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. 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 ϕ 0 {displaystyle phi _{0}} : f = f 0 + β y {displaystyle f=f_{0}+eta y} , where f 0 {displaystyle f_{0}} is the Coriolis parameter at ϕ 0 {displaystyle phi _{0}} , β = ( d f / d y ) | ϕ 0 = 2 Ω cos ⁡ ( ϕ 0 ) / a {displaystyle eta =(mathrm {d} f/mathrm {d} y)|_{phi _{0}}=2Omega cos(phi _{0})/a} is the Rossby parameter, y {displaystyle y} is the meridional distance from ϕ 0 {displaystyle phi _{0}} , Ω {displaystyle Omega } is the angular rotation rate of the Earth, and a {displaystyle a} is the Earth's radius.