From AMS Glossary
A dimensionless number, Bu, for atmospheric or oceanographic flow expressing the ratio between density stratification in the vertical and the earth's rotation in the horizontal:
where N is the Brunt–Väisälä frequency, Ω is the angular rotation rate of the earth, H is the scale height of the atmosphere, L is a horizontal length scale of typical motions, Ro is the Rossby number, Fr is the Froude number, and RD is the Rossby deformation radius.
Bu is often of order one for many atmospheric phenomena, meaning that both stratification and rotation play nearly equal roles in governing vertical and other motions in the fluid.
Cushman–Roisin 1994. Introduction to Geophysical Fluid Dynamics. 320 pp.