The mean wall-normal gradients of the Reynolds shear stress and the turbulent kinetic energy have direct connections to the transport mechanisms of turbulent-boundary-layer flow. According to the Stokes–Helmholtz decomposition, these gradients can be expressed in terms of velocity–vorticity products. Physical experiments were conducted to explore the statistical properties of some of the relevant velocity–vorticity products. The high-Reynolds-number data (Rθ≃O(106), where θ is the momentum thickness) were acquired in the near neutrally stable atmospheric-surface-layer flow over a salt playa under both smooth- and rough-wall conditions. The low-Rθdata were from a database acquired in a large-scale laboratory facility at 1000 >Rθ> 5000. Corresponding to a companion study of the Reynolds stresses (Priyadarshana & Klewicki,Phys. Fluids, vol. 16, 2004, p. 4586), comparisons of low- and high-Rθas well as smooth- and rough-wall boundary-layer results were made at the approximate wall-normal locationsyp/2 and 2yp, whereypis the wall-normal location of the peak of the Reynolds shear stress, at each Reynolds number. In this paper, the properties of thevωz,wωyanduωzproducts are analysed through their statistics and cospectra over a three-decade variation in Reynolds number. Hereu,vandware the fluctuating streamwise, wall-normal and spanwise velocity components and ωyand ωzare the fluctuating wall-normal and spanwise vorticity components. It is observed thatv–ωzstatistics and spectral behaviours exhibit considerable sensitivity to Reynolds number as well as to wall roughness. More broadly, the correlations between thevand ω fields are seen to arise from a ‘scale selection’ near the peak in the associated vorticity spectra and, in some cases, near the peak in the associated velocity spectra as well.
Applications that require the measurement of the spatially averaged velocity over a given area segment can be addressed by the thermal transient anemometer (TTA). The operating principle can be characterized as follows: (i) elevate the temperature of the multi-X patterned sensor—that appropriately samples the area of interest—to an initial overheat condition, (ii) allow the sensor to cool by the heat transfer of the passing fluid (plus end conduction effects), (iii) execute a calibration such that the exponential decay of the sensor resistance can be characterized by the time constant, τ, and (iv) infer the spatially averaged velocity ⟨U⟩—or the spatially averaged density–velocity product ⟨ρU⟩—from the relationship Note that A″, B″, n are defined by the calibration data. A description of the enabling electronics, demonstration measurements in a calibration air stream and the post-processing strategy to account for ambient temperature changes between calibration and test data are presented in order to characterize this instrument.
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