# Ursell Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Ursell Number (1923 – 2012) is a dimensionless number that indicates the nonlinearity of long surface gravity waves on a fluid layer.

## FORMULA

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

Where:

$$U$$ = Ursell Number

$$H$$ = the wave height, the difference between the elevations of the wave crest and trough

$$h$$ = the mean water depth

$$\lambda$$ = the wavelength, which has to be large compared to the depth, $$\lambda \gg h$$