Dimensional analysis and overlap arguments lead to a prediction of a region in the streamwise velocity spectrum of wall-bounded turbulent flows in which the dependence on the streamwise wave number, kappa(1), is given by kappa(1)(-1). Some recent experiments have questioned the existence of this region. In this Letter, experimental spectra are presented which support the existence of the kappa(1)(-1) law in a high-Reynolds-number boundary layer. This Letter presents the experimental results and discusses the theoretical and experimental issues involved in examining the existence of the kappa(1)(-1) law and the reasons why it has proved so elusive.

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.

A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.

In experiments recently performed at Melbourne, Pitot-tube mean velocity profiles in a boundary layer disagreed with those obtained with hot wires. The standard MacMillan (1956) correction for the probe displacement effect and a correction for turbulence intensity were both required for obtaining agreement between the two sets of mean velocity data. We were thus motivated to reanalyse the Princeton superpipe data using the same two corrections. The result is a plausible conclusion that the superpipe is rough at the higher Reynolds numbers and its data follow the Colebrook (1939) formula for commercial pipes rather well. It also appears that the logarithmic law of the wall is valid, with a Kármán constant close to that found recently by Österlund (1999) from boundary layer measurements with a hot wire. The smooth regime in the pipe gave almost the same additive constant for the log-law as Österlund's. A comparison between the superpipe data and the pipe data of Perry, Henbest & Chong (1997) suggests that the conventional velocity defect law may be valid down to lower Reynolds numbers than concluded by Zagarola & Smits (1998).

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