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

\(U = \frac {H} {h}  \; \left( \frac {\lambda} {h} \right)^2  =  \frac {H \lambda^2}  {h^3}  \)          \( Ursell \; number  \;=\;   \frac { wave \; height } { mean \; water \; depth }  \; \left( \frac { wavelength } { mean \; water \; depth } \right)^2  =  \frac { wave \; height  \;\;x\;\;  wavelength^2}  { mean \; water \; depth^3}  \)

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, \(\lambda \gg h\)

 

Tags: Equations for Gravity