From AMS Glossary
A nondimensional number representing the ratio of viscous to inertial forces in the nondimensionalized governing equations for Langmuir circulation:
where νT is the eddy viscosity, 2S0 and 1/2β are the surface value and e-folding depth of the Stokes's drift current, respectively, and u* is the friction velocity.
This parameter can also be interpreted as expressing the balance between the rate of diffusion of streamwise vorticity by eddy viscosity and the rate of production of streamwise vorticity by vortex stretching accomplished by the Stokes's drift. The Langmuir number is inversely related to the Reynolds number.