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

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 epsilon at a height of 15 m above the bottom in a 55 m deep tidal channel. One pair of probes measures partial differential w/ partial differential x while the other measures partial differential upsilon/ partial differential x, where w and upsilon 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 epsilon over bar L=7.5 nu( partial differential w/ partial differential x)2 over bar L (and similarly for the upsilon component), for averaging lengths, L ranging from 1 to 10(4) Kolmogorov lengths. While the rate of dissipation fluctuates by more than a factor of 100, the fluctuations of the differences of ln(epsilon over bar L) between pairs of probes are stationary, zero mean, and distributed normally for averaging lengths of L = & SIM;30 to 10(4) Kolmogorov lengths. The variance of the differences, sigma ln epsilon 2, scales as L-7/9, independent of stratification for buoyancy Reynolds numbers larger than & SIM;600, and for dissipation rates from & SIM;10(-10) to & SIM;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 epsilon estimate such as the 95% interval CI95(epsilon)=epsilon exp(& PLUSMN;1.96 sigma ln epsilon). This result also applies to the traditional epsilon estimates that are made by way of spectral integration, after L is adjusted for the truncation of the shear spectrum.Significance StatementThe 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.

Automated summary

The study provides a method to estimate the statistical uncertainty of a dissipation estimate based on a finite length of turbulence shear data.