# Ursell Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Ursell number, abbreviated as U, is a dimensionless number that indicates the nonlinearity of long surface gravity waves on a fluid layer.

### Ursell Number FORMULA

$$\large{ U = \frac {H} {h} \; \left( \frac {\lambda} {h} \right)^2 = \frac {H \; \lambda^2} {h^3} }$$

Where:

$$\large{ U }$$ = Ursell number

$$\large{ h }$$ = mean water depth

$$\large{ H }$$ = the wave height, the difference between the elevations of the wave crest and trough

$$\large{ \lambda }$$  (Greek symbol lambda) = the wavelength, which has to be large compared to the depth, $$\large{ \lambda \gg h }$$