Details

The surface elevation of a cnoidal wave takes the form

,

where is the elevation, is the wave height, is the phase velocity (the rate at which the phase of the wave propagates), is the wavelength, and is the Jacobi elliptic function (hence the name cnoidal). is the complete elliptic integral of the first kind, with being the elliptic parameter that for large values produces smoother troughs and more pronounced crests than in the case of a sine wave.

Reference

[1] Wikipedia. "Cnoidal Wave." (May 16, 2013) en.wikipedia.org/wiki/Cnoidal_wave.