Ursell Number

on . Posted in Dimensionless Numbers

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, \(\large{\lambda \gg h}\) \(\large{ft}\) \(\large{m}\)


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Tags: Gravity Equations Fluid Equations