Alexander Praskovsky

Measurements of the Kolmogorov constant and intermittency exponent at very high Reynolds numbers

Characteristics of turbulence in the inertial range are experimentally studied in the atmospheric surface layer over the range of the Taylor microscale based Reynolds number Rλ≊(2.8–12.7)×103 and in a large wind tunnel (in a mixing layer at Rλ≊2.0×103 and a return channel at Rλ≊3.2×103). The intermittency exponent μ, estimated from the correlation function of energy dissipation Ree(r)=〈e(x)e(x+r)〉∝r−μ, is found to be independent of Reynolds number and approximately equal to 0.20. No ‘‘measurable’’ deviation from the −5/3 exponent in the ‘‘five‐thirds’’ law is found. On the other hand, the Kolmogorov constant C in this law is found to be weakly dependent on Rλ. This dependence is well described by the power law C∝R−μ/2λ≊R−0.10λ at μ≊0.20.

Comprehensive measurements of the intermittency exponent in high Reynolds number turbulent flows

The intermittency exponent μ is determined from comprehensive measurements in the mixing layer (Rλ ≈ 2.0 × 103) and in the return channel (Rλ ≈ 3.2 × 103) of a large wind tunnel as well as in an atmospheric surface layer at Rλ ≈ (3.3–12.7) × 103. To estimate the value of μ and its dependence on Rλ and the flow conditions, different methods of data processing are applied to the same data base, i.e., μ is defined by its scaling behaviour in the inertial range of centered and non-centered correlation functions and spectra of energy dissipation, second order moments of r and lnr, etc. (Here Rλ is the Taylor microscale based Reynolds number, and r is the energy dissipation averaged over a segment of length r.) It is found that these methods do not define a unique value of μ but a set of different scaling exponents, and these exponents stay systematically different over the range of flow conditions which was studied. No tendency for these exponents to collapse is observed up to Rλ = 12.7 × 103.

Fractal Geometry of Isoconcentration Surfaces in a Smoke Plume

Abstract The fractal properties of isoconcentration surfaces in a smoke plume are studied in an atmospheric boundary layer wind tunnel. Instantaneous high-resolution two-dimensional images of the fine particle concentration at Schmidt number Sc → ∞ were obtained in three plume cross sections with a video imaging technique. The fractal dimension D of isoconcentration contours is estimated with box-counting and area-perimeter methods; the range of thresholds is 0.5 ≤ c*/c ≤ 1.5, where c is the mean particle concentration for a particular image and c* is the threshold. Using the box-counting method, the local values of D = −d(log Nϵ)/d(log ϵ) are found to be constant over variations in ϵ that are more than a decade, where Nϵ, is the number of boxes with size ϵ required to cover an isoconcentration curve. Using the area-perimeter method, the fractal dimension is estimated with the relation P ∼ AD/2, where P and A denote the perimeter and area of the individual closed isoconcentration curves. The noise influ...

On the Lighthill relationship and sound generation from isotropic turbulence

In 1952 Lighthill (1952) developed a theory for determining the sound generated by a turbulent motion of a fluid. With some statistical assumptions, Proudman (1952) applied this theory to estimate the acoustic power of isotropic turbulence. Recently, Lighthill established a simple relationship that relates the fourth-order retarded-time and space covariance of his stress tensor to the corresponding second-order covariance and the turbulent flatness factor, without making statistical assumptions for a homogeneous turbulence. Lilley (1994) revisited Proudmans work and applied the Lighthill relationship to evaluate the radiated acoustic power directly from isotropic turbulence. After choosing the time separation dependence in the two-point velocity time and space covariance based on the insights gained from direct numerical simulations, Lilley concluded that the Proudman constant is determined by the turbulent flatness factor and the second-order spatial velocity covariance. In order to estimate the Proudman constant at high Reynolds numbers, we analyzed a unique data set of measurements in a large wind tunnel and atmospheric surface layer that covers a range of the Taylor microscale-based Reynolds number 2.0×103≤Rλ≤12.7×103. Our measurements demonstrate that the Lighthill relationship is a good approximation, providing additional support to Lilleys approach. The flatness factor is found between 2.7 and 3.3 and the second-order spatial velocity covariance is obtained. Based on these experimental data, the Proudman constant is estimated to be 0.68–3.68.

Further experimental support for the Kolmogorov refined similarity hypothesis

The validity of the Kolmogorov refined similarity hypothesis (RSH) is tested experimentally in the mixing layer and in the return channel of a large wind tunnel, at Rλ≈2.0×103 and 3.2×103, respectively. The energy dissipation rate is estimated from the longitudinal gradient of both the longitudinal ∂u/∂x and transverse ∂w/∂x velocity components, and the results are in good agreement with RSH in both cases.

Spatial-Temporal Differential Analysis for Profiling the Atmosphere, 2, Experimental Results

We consider an application of the spatial-temporal differential analysis (STDA) to measuring characteristics of the atmosphere with spaced antenna wind profilers. STDA is a new method for processing multiple signals which utilizes spatial and temporal scintillations in the instantaneous signal power on the radar antenna. To test the practical potential of STDA, we used actual signals from the multiple antennas profiling radar (MAPR). The goal was to measure mean horizontal winds and characteristics of atmospheric turbulence in the presence of intensive ground clutter. The STDA results in the atmospheric boundary layer at a height of 300 m above the ground are compared with simultaneous measurements by a sonic anemometer located atop a 300-m tower 600 m distant from MAPR. Second-order structure functions for multiple radar signals were used for the processing. We demonstrate that this simplified STDA technique provides a good performance by reliably measuring mean winds in cluttered environment It also enables comprehensive measurements of atmospheric turbulence which no other known methodology is able to provide