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. PACS: 47.27.Jv High-Reynolds-number turbulence; 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion; 02.50.Sk Multivariate analysisTime 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 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 note 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 been applied to convert the time series into spatial cuts. Upon using the method of Ref.[2], the Reynolds number R λ = u 2 λ/ν, based on the Taylor microscale λ = u 2 / (∂u/∂x) 2 , was determined to be 9000. The angular brackets denote a temporal average throughout the paper. The estimated ratio between integral length L, defined through the integral of the two-point correlation of the component velocity fluctuation in the streamwise direction, and the dissipation scale η = (ν 3 / ε ) 1/4 , is 5 × 10 4 . In units of L the record length of the time series is L record /L = 1000. The inertial range of scales is determined by examining the scaling of the third-order structure function; within the inertial range so determined, the power spectra show a well-defined slope close to −5/3. Because of instrument and cable noise, the spectral density has some amount of noise contamination towards the smallest scales. In order to ensure a proper construction of the derivatives ∂v i /∂x = (v i (x + ∆x) − v i (x))/∆x, the noise part has been removed from the velocity signal by using a Wiener filter.The true e...
Wake-flow data of the Nysted offshore wind farm is analysed with the engineering wake model of Jensen. Two-parameter fits referring to wake-decay parameter and wind direction are made to each individual 10 min-averaged recording of turbine powers. The fitted wind direction neither agrees with the measurements at the meteorological masts nor the turbine orientations, but is in agreement with the power deficit ratios between second-and first-row turbines. The fitted wake-decay parameter varies roughly between k = 0.02 and 0.04, depending on the wind direction with respect to the wind farm geometry. Its average
Geometrical random multiplicative cascade processes are often used to model positivevalued multifractal fields such as the energy dissipation in fully developed turbulence. We propose a dynamical generalization describing the energy dissipation in terms of a continuous and homogeneous stochastic field in one space and one time dimension. In the model, correlations originate in the overlap of the respective spacetime histories of field amplitudes. The theoretical two-and three-point correlation functions are found to be in good agreement with their equal-time counterparts extracted from wind tunnel turbulent shear flow data.
We consider the turbulent energy dissipation from one-dimensional records in experiments using air and gaseous helium at cryogenic temperatures, and obtain the intermittency exponent via the two-point correlation function of the energy dissipation. The air data are obtained in a number of flows in a wind tunnel and the atmospheric boundary layer at a height of about 35 m above the ground. The helium data correspond to the centerline of a jet exhausting into a container. The air data on the intermittency exponent are consistent with each other and with a trend that increases with the Taylor microscale Reynolds number, R(lambda), of up to about 1000 and saturates thereafter. On the other hand, the helium data cluster around a constant value at nearly all R(lambda), this being about half of the asymptotic value for the air data. Some possible explanation is offered for this anomaly.
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