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 formulasVariables
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) |