Sampling Turbulent Dissipation

Abstract

Recently it has been argued that in many regions of the ocean the Osborn?Cox model accurately determines the total long-term diapycnal flux of a tracer ? if the mean gradient and dissipation in the model are long-time averages. The mean gradient is easily determined, but averaging the scalar dissipation ? = 2?|???|2 is notoriously difficult because of its highly intermittent distribution. The distribution of ? has long been known to be approximately lognormal, and Baker and Gibson suggest estimating (?) by fitting observations to a lognormal probability distribution. There are four reasons why this does not apply to the observations needed to find long-term averages of ?. First, the theoretical arguments for the lognormal distribution apply to dissipation under a single set of local macroscopic factors (shear, stability, etc.) and low-frequency modulation of macroscopic factors is likely to cause slow changes of the parameters of the local lognormal distribution, leading to a different distribution for the total variability. Second, it is |??| that is most apt to be lognormal, whereas measurements are usually of a single gradient component ?z0; if |??| is lognormal and isotropic. then |?z| is not lognormal. Third, correcting for instrumental response often requires that spatial averages of the squared gradient be processed and averages of lognormal variables are not lognormal. Finally, even if |???| were lognormal, very small errors in the estimated mean gradient would upset the distribution. Examination of these departures from lognormality and their effect on estimating (?) indicates that methods based on knowing the form of the sampling distribution are dangerous. The procedure of fitting ? observations to a lognormal distribution can give quite erroneous results. For this reason direct arithmetic averaging appears to be the best analysis procedure. Similar considerations apply to sampling kinetic energy dissipation ? = 2??u:?u although it is more difficult to show that ? should have a lognormal distribution or to relate the distribution of total dissipation to that of shears measured.