Beta plane

Article summary

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-called f-plane approximation, this variation is ignored, and a value of f appropriate for a particular latitude is used throughout the domain. This approximation can be visualized as a tangent plane touching the surface of the sphere at this latitude. A more accurate model is a linear Taylor series approximation to this variability about a given latitude \phi_0 : f = f_0 + \beta y , where f_0 is the Coriolis parameter at \phi_0 , \beta = (\mathrm{d}f/\mathrm{d}y)|_{\phi_0} = 2\Omega\cos(\phi_0)/a is the Rossby parameter, y is the meridional distance from \phi_0 , \Omega is the angular rotation rate of the Earth, and a is the Earth's radius. In analogy with the f-plane, this approximation is termed the beta plane, even though it no longer describes dynamics on a hypothetical tangent plane. The advantage of the beta plane approximation over more accurate formulations is that it does not contribute nonlinear terms to the dynamical equations; such terms make the equations harder to solve. The name 'beta plane' derives from the convention to denote the linear coefficient of variation with the Greek letter β.…

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