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1The effects of molecular viscosity are utterly negligible in the atmosphere and ocean, except very close to solid boundaries. Small-scale turbulent motions can in some ways act like viscosity, with an ''effective eddy viscosity'' that is much larger than the molecular value. However, even these effects are usually negligible away from the boundaries.

2We have actually anticipated something here that is evident only a posteriori: vertical advection makes a negligible contribution to (u ■ V) u.

Carl-Gustav Rossby (1898—1957). Swedish-born meteorologist, one of the major figures in the founding of modern dynamical study of the atmosphere and ocean. In 1928, he was appointed chair of meteorology in the Department of Aeronautics at MIT. This group later developed into the first Department of Meteorology in an academic institution in the United States. His name is recalled ubiquitously in Rossby waves, the Rossby number, and the Rossby radius of deformation, all ideas fundamental to the understanding of all planetary scale fluids.

■ 0, the small Rossby number assumption breaks down, as will be seen, for example, in

Equation 7-2 defines geostrophic balance, in which the pressure gradient is balanced by the Coriolis term. We expect this balance to be approximately satisfied for flows of small Ro. Another way of saying the same thing is that if we define the geostrophic wind, or current, to be the velocity ug that exactly satisfies Eq. 7-2, then u ~ ug in such flows. Since z x z x u = -u, Eq. 7-2 gives

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