Present theories of the dynamics of the outer planet atmospheres are limited by the absence of direct observations of the wind and temperature layering below their visible cloud decks. We show that if the potential vorticity is assumed to be small at low latitudes, then cloud-tracked wind measurements of the equatorial flow on Jupiter, Saturn, Uranus, and Neptune can be used to constrain their vertical stratification at deeper levels. A Richardson number between 1.2 and 4 is indicated for all the giant planets, which at their rapid rotation implies a much more vertical isentropic structure at these levels than is realized in the terrestrial atmospheres. These conditions signify the likely presence of a unique but as yet unstudied regime for the jovian meteorology, illustrated by a new ''Richardson-Rossby'' diagram for comparative planetary circulations. The Jupiter case will be directly tested by the Galileo atmospheric entry probe. ¿ American Geophysical Union 1995