The finite size of a transducer-sensing element limits its space resolution of a pressure field associated with a local turbulent flow. Such pressure fields are translated at a speed comparable to the characteristic velocity of the flow. Consequently, a lack of resolution in space causes an apparent inability to resolve in time. This problem—an example of the mapping of a random function of several variables by a linear operator—is examined here. With the help of a formalism which has been previously discussed and of some recent experimental information about the spatial structure of turbulent pressure fields in boundary layers, the mapping or distortion of statistical quantities associated with the second-order moments of the pressure field is given. The attenuation of the frequency spectral density and of the cross-spectral density is given explicitly in table form and in asymptotic form. The numerical results indicate that the attenuation caused by the finite size of transducers is generally more severe than previous computations had suggested, mainly because the lateral correlation of pressure is highly frequency-dependent, a typical turbulent pressure-wave component being inclined to the stream direction at roughly 45 degrees. The results are applied to an evaluation of contemporary measurements of turbulent pressure fields in shear flows. It is shown that the transducer size used introduces undesirable large errors in these measurements, which lead to doubts even about the magnitude of the intensity of turbulent pressure fluctuations. Asymptotic formulas for the attenuation of large transducers are given which yield estimates of the degree to which a flush-mounted sonar receiver immersed in a boundary layer is able to reject the background noise provided by turbulent pressure fluctuations.

The paper is discussion of measurements of the statistical properties of the pressure field at the wall of turbulent attached shear flows. These measurements have been made only in part by the author. A preliminary discussion is given of the important limitations imposed by the imperfect space resolution of contemporary pressure transducers. There follows a discussion of the appropriate scales of the pressure field. It is shown that measurements of the longitudinal cross-spectral densities lead to similarity variables for the space-time covariance of the pressure and for the corresponding spectra. The existence of these similarity variables may be due to the dispersion of the sources of pressure by the mean velocity gradient. Such a mechanism is illustrated by a simple model. Lateral cross-spectral densities also lead approximately to similarity variables.Computations based directly upon detailed pressure-velocity correlation measurements by Wooldridge & Willmarth reveal that an important part of the pressure at the wall of a boundary layer is contributed by source terms which are quadratic in the turbulent velocity fluctuations; the interaction of the mean strain rate with normal velocity fluctuations, being in effect limited to a region very near the wall, supplies a dominant contribution only at high frequencies and its scales, downstream convective speed and convective memory are markedly smaller than those of the observed wall pressure.The inner part of the Law of the Wall region (y* [les ] 100) seems to be substantially free of pressure sources and within that region (a) the pressure can be given in terms of its boundary value, and (b) the local velocity field is dependent upon but unbale to affect appreciably the turbulent pressures.

The prevalence in a turbulent mixing layer of dynamical events with a coherent history over substantial times suggests that it is profitable to study in detail entirely deterministic versions of this flow and to attempt to use a simplified synthesis of these solutions as the fundamental representation in a stochastic treatment of the layer. It is proposed that the deterministic representation of the flow be achieved by the embedding of a short hierarchy of motions which are studied in detail, though not exhaustively, in Parts 1, 2 and 3. Part 1 deals with the fundamental or first-order motion, which is the evolution of a layer constrained to be purely two-dimensional.

A number of initial- and boundary-value problems for the Boussinesq equations are solved by a finite-difference technique, in an attempt to see how a stably-stratified horizontal shear layer rolls up into horizontally periodic billows of concentrated vorticity, such as are frequently observed in the atmosphere and oceans. This paper describes the methods, results and accuracy of the numerical simulations. The results are further analysed and approximately reproduced by a simple semi-analytic model in Corcos & Sherman (1976).

… in hydrodynamic turbulence … the fate of vortices extending in the direction of motion is of great importance (J. M. Burgers 1948).We examine an elementary model of the dynamics of streamwise vorticity in a plane mixing layer. We assume that the vorticity is unidirectional and subjected to a two-dimensional spatially uniform strain, positive along the direction of vorticity. The equations of motion are solved numerically with initial conditions corresponding to a strain-viscous-diffusion balance for a layer with a sinusoidal variation of vorticity. The numerical results are interpreted physically and compared to those of an asymptotic analysis of the same problem by Neu. It is found that strained vortex sheets are fundamentally unstable unless their local strength nowhere exceeds a constant (somewhat larger than 2) times the square root of the product of strain and viscosity. The instability manifests itself by the spanwise redistribution of the vorticity towards the regions of maximum strength. This is accompanied by the local rotation of the layer and the intensification of the vorticity. The end result of this evolution is a set of discrete round vortices whose structure is well approximated by that of axially symmetric vortices in an axially symmetric strain. The phenomenon can proceed (possibly simultaneously) on two separate lengthscales and with two correspondingly different timescales. The first lengthscale is the initial spanwise extent of vorticity of a given sign. The second, relevant to initially thin and spanwise slowly varying vortex layers, is proportional to the layer thickness. The two types of vorticity focusing or collapse are studied separately. The effect of the first on the diffusion rate of a scalar across the layer is calculated. The second is examined in detail for a spanwise-uniform layer: First we solve the eigenvalue problem for infinitesimal perturbations and then use the eigenfunctions as initial conditions for a numerical finite-differences solution. We find that the initial instability is similar to that of unstrained layers, in that roll-up and pairings also follow. However, at each stage a strain-diffusion balance eventually imposes the same cross-sectional lengthscale and each of these events leads to an intensification of the local value of the vorticity.The parameters upon which collapse and its timescale depend are related to those which are known to govern a mixing layer. The results suggest that the conditions for collapse of strained vortex sheets into concentrated round vortices are easily met in a mixing layer, even at low Reynolds numbers, so that these structures whose size is the Taylor microscale are far more plausibly typical than are vortex sheets on that scale. We found that they raise significantly the diffusion rate of scalar attributes by enhancing the rate of growth of material surfaces across which diffusion takes place. Finally, experimental methods that rely on the visualization of the gradient of scalar concentration are shown to be unable to reveal the presence of streamwise vorticity unless that vorticity has already gathered into concentrated vortex tubes.