| Section R | R index | 541-549 of 589 terms |
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Rossby number—A dimensionless number relating the ratio of inertial to Coriolis forces for a given flow of a rotating fluid. Explicitly, the Rossby number is  where U is the velocity scale, f is the Coriolis parameter, and L is the horizontal length scale. This number plays a fundamental role in defining the regime of large-scale geophysical fluid dynamics. Large-scale flows are defined as those that are significantly influenced by the earth's rotation and with sufficiently large L for Ro to be order one or less (e.g., flows with sufficiently small Rossby number are in geostrophic balance).
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Rossby radius of deformation—1. The distance that cold pools of air can spread under the influence of the Coriolis force. A cold pool will initially spread out toward and under warmer air because of higher pressure under the cold, denser air. However, as the spreading velocity increases, the Coriolis force will increasingly turn the velocity vector until it is parallel, rather than perpendicular, to the pressure gradient. At this point, no further spreading will occur and the winds will be in geostrophic equilibrium. The final equilibrium distance traveled by the edge of the cold air equals the external Rossby radius of deformation, λR:  where g is gravitational acceleration, H is the initial depth of the cold pool, Δθ is the potential temperature contrast between the cold and surrounding warm air, θ0 is the absolute potential temperature of the warm air, and fc is the Coriolis parameter. 2. An internal Rossby radius of deformation can be defined for fluids with a gradient of potential temperature rather than a temperature interface:  where NBV is the average Brunt–Väisälä frequency within the troposphere and ZT is the depth of the troposphere. This radius is important for determining the phase speed and wavelength of baroclinic waves (Rossby waves) in the general circulation. An alternative definition for internal Rossby radius of deformation is  where G is the geostrophic wind speed and zi is the depth of the atmospheric boundary layer, approximated here as zi = G/NBV. This form is useful in determining boundary layer (Ekman) pumping through the top of the boundary layer.
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Rossby regime—A type of flow pattern in a rotating fluid with differential radial heating in which the major radial transport of heat and momentum is effected by horizontal eddies of low wavenumber. This regime occurs for low values of the Rossby number (on the order of 0.1). The term has been used in connection with dishpan experiments, but applies as well to the atmosphere of the earth and other planets.
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Rossby wave—(Also called planetary wave.) A wave on a uniform current in a two-dimensional nondivergent fluid system, rotating with varying angular speed about the local vertical (beta plane). This is a special case of a barotropic disturbance, conserving absolute vorticity. Applied to atmospheric flow, it takes into account the variability of the Coriolis parameter while assuming the motion to be two-dimensional. The wave speed c is given by  where  is the mean westerly flow, β is the Rossby parameter, and K2 = k2 + l2, the total wavenumber squared. (This formula is known as the Rossby formula, long-wave formula, or planetary-wave formula.) A stationary Rossby wave is thus of the order of the distance between the large-scale semipermanent troughs and ridges in the middle troposphere. The Rossby wave moves westward relative to the current, in effect slowing the eastward movement of long-wave components relative to the short-wave components in a barotropic flow. This effect is important in a numerical forecast with a barotropic model, but attempts to apply the formula to actual contour patterns considered as waves have less dynamic justification and correspondingly less success. See long wave.
Holton, J. R., 1992: An Introduction to Dynamic Meteorology, 3d edition, Academic Press, 216–222.
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rotary current—A tidal current that flows continuously, with the direction of flow changing through all points of the compass during a tidal cycle; found away from coastal or shallow water flow restrictions, where reversing currents are more probable. Compare reversing current; see current ellipse.
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