Ursell Number

Written by Jerry Ratzlaff. 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, \(\lambda \gg h\)