D. A. Shah

Turbulent energy dissipation in a wake

The average turbulent energy dissipation is often estimated by assuming isotropy and measuring the temporal derivative of the longitudinal velocity fluctuation. In this paper, the nine major terms that make up the total dissipation have been measured in the self-preserving region of a cylinder wake for a small turbulence Reynolds number. The results indicate that local isotropy is not satisfied; the isotropic dissipation, computed by assuming isotropic relations, being smaller than the total dissipation by about 45% on the wake centreline and by about 80% near the wake edge. Indirect verification of the dissipation measurements is provided by the budget of the turbulent kinetic energy. This budget leads to a plausible distribution for the pressure diffusion term, obtained by difference.

Scaling of the ‘‘bursting’’ period in turbulent boundary layer and duct flows

Measurements have been made in fully developed turbulent duct and boundary layer flows of the average bursting period over a one decade variation in Reynolds number. The bursting period was determined by two methods: the variable interval time averaging scheme in the form used by Blackwelder and Haritonidis [J. Fluid Mech. 132, 87 (1983)] and the modified u‐level scheme of Luchik and Tiederman [J. Fluid Mech. 174, 529 (1987)] in which ejections from the same burst are grouped. All these authors concluded that the bursting period scaled on inner variables. The present results indicate that this conclusion is valid only over a relatively small Reynolds number range, in which low Reynolds number effects are known to be important. At higher Reynolds numbers, scaling on mixed variables provides the best agreement with the data although scaling on outer variables cannot be ruled out.

Characteristics of vorticity fluctuations in a turbulent wake

Measurements of the lateral components of the vorticity fluctuation have been made in the self-preserving turbulent wake of a circular cylinder. Each component was obtained separately using two X -wires separated in the appropriate lateral directions. The two velocity derivatives which make up the streamwise vorticity component were also determined but not simultaneously. An approximation to the streamwise vorticity was made from these measurements. Moments, probability density functions and spectra of the three vorticity components across the wake are presented and discussed. The high-wavenumber behaviour of the spectra is compared with calculations, based on local isotropy. Satisfactory agreement with the calculations is obtained for the lateral vorticity components over a significant high-wavenumber range. The approximated streamwise vorticity spectrum tends towards the isotropic calculation at very large wavenumbers.

A constant temperature hot-wire anemometer

A constant temperature anemometer is described which is designed to operate hot wires with diameters in the range 0.63-5 mu m. A special feature of the design is the use of separate current sources to supply the different halves of the bridge. This feature eliminates the need for dynamic stability compensation, necessary for commercial constant temperature anemometers. The frequency response of the present circuit compare favourably with that of a commercial circuit. The probability density and spectral density functions of the longitudinal velocity fluctuation, obtained with wires of different diameters, are in good agreement with those obtained with a commercial circuit.

Spectra of velocity derivatives in a turbulent wake

One‐dimensional spectra have been measured in the self‐preserving wake of a circular cylinder for each of the nine major velocity derivatives that feature in the average dissipation of turbulent kinetic energy. The comparison between measured spectra and isotropic calculations indicates that isotropy is approached only at high wavenumbers, especially for spectra of derivatives with respect to lateral directions of lateral velocity fluctuations. This result is discussed in the context of the organized large scale motion.

On the origin of the organised motion in the turbulent far-wake of a cylinder

Spectra and spectral coherences of mainly the lateral velocity fluctuations, measured in the wake of a circular cylinder, strongly suggest that the origin of the far-wake organised motion can be traced back to the cylinder. A possible mechanism for the development of the organised motion is suggested.

Dissipation and vorticity spectra in a turbulent wake

A reasonable spectral analogy is found between the temperature dissipation and either the energy dissipation or the vorticity in the turbulent far wake of a circular cylinder. The high‐wavenumber behavior of the spectra of vorticity, energy dissipation, and temperature dissipation is consistent with isotropy.

Selection of wires and wire spacing for X-wires

X-wires are commonly used to obtain two components of the fluctuating velocity in a turbulent flow. Data obtained from the experiments of others and from our own experiments is used to provide design information that can be used as a guide in the selection of diameter, length and spacing of the wires that are used to make such X-wires. The selection is based on an expectancy that the errors in the measured data will then not exceed 4%. Selections for lower expected errors can also be made. Although the experiments have been carried out in specific flows, the results are reported in terms of the Kolmogorov flow scale and it is expected that they will therefore have general applicability.

The organized motion outside a turbulent wake

Velocity fluctuations are measured in both the intermittent and irrotational regions outside the turbulent/nonturbulent interface of a self‐preserving wake. In the outer part of the intermittent region, there is a tendency for all the predictions of the theory of Phillips [Proc. Cambridge Philos. Soc. 51, 220 (1955)] to be satisfied by the nonturbulent data. At larger distances from the interface, the level of the velocity fluctuations becomes comparable with the background turbulence but the organized motion induced by coherent structures within the wake can still be identified. The contribution of this motion to the normal stresses satisfies irrotationality and homogeneity and the amplitude of this motion decays in a manner consistent with Phillips’ theory.

Scaling of wall shear stress fluctuations in a turbulent duct flow

Instantaneous fluctuations of the wall shear stress have been measured in a fully developed turbulent duct flow over a factor of 10 variation in the Reynolds number. Distributions for the average frequency of detections obtained using the variable-interval time averaging technique suggest that scaling on outer variables or perhaps a mixture of outer and inner variables is more appropriate than scaling on inner variables when the Reynolds number is sufficiently large. The Reynolds number behavior of the average frequencies of zero crossings and local maxima of the shear stress fluctuation rules out the possibility of outer scaling and indicates a weak Reynolds number dependence when scaled on inner variables. These apparently conflicting trends are discussed in the context of published results on the scaling of wall shear stress fluctuations.