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Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.

There has been a considerable difference in opinion as to what is the proper exponent m. The two relations most often considered are m = -2/3 and m = -3/4. These are usually justified by recognizing that the concentration boundary layer is so thin for large Sc that the velocity field within 6, can be represented as a Taylor series expansion in terms of the dimensionless distance from the wall yf. By using an analogy between momentum transfer and mass transfer, it is argued that the eddy diffusivity is given as E / V 'y f n , where n is an integer greater than or equal to 3. (See pages 343-7 of the book by Monin and Yaglom, 1965.) In order to establish the correct exponent m, it is necessary to obtain very precise measurements over a wide range of Schmidt numbers, since the difference between the Sc-2'8 and the Sc-314 relations is not great. A considerable number of experimental studies have been directed toward this goal. However, there is enough disagreement among the results of different investigators that the problem has not been conclusively resolved.During the course of a study on the influence of Schmidt number on the frequency of mass transfer fluctuations, we obtained the very extensive set of measurements of f(Sc) presented here. Because of the care given to the execution of these experiments, we feel that a greater precision was attained than in previous investigations.

over a wavy wall 257 Abstract Measurements of the spatial and time variation of two components of the velocity have been made over a sinusoidal solid wavy boundary with a height to length ratio of 2a/2 = 0.10 and with a dimensionless wave number of ~ + = (27t/2) (v/u*)= 0.02. For these conditions, both intermittent and time-mean flow reversals are observed near the troughs of the waves. Statistical quantities that are determined are the mean streamwise and normal velocities, the root-meansquare of the fluctuations of the streamwise and normal velocities, and the Reynolds shear stresses. Turbulence production is calculated from these measurements.The flow is characterized by an outer flow and by an inner flow extending to a distance of about c~-1 from the mean level of the surface. Turbulence production in the inner region is fundamentally different from flow over a flat surface in that it is mainly associated with a shear layer that separates from the back of the wave. Flow close to the surface is best described by an interaction between the shear layer and the wall, which produces a retarded zone and a boundary-layer with large wall shear stresses.Measurements of the outer flow compare favorably with measurements over a flat wall if velocities are made dimensionless by a friction velocity defined with a shear stress obtained by extrapolating measurements of the Reynolds stress to the mean levels of the surface (rather than from the drag on the wall).

A principal theoretical problem in understanding wall turbulence is the determination of how turbulence is created and sustained, i.e., the explanation of how energy is transferred from the mean flow to the turbulence. Flow-oriented vortical eddies have been associated with large Reynolds stresses and with the production of turbulence in the viscous region close to the wall. Their creation and evolution are investigated in a high-resolution direct numerical simulation of turbulent flow in a channel. An important finding is that they regenerate themselves by a process that appears to be weakly dependent on the outer flow. This involves the enhancement of streamwise vorticity at the wall, of opposite sign, at a location where a stress-producing eddy lifts from the wall.