# Ursell Number

## Description

In fluid dynamics, the Ursell number indicates the nonlinearity of long surface gravity waves on a fluid layer. This dimensionless parameter is named after Fritz Ursell, who discussed its significance in 1953.

The Ursell number is derived from the Stokes wave expansion, a perturbation series for nonlinear periodic waves, in the long-wave limit of shallow water — when the wavelength is much larger than the water depth.

Related formulas## Variables

U | Ursell number (dimensionless) |

H | wave height, i.e. the difference between the elevations of the wave crest and trough (m) |

λ | mean water depth (m) |

h | wavelength, which has to be large compared to the depth, λ ≫ h. (m) |