Hough function

In applied mathematics, the Hough functions are the eigenfunctions of Laplace's tidal equations which govern fluid motion on a rotating sphere. As such, they are relevant in geophysics and meteorology where they form part of the solutions for atmospheric and ocean waves.

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Each Hough mode is a function of latitude and may be expressed as an infinite sum of associated Legendre polynomials; the functions are orthogonal over the sphere in the continuous case. Thus they can also be thought of as a generalized Fourier series in which the basis functions are the normal modes of an atmosphere at rest.

References

• R. Lindzen, "The Interaction of Waves and Convection in the Tropics", Journal of the Atmospheric Sciences, v.60,24, p.3009-3020[1]

See also

• Secondary circulation
• Legendre polynomials
• Primitive equations