On Richardson's Number as a Criterion for Laminar-Turbulent-Laminar Transition in the Ocean and Atmosphere


  • J. D. Woods


Dye-tracer experiments in the seasonal oceanic theormocline have revealed a microstructure with a significant fluctuation of shear and density gradient within a vertical distance of 1 cm. It has proved possible to relate the occurrence of localized spots of turbulence with this structure and with internal waves traveling along especially (statically) stable ‘sheets’ within the thermocline. The thermocline microstructure has a predominant vertical scale of a few decimeters, the sheet waves have wavelengths in the range 5–10 meters, and the turbulence occurs at a Reynolds number in the range 200–1000. Similar features are found on a very much larger scale in the atmosphere, although the methods of investigation (mainly instrumented aircraft) used here are incapable of yielding the detailed information obtained by divers working in the thermocline. It seems useful, therefore, to treat the observations of microstructure, waves, and turbulence in the thermocline as a possible model for the corresponding features in the atmosphere. This leads to some predictions concerning the atmosphere microstructure and also to suggestions for the planning of experimental investigations. The available evidence from the atmosphere appears to support the predictions that (1) the critical gradient Richardson number for reverse transition occurs at about unity regardless of the Reynolds number of the turbulence, and (2) that most of the atmosphere (with the exception of clouds and the boundary layer) is in laminar flow.