atmospheric dynamics Meteorology is the scientific study of the Earth's atmosphere and short-term atmospheric phenomena (i.e. weather), with a focus on weather forecasting. It has applications in the military, aviation, energy production, transport, agriculture, ...

and physical

oceanography Oceanography (), also known as oceanology, sea science, ocean science, and marine science, is the scientific study of the ocean, including its physics, chemistry, biology, and geology. It is an Earth science, which covers a wide range of to ...

, the Rossby radius of deformation is the length scale at which rotational effects become as important as

buoyancy Buoyancy (), or upthrust, is the force exerted by a fluid opposing the weight of a partially or fully immersed object (which may be also be a parcel of fluid). In a column of fluid, pressure increases with depth as a result of the weight of t ...

gravity wave In fluid dynamics, gravity waves are waves in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere and the oc ...

effects in the evolution of the flow about some disturbance. For a

barotropic In fluid dynamics, a barotropic fluid is a fluid whose density is a function of pressure only. The barotropic fluid is a useful model of fluid behavior in a wide variety of scientific fields, from meteorology to astrophysics. The density of most ...

ocean The ocean is the body of salt water that covers approximately 70.8% of Earth. The ocean is conventionally divided into large bodies of water, which are also referred to as ''oceans'' (the Pacific, Atlantic, Indian Ocean, Indian, Southern Ocean ...

, the Rossby radius is

L_R \equiv \frac

, where

\,g

is the

gravitational acceleration In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag (physics), drag). This is the steady gain in speed caused exclusively by gravitational attraction. All bodi ...

\,D

is the water depth, and

\,f

is the Coriolis parameter. For ''f'' = 1×10⁻⁴ s⁻¹ appropriate to 45° latitude, g = 9.81 m/s² and ''D'' = 4 km, ''L_R'' ≈ 2000 km; using the same latitude and gravity but changing D to 40 m; ''L_R'' ≈ 200 km. The ''n''th

baroclinic In fluid dynamics, the baroclinity (often called baroclinicity) of a stratified fluid is a measure of how misaligned the gradient of pressure is from the gradient of density in a fluid. In meteorology, a baroclinic flow is one in which the dens ...

Rossby radius is: :

L_ \equiv \frac

, where

\,N

is the Brunt–Väisälä frequency,

\,H

is the scale height, and ''n'' = 1, 2, .... In Earth's atmosphere, the ratio ''N''/''f''₀ is typically of order 100, so the Rossby radius is about 100 times the vertical scale height, ''H''. For a vertical scale associated with the height of the

tropopause The tropopause is the atmospheric boundary that demarcates the lowest two layers of the atmosphere of Earth – the troposphere and stratosphere – which occurs approximately above the equatorial regions, and approximately above the polar regi ...

, ''L''_{''R'', 1} ≈ 1000 km, which is the predominant scale seen on weather charts for

cyclones In meteorology, a cyclone () is a large air mass that rotates around a strong center of low atmospheric pressure, counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere as viewed from above (opposite to an ant ...

and

anticyclones A high-pressure area, high, or anticyclone, is an area near the surface of a planet where the atmospheric pressure is greater than the pressure in the surrounding regions. Highs are middle-scale meteorological features that result from interpl ...

. This is commonly called the

synoptic scale In meteorology, the synoptic scale (also called the large scale or cyclonic scale) is a horizontal length scale of the order of or more. This corresponds to a horizontal scale typical of mid-latitude depressions (e.g. extratropical cyclones). ...

. In the ocean, the Rossby radius varies dramatically with latitude. Near the equator it is larger than 200 km, while in the high latitude regions it is less than 10 km. Nurser, A. J. G., & Bacon, S., 2014, The Rossby radius in the Arctic Ocean, Ocean Sci., 10, 967-975, doi: 10.5194/os-10-967-2014 The size of ocean eddies varies similarly; in low latitude regions, near the equator, eddies are much larger than in high latitude regions. The associated dimensionless parameter is the Rossby number. Both are named in honor of Carl-Gustav Rossby.

References

{{DEFAULTSORT:Rossby Radius Of Deformation Atmospheric dynamics Oceanography Radii