Hough function

<p>In <a href="/facts/Applied_mathematics/qyqklXXm">applied mathematics</a>, the Hough functions are the <a href="/facts/Eigenfunctions/62EJS0XB">eigenfunctions</a> of <a href="/facts/Primitive_equations/IqxpAdKv">Laplace's tidal equations</a> which govern <a href="/facts/Secondary_circulation/Ch4rvDSM">fluid motion on a rotating sphere</a>. As such, they are relevant in <a href="/facts/Geophysics/ywVQ1sAQ">geophysics</a> and <a href="/facts/Meteorology/xblFr28q">meteorology</a> where they form part of the solutions for <a href="/facts/Tide/zNstvWPv">atmospheric and ocean waves</a>. These functions are named in honour of <a href="/facts/Sydney_Samuel_Hough/Pk1jrHol">Sydney Samuel Hough</a>.
</p><p>Each Hough mode is a function of <a href="/facts/Latitude/IBYqkjhU">latitude</a> and may be expressed as an infinite sum of <a href="/facts/Associated_Legendre_polynomials/cc74eGon">associated Legendre polynomials</a>; the functions are <a href="/facts/Orthogonal/JVIjYPog">orthogonal</a> over the sphere in the continuous case. Thus they can also be thought of as a <a href="/facts/Generalized_Fourier_series/jpd2a7nM">generalized Fourier series</a> in which the <a href="/facts/Basis_function/Bt7jqjY2">basis functions</a> are the <a href="/facts/Normal_mode/XCsvQpuI">normal modes</a> of an atmosphere at rest.
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Hough function open-in-new

Hough function