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
|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)|