On the Scale-dependence of the Gradient Richardson Number in the Residual Layer

We present results of a technique for examining the scale-dependence of the gradient Richardson number, Ri, in the nighttime residual layer. The technique makes use of a series of high-resolution, in situ, vertical profiles of wind speed and potential temperature obtained during CASES-99 in south-eastern Kansas, U.S.A. in October 1999. These profiles extended from the surface, through the nighttime stable boundary layer, and well into the residual layer. Analyses of the vertical gradients of both wind speed, potential temperature and turbulence profiles over a wide range of vertical scale sizes are used to estimate profiles of the local Ri and turbulence structure as a function of scale size. The utility of the technique lies both with the extensive height range of the residual layer as well as with the fact that the sub-metre resolution of the raw profiles enables a metre-by-metre ‘sliding’ average of the scale-dependent Richardson number values over hundreds of metres vertically. The results presented here show that small-scale turbulence is a ubiquitous and omnipresent feature of the residual layer, and that the region is dynamic and highly variable, exhibiting persistent turbulent structure on vertical scales of a few tens of metres or less. Furthermore, these scales are comparable to the scales over which the Ri is less than or equal to the critical value of Ri _c of 0.25, although turbulence is also shown to exist in regions with significantly larger Ri values, an observation at least consistent with the concept of hysteresis in turbulence generation and maintenance. Insofar as the important scale sizes are comparable to or smaller than the resolution of current models, it follows that, in order to resolve the observed details of small Ri values and the concomitant turbulence generation, future models need to be capable of significantly higher resolutions.