, , and the mean anomaly, M, which increases linearly with time. See separate entries for these quantities.

orogeny The creation of a mountain range.

orographic cloud A cloud that forms because of forcing of the air motion by the Earth’s topography, as cap clouds, lee wave clouds, etc.

Orowan’s equation The main relationship for the physics of plastic deformation, expressing the strain rate (ε) caused by the motion (glide or climb) of dislocations of Burgers vector b, with an average velocity (v)¯ and the density of mobile dislocations being ρm,

ε = ρmbv¯ .

It is the master equation, from which many constitutive equations expressing microscopic deformation models can be derived.

orthogonal Perpendicular; lines drawn perpendicular to the crests of water waves are referred to as wave orthogonals.

Osborn–Cox method See Cox number, dissipation of temperature variance.

Osborn model Method to infer turbulent density fluxes from the measurement of the dissipation rate of turbulent kinetic energy . The vertical turbulent density flux is normally expressed via the eddy diffusivity Kρ

w ρ = −Kρ ∂ρ ∂z

where w is the vertical velocity in the z direction, the primes denote turbulent fluctuations from the mean (see Reynolds decomposition), and the over-bar denotes a suitable spatial average that is longer than the typical length scales of the turbulence, but shorter than any energy containing scales. Under the assumption that the turbulence is steady in time and homogeneous in space, the equation describing the turbulent kinetic energy (TKE) reduces to the so-called TKE- balance equation

P = B +

where P = −u w (∂U/∂z) represents the mechanical production of turbulent kinetic energy, B = g/ρ−1w ρ the destruction of TKE by buoyancy, and is the rate of dissipation of TKE. The buoyancy term can be parameterized by the non-dimensional flux Richardson number Rif ≡ B/P . Substitution of Rif into the TKE- balance equation expresses the vertical density flux in terms of the dissipation rate

				Rif
gρ−1w ρ =							= - .
			1	−	Ri
						f

The quantity - = Rif /(1 − Rif ) is often referred to as the mixing efficiency.

oscillating universe If the universe is closed, i.e., it has enough mass or equivalently expands slowly enough for the gravitational pull of matter to cause it to contract back to zero size in the far future, this may be repeated as a cycle. The temperature and density would increase without limit as the contraction intensifies, would go formally to infinity, and then decrease again as the universe expands. This model of cosmic evolution parallels the ancient idea of the cyclic universe — one that undergoes a never-ending sequence of rebirths, each time rising phoenixlike from the ashes of its previous demise. In the modern viewpoint, the bounce may occur in a very high temperature quantum gravity epoch.

O star Star of spectral type O.

Ostriker–Thompson–Witten scenario (1986) Closed loops of superconducting cosmic strings formed during string network interactions will oscillate and radiate gravitationally. This energy

© 2001 by CRC Press LLC