T. B. Nickels

Hot-wire spatial resolution issues in wall-bounded turbulence

Careful reassessment of new and pre-existing data shows that recorded scatter in the hot-wire-measured near-wall peak in viscous-scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of the Reynolds number and viscous-scaled wire length l + . An empirical expression is given to account for these effects. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of the Reynolds number. We also investigate the appearance of the so-called outer peak in the broadband streamwise intensity, found by some researchers to occur within the log region of high-Reynolds-number boundary layers. We show that the ‘outer peak’ is consistent with the attenuation of small scales due to large l + . For turbulent boundary layers, in the absence of spatial resolution problems, there is no outer peak up to the Reynolds numbers investigated here ( Re τ = 18830). Beyond these Reynolds numbers – and for internal geometries – the existence of such peaks remains open to debate. Fully mapped energy spectra, obtained with a range of l + , are used to demonstrate this phenomenon. We also establish the basis for a ‘maximum flow frequency’, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated. It is shown that where this criterion is not met (in this instance due to insufficient anemometer/probe response), an outer peak can be reproduced in the streamwise intensity even in the absence of spatial resolution problems. It is also shown that attenuation due to wire length can erode the region of the streamwise energy spectra in which we would normally expect to see k x −1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the k x −1 region of self-similarity. Not surprisingly, the attenuated spectra also indicate that Kolmogorov-scaled spectra are subject to substantial errors due to wire spatial resolution issues. These errors persist to wavelengths far beyond those which we might otherwise assume from simple isotropic assumptions of small-scale motions. The effects of hot-wire length-to-diameter ratio ( l / d ) are also briefly investigated. For the moderate wire Reynolds numbers investigated here, reducing l / d from 200 to 100 has a detrimental effect on measured turbulent fluctuations at a wide range of energetic scales, affecting both the broadband intensity and the energy spectra.

On the limitations of Taylor's hypothesis in constructing long structures in a turbulent boundary layer

Taylors hypothesis of frozen flow has frequently been used to convert temporal experimental measurements into a spatial domain. This technique has led to the discovery of long meandering structures in the log-region of a turbulent boundary layer. There is some contention over whether Taylors approximation is valid over large distances. This paper presents an experiment that compares velocity fields constructed using Taylors approximation with those obtained from particle image velocimetry (PIV), i.e. spatial data, obtained in the logarithmic region of a turbulent boundary layer.

Some predictions of the attached eddy model for a high Reynolds number boundary layer.

Many flows of practical interest occur at high Reynolds number, at which the flow in most of the boundary layer is turbulent, showing apparently random fluctuations in velocity across a wide range of scales. The range of scales over which these fluctuations occur increases with the Reynolds number and hence high Reynolds number flows are difficult to compute or predict. In this paper, we discuss the structure of these flows and describe a physical model, based on the attached eddy hypothesis, which makes predictions for the statistical properties of these flows and their variation with Reynolds number. The predictions are shown to compare well with the results from recent experiments in a new purpose-built high Reynolds number facility. The model is also shown to provide a clear physical explanation for the trends in the data. The limits of applicability of the model are also discussed.

Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 1. Vortex packets

Experimental measurements of the three-dimensional (3D) velocity field in a moderate Reynolds number zero pressure-gradient boundary layer are presented. The measurements are analysed to produce 3D correlations and conditional averaging techniques are used to further elucidate the underlying structure. The results show clear evidence of vortex-packet-type structures and shed new light on the detailed 3D structure of such packets in a real zero pressure-gradient boundary layer.

Inner scaling for wall-bounded flows subject to large pressure gradients

In this paper the scaling of the mean velocity profile and Reynolds stresses is considered for the case of turbulent near-wall flows subjected to strong pressure gradients. Strong pressure gradients are defined as those in which the streamwise pressure gradient non-dimensionalized with inner variables,

Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 2. Long structures

p_x^+

The logarithmic structure function law in wall-layer turbulence

, is greater than 0.005. A range of values of this parameter (

Functional morphology of the nasal region of a hammerhead shark

{-}0.02\,{ ) is examined in this paper. An appropriate functional form for the mean velocity profile is developed and used to parameterize available data. A physical model for the parametric variation with pressure gradient is then developed. This model is based on the concept of a universal critical Reynolds number for the sublayer which explains (both qualitatively and quantitatively) the variation of the important parameters in the inner flow. In particular this gives an explanation for the shift in the apparent log-law due to pressure-gradient effects and provides an appropriate scaling for the Reynolds stresses. It is shown that this model is not only physically plausible but is also consistent with the available data.

On the different contributions of coherent structures to the spectra of a turbulent round jet and a turbulent boundary layer

Three-dimensional (3D) measurements of a turbulent boundary layer have been made using high-speed particle image velocimetry (PIV) coupled with Taylors hypothesis, with the objective of characterising the very long streamwise structures that have been observed previously. The measurements show the 3D character of both low- and high-speed structures over very long volumes. The statistics of these structures are considered, as is their relationship to the important turbulence quantities. In particular, the length of the structures and their wall-normal extent have been considered and their relationship to the other components of the velocity fluctuations and the instantaneous stress.

On the asymptotic similarity of the zero-pressure-gradient turbulent boundary layer

The k - 1 spectral law for near-wall turbulence has received only limited experimental support, the most convincing evidence being that of Nickels et al. (Phys. Rev. Lett. vol. 95, 2005, 074501.1). The real-space analogueof this law is a logarithmic dependence on r of the streamwise longitudinal structure function. We show that, unlike the k - 1 law, the logarithmic law is readily seen in the experimental data. We argue that this difference arises from the finite value of Reynolds number in the experiments. Reducing the Reynolds number is equivalent to restricting the range of eddy sizes which contribute to the k - 1 , or lnr, laws. While the logarithmic law is relatively insensitive to a truncation in the range of eddy sizes (it continues to hold over the relevant range of eddy sizes), it turns out that the k - 1 law is not. This is a direct consequence of the so-called aliasing problem associated with one-dimensional spectra, whereby energy is systematically and artificially displaced to small wavenumbers.