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

Abstract

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.

Simultaneous observations of a Mesospheric Inversion Layer and turbulence during the ECOMA-2010 rocket campaign

“…7 where the colour red shows regions with N 2 < 0 and dark and light blue areas represent Ri < 1/4 and Ri < 1, respectively. The Ri < 1/4 is a favourable condition for instability to start, whereas Ri < 1 describes still favourable condition for instability to persist (Woods, 1969). The two downward progressing upper MILs are marked by the black arrows similar to what shown in Fig.…”

Critical Richardson numbers and gravity waves

“…When that occurs, one first enters a weakly non-linear regime and then finally in a turbulent regime where the nonlinearities dominate. We refer the reader to an illustrative depiction of these successive processes (Woods 1969) which highlights the different physical regimes of laminar, weakly non-linear and strongly non-linear regimes. Given a stable laminar sheet of thickness h, Kelvin-Helmholtz instabilities gradually erode and entrain fluid parcels above and below h. The process leads to an incrase of h which ceases when the thickness has become about four times the original value h. Woods (1969) concluded that "since the final thickness is nearly four times the original value, the final Richardson number is also four times the value prior to the instability".…”

Generation of billow-like wavy folds by fluidization at high temperature in Nojima fault gouge: microscopic and rock magnetic perspectives

“…Under such temperature and pressure conditions, Schmelzer et al (2005) showed that the viscosity of water [pore fluid (η m )] is 9.137 × 10 −5 Pa s, being approximately 1.0 × 10 −4 Pa s. Therefore, if micrometer-sized finely comminuted products approximate to an equivalent diameter spherical particle, total viscosity (η s ) is 1.0 × 10 −2 Pa s. Due to frictional heating, the pore fluid expands in volume (e.g., Lachenbruch 1980). If the permeability of the fault slip zone decreases, the volume fraction of fault gouge decreases; this suggests that the total fluid viscosity of the fault slip zone further reduces below 1.0 × 10 −2 Pa s. Although Woods (1969) has demonstrated that KH instability can be generated under high Reynolds number conditions, we cannot deduce the concrete Reynolds number due to the difficulty in the estimation of the flow velocity in fault gouge. With regard to shear flow, viscosity dissipates disturbance energy and stabilizes the flow.…”