Ursell Number

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

 

Ursell Number formula
\(\large{ U = \frac {H} {h}  \; \left( \frac {\lambda} {h} \right)^2  =  \frac {H \; \lambda^2}  {h^3}  }\)
Symbol	English	Metric
\(\large{ U }\) = Ursell number	\(\large{dimensionless}\)
\(\large{ h }\) = mean water depth	\(\large{ft}\)	\(\large{m}\)
\(\large{ H }\) = the wave height, the difference between the elevations of the wave crest and trough	\(\large{ft}\)	\(\large{m}\)
\(\large{ \lambda }\)  (Greek symbol lambda) = the wavelength, which has to be large compared to the depth, \(\large{\lambda \gg h}\)	\(\large{ft}\)	\(\large{m}\)