On the effects of surrogacy of energy dissipation in determining the intermittency exponent in fully developed turbulence

– The two-point correlation function of the energy dissipation, obtained from a one-point time record of an atmospheric boundary layer, reveals a rigorous power law scaling with intermittency exponent μ ≈ 0.20 over almost the entire inertial range of scales. However, for the related integral moment, the power law scaling is restricted to the upper part of the inertial range only. This observation is explained in terms of the operational surrogacy of the construction of energy dissipation, which influences the behaviour of the correlation function for small separation distances. Time records of turbulent velocity at a single point in space, obtained using a hot-wire or a laser Doppler anemometer, are usually interpreted, via Taylor’s frozen-flow hypothesis, as one-dimensional spatial cuts through the flow. Velocity structure functions can then be obtained readily from such observables. In addition to the velocity, other quantities of interest include enstrophy and energy dissipation. These quantities cannot be constructed in full from the measured one-point velocity time series (of one or two components of velocity) and so are replaced for further analysis by the so-called surrogate fields. These surrogate fields usually take the form of a single component of a many-component field. In this letter we concentrate on the surrogacy issue of energy dissipation and discuss its impact on the extraction of the intermittency exponent. To illustrate the issue, we choose turbulence measurements in an atmospheric boundary layer, made under nominally steady and nearly neutral conditions, in which a hot-wire probe mounted on top of a tower recorded time-series of both streamwise and vertical velocity components; for details of the experimental setup, see ref. [1]. The frozen-flow hypothesis has