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

UUrsell number (dimensionless)
Hwave height, i.e. the difference between the elevations of the wave crest and trough (m)
λmean water depth (m)
hwavelength, which has to be large compared to the depth, λ ≫ h. (m)