The Statistics of Oceanic Turbulence Measurements. Part I: Shear Variance and Dissipation Rates

Abstract

Abstract An empirically derived statistic is used to estimate the confidence interval of a dissipation estimate that uses a finite amount of shear data. Four collocated shear probes, mounted on a bottom anchored float, are used to measure the rate of dissipation of turbulence kinetic energy ϵ at a height of 15 m above the bottom in a 55 m deep tidal channel. One pair of probes measures ∂w/∂x while the other measures ∂υ/∂x, where w and υ are the vertical and lateral velocity. The shear-probe signals are converted into a regularly resampled space series to permit the rate of dissipation to be estimated directly from the variance of the shear using (and similarly for the υ component), for averaging lengths, L ranging from 1 to 104 Kolmogorov lengths. While the rate of dissipation fluctuates by more than a factor of 100, the fluctuations of the differences of between pairs of probes are stationary, zero mean, and distributed normally for averaging lengths of L = ∼30 to 104 Kolmogorov lengths. The variance of the differences, , scales as L−7/9, independent of stratification for buoyancy Reynolds numbers larger than ∼600, and for dissipation rates from ∼10−10 to ∼10−5 W kg−1. The variance decreases more slowly than L−1 because the averaging is done in linear space while the variance is evaluated in logarithmic space. This statistic provides the confidence interval of an ϵ estimate such as the 95% interval . This result also applies to the traditional ϵ estimates that are made by way of spectral integration, after L is adjusted for the truncation of the shear spectrum. Significance Statement The results reported here can be used to estimate the statistical uncertainty of a dissipation estimate that is derived from a finite length of turbulence shear data.