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; a linear approximation to this variability about a given latitude (in the sense of a Taylor series expansion) can be visualized as a tangent plane touching the surface of the sphere at this latitude. The relevant dynamics can then be cast in a planar, Cartesian coordinate system rather than a spherical one. The name 'beta plane' derives from the convention to denote the linear coefficient of variation with the Greek letter β.

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The beta plane approximation is useful for the theoretical analysis of many phenomena in geophysical fluid dynamics since it makes the equations much more tractable, yet retains the important information that the Coriolis parameter varies in space. In particular, Rossby waves, the most important type of waves if one considers large-scale atmospheric and oceanic dynamics, depend on the variation of f as a restoring force; they do not occur if the Coriolis parameter is approximated only as a constant.

References

• Holton, J. R., An introduction to dynamical meteorology, Academic Press, 1992
• Pedlosky, J., Geophysical fluid dynamics, Springer-Verlag New York, 1987

See also

• Coriolis effect
• Coriolis frequency
• Baroclinic instability