Shear, Strain, and Richardson Number Variations in the Thermocline. Part I: Statistical Description

Abstract

Quasi-continuous depth?time observations of shear (5.5-m, 6-min resolution) and strain, (??/?z, (2-m, 2.1- min resolution) obtained from the R/P FLIP are applied to a study of Richardson number (Ri) statistics. Data were collected off the coast of central California in the 1990 Surface Waves Processes Experiment. Observations are presented in Eulerian and in isopycnal-following frames. In both frames, shear variance is found to scale as N2 in the thermocline, in agreement with previous findings of Gargett et al. The probability density function for squared shear magnitude is very nearly exponential. Strain variance is approximately uniform with depth. The magnitude of the fluctuations is sufficient to influence the Ri field significantly at finescale. To model the Richardson number, the detailed interrelationship between shear and strain must be specified. Two contrasting hypotheses are considered: One (H I) holds that fluctuations in the cross-isopycnal shear are independent of isopycnal separation. The other (H II) states that the cross-isopycnal velocity difference is the quantity that is independent of separation. Model probability density functions for Ri are developed under both hypotheses. The consideration of strain as well as shear in the Richardson calculation increases the probability of occurrence of both extremely low and high values of Ri. The observations confirm this general prediction. They also indicate that, while neither hypothesis is strictly correct, H II appears to be a much better approximation over the most commonly observed values of Ri.