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.
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.