Friction and Viscous Flow

Abstract

The observed persistence over several days of large-scale waves in the atmosphere and the oceans reinforces the impression that frictional forces are weak, almost everywhere, when compared with the Coriolis acceleration and the pressure gradient. Friction rarely upsets the geostrophic balance to lowest order. Indeed, for many flows it is probably also true that the dissipa-tive time scale is long compared to the advective time scale, i.e., that the frictional forces are weak in comparison with the nonlinear relative acceleration. Nevertheless friction, and the dissipation of mechanical energy it implies, cannot be ignored. The reasons are simple yet fundamental. For the time-averaged flow, i.e., for the general circulation of both the atmosphere and the oceans, the fluid motions respond to a variety of essentially steady external forcing. The atmosphere, for example, is set in motion by the persistent but spatially nonuniform solar heating. This input of energy produces a mechanical response, i.e., kinetic energy of the large-scale motion, and eventually this must be dissipated if a steady state—or at least a statistically stable average state of motion—is to be maintained. This requires frictional dissipation. In addition, the driving force itself may be frictional, as in the case of the wind-driven oceanic circulation.