| Section C | C index | 311-319 of 1157 terms |
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circular vortex—A flow in parallel planes in which streamlines and other isopleths are concentric circles about a common axis. One atmospheric model of easterly and westerly winds is a circular vortex about the earth's polar axis. The stability properties of this model have been extensively investigated.
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circulation index—A measure of the magnitude of one of several aspects of large-scale atmospheric circulation patterns. Indices most frequently measured represent the strength of the zonal (east–west) or meridional (north–south) components of the wind, at the surface or at the upper levels, usually averaged spatially and often averaged in time. See meridional index, zonal index.
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circulation integral—The line integral of an arbitrary vector taken around a closed curve. Thus,  is the circulation integral of the vector a around the closed curve and dr is an infinitesimal vector element of the curve. If the vector is the velocity, this integral is called the circulation.
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circulation theorem—1. V. Bjerknes's circulation theorem: 1) With reference to an absolute coordinate system, the rate of change of the absolute circulation dCa/dt of a closed individual fluid curve, that is, one that will consist always of the same fluid particles, is equal to the number of pressure–volume solenoids Nα,−p embraced by the curve  where the circulation has the same sense as the solenoids, the sense of the rotation from volume ascendent to pressure gradient. 2) With reference to a relative coordinate system (specifically, the rotating earth), the rate of change of circulation relative to the earth dC/dt of an arbitrary closed individual fluid curve is determined by two effects: a) the solenoid effect that tends to change the circulation in the sense of the solenoids by an amount per unit time equal to the number of solenoids embraced by the curve; and b) the inertial effect that tends to decrease the circulation by an amount per unit time proportional to the rate at which the projected area of the curve in the equatorial plane expands:  where Ω is the angular speed of the earth's rotation and A is the equatorial projection of the curve. This is the most useful form of Bjerknes's circulation theorem. It permits the qualitative examination of many types of frictionless atmospheric motion that are too complicated for complete analytic treatment, for example, the sea breeze. 2. Kelvin's circulation theorem: The rate of change of the circulation dC/dt of a closed individual fluid curve is equal to the circulation integral of the acceleration  around the curve:  where dr is a vector line element of the curve. 3. Höiland's circulation theorem: An arbitrary closed tubular fluid filament with constant cross section has a total mass acceleration along itself equal to the resultant of the force of gravitation along the filament:  where is the fluid density,  is the absolute vector acceleration, and dφa is the variation of the gravitational potential from the initial to the terminal point of the vector element dr. This theorem is particularly useful in the study of the stability of fluid flow.
Gill, A. E., 1982: Atmosphere–Ocean Dynamics, Academic Press, 226–231, 237–241.
Holton, J. R., 1992: An Introduction to Dynamic Meteorology, 3d edition, Academic Press, 87–92.
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circulation type—A characteristic circulation feature, typically with analogs. An example of a circulation type is an omega block, characterized by a high-amplitude cut-off ridge surrounded to its east and west by high-amplitude cut-off troughs.
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circulation—1. The flow or motion of a fluid in or through a given area or volume. 2. A precise measure of the average flow of fluid along a given closed curve. Mathematically, circulation is the line integral  about the closed curve, where v is the fluid velocity and dr is a vector element of the curve. By Stokes's theorem, the circulation about a plane curve is equal to the total vorticity of the fluid enclosed by the curve. The given curve may be fixed in space or may be defined by moving fluid parcels. See circulation theorem.
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