geophysical Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' som ...

fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...

, the ''f''-plane approximation is an approximation where the

Coriolis parameter The Coriolis frequency ''ƒ'', also called the Coriolis parameter or Coriolis coefficient, is equal to twice the rotation rate ''Ω'' of the Earth multiplied by the sine of the latitude \varphi. :f = 2 \Omega \sin \varphi.\, The rotation rate ...

, denoted ''f'', is set to a constant value. This approximation is frequently used for the analysis of highly idealized tropical cyclones. Using a constant Coriolis parameter prevents the formation of

beta gyre Beta (, ; uppercase , lowercase , or cursive ; grc, βῆτα, bē̂ta or ell, βήτα, víta) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Modern Greek, it represents the voiced labiod ...

s which are largely responsible for the North-westward direction of most tropical cyclones.

Rossby waves Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating fluids. They were first identified by Sweden-born American meteorologist Carl-Gustaf Arvid Rossby. They are observed in the atmospheres and ...

also depend on variations in ''f'', and do not occur in the ''f''-plane approximation. In reality, the Coriolis parameter varies with

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

, and so the ''f''-plane approximation is not appropriate when considering flows over large length scales. The ''f''-plane approximation is also poor near the equator, where variations in ''f'' are on the same

order of magnitude An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic dis ...

as ''f''. The

beta plane In geophysical fluid dynamics, an approximation whereby the Coriolis parameter, ''f'', is set to vary linearly in space is called a beta plane approximation. On a rotating sphere such as the Earth, ''f'' varies with the sine of latitude; in the so ...

approximation is an improvement on the ''f''-plane approximation which takes leading-order variations in ''f'' into account.

References

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Isaac Held Isaac Meyer Held (born 1948) is an American meteorologist. He is a senior research scientist at the Geophysical Fluid Dynamics Laboratory. Held was elected to the United States National Academy of Sciences in 2003. Biography Born to refugee pare ...

Rotating radiative-convective equilibrium

References

See also