The Scruton number Sc is an important parameter for vortex-induced vibration (excitation) of structures, vibrations caused by rain or wind, dry inclined cable galloping, and wake galloping, the unstable airflow that forms around bridge cables and other cylindrically-structured buildings.^[1] It is named after Christopher "Kit" Scruton, a British industrial dynamics engineer.^[2][3]

It is defined by:^[4]

${\displaystyle Sc={\frac {2\delta _{s}m_{e}}{\rho b_{\text{ref}}^{2}}},}$

where

${\displaystyle \delta _{s}}$	is the structural damping expressed by the logarithmic damping decrement,
${\displaystyle m_{e}}$	is the effective mass per unit length,
${\displaystyle \rho }$	is the density of the air, or liquid,
${\displaystyle b_{\text{ref}}}$	is the characteristic width of the structure.

References