Ursell Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Ursell Number

Ursell number ( \(U\) ) (dimensionless number) indicates the nonlinearity of long surface gravity waves on a fluid layer.

Ursell Number FORMULA

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

Where:

\(\large{ U }\) = Ursell number

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

\(\large{ h }\) = the mean water depth

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

 

Tags: Equations for Gravity