Abstract
Energy dissipation rates are an important characteristic of turbulence; however, their magnitude in observational profiles can be incorrectly determined owing to their irregular appearance during vertical evolution. By analysing the data obtained from oceanic turbulence measurements, we demonstrate that the vertical sequences of energy dissipation rates exhibit a scaling property. Utilising this property, we propose a method to estimate the population mean for a profile. For scaling in the observed profiles, we demonstrate that our data exhibit a statistical property consistent with that exhibited by the universal multifractal model. Meanwhile, the population mean and its uncertainty can be estimated by inverting the probability distribution obtained by Monte Carlo simulations of a cascade model; to this end, observational constraints from several moments are imposed over each vertical sequence. This approach enables us to determine, to some extent, whether a profile shows an occasionally large mean or whether the population mean itself is large. Thus, it will contribute to the refinement of the regional estimation of the ocean energy budget, where only a small amount of turbulence observation data is available.
Highlights
Energy dissipation rates are an important characteristic of turbulence; their magnitude in observational profiles can be incorrectly determined owing to their irregular appearance during vertical evolution
We first distinguish the ’mean energy dissipation rate’, which refers to the sample mean over a profile, and the ’energy input rate’, which refers to the population mean for a profile
We have analysed the observed data obtained from oceanic turbulence measurements and shown that the vertical sequences of energy dissipation rates in a profile have an intermittent structure that obeys a scaling law
Summary
Energy dissipation rates are an important characteristic of turbulence; their magnitude in observational profiles can be incorrectly determined owing to their irregular appearance during vertical evolution. By analysing the data obtained from oceanic turbulence measurements, we demonstrate that the vertical sequences of energy dissipation rates exhibit a scaling property. Utilising this property, we propose a method to estimate the population mean for a profile. The population mean and its uncertainty can be estimated by inverting the probability distribution obtained by Monte Carlo simulations of a cascade model; to this end, observational constraints from several moments are imposed over each vertical sequence This approach enables us to determine, to some extent, whether a profile shows an occasionally large mean or whether the population mean itself is large. This theory stated that [1] log εr , which is the logarithm of the spatially averaged energy dissipation rate over scale r, obeys a Gaussian distribution, and [2] the its variance obeys macrostructure of σfll2oogwε;r
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