The geometry of solution trajectories for three first-order coupled linear differential equations can be related and classified using three matrix invariants. This provides a generalized approach to the classification of elementary three-dimensional flow patterns defined by instantaneous streamlines for flow at and away from no-slip boundaries for both compressible and incompressible flow. Although the attention of this paper is on the velocity field and its associated deformation tensor, the results are valid for any smooth three-dimensional vector field. For example, there may be situations where it is appropriate to work in terms of the vorticity field or pressure gradient field. In any case, it is expected that the results presented here will be of use in the interpretation of complex flow field data.

In this paper the dimensional-analysis approach to wall turbulence of Perry & Abell (1977) has been extended in a number of directions. Further recent developments of the attached-eddy hypothesis of Townsend (1976) and the model of Perry & Chong (1982) are given, for example, the incorporation of a Kolmogoroff (1941) spectral region. These previous analyses were applicable only to the 'wall region' and are extended here to include the whole turbulent region of the flow. The dimensionalanalysis approach and the detailed physical modelling are consistent with each other and with new experimental data presented here.

I n this paper an attempt is made to formulate a model for the mechanism of wall turbulence that links recent flow-visualization observations with the various quantitative measurements and scaling laws established from anemometry studies. Various mechanisms are proposed, all of which use the concept of the horse-shoe, hairpin or 'A' vortex. It is shown that these models give a connection between the mean-velocity distribution, the broad-band turbulence-intensity distributions and the turbulence spectra. Temperature distribut'ions above a heated surface are also considered. Although this aspect of the work is not yet complete, the analysis for this shows promise. A . E . Perry and M . S. Chong) Laws 1 and 3 work on a rough wall Conditions z+ 2 100, z/AE < 0.1 z+ 3 100, f7 = O(1) z/AE < 0.1, z+ > 100, z/AE < 0.1 z+ > 100, z/AE < 0.1 z+ 2 100, Prediction, vol. 2. bulent boundary layer. Phys. Fluids 16, 725-737. Fluid MecA. 50, 233. Naval Arch. M a r . Engrs 62, 333-351. J . Fluid Mech. 107, 297-337. 257-271. and rough-wall pipes. J . Fluid Mech. 79, 785-799. pressure gradient turbulent boundary layers. J . Fluid Mech. 25, 299-320. 299-315. structures in coflowing jets and wakes. J . Fluid Mech. 101, 243-256. 104, 285-403.Mech. 104, 45-53. 534-542.A 209, 418-430.

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 (Reτ = 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 kx−1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the kx−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.

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