Effects Of Mean Shear Research Articles

Concerning the effects of mean shear on the fine-scale structure of concentration fluctuations in a plume dispersing in the atmospheric surface layer

The effect of mean shear (large-eddy motion) on the small-scale plume concentration structure is investigated experimentally using high-resolution plume concentration fluctuation measurements made simultaneously at two different heights in a plume dispersing in the very high-Reynolds number turbulent flow of the atmospheric surface layer (where the Taylor microscale based Reynolds number Re λ ≈ 5200). The generalized dimension spectra of a one-dimensional surrogate of the concentration variance dissipation rate are presented as a function of the mean shear. It is shown that the mean shear (due to the large-eddy motions in the flow) have a persistent effect on the small-scale plume concentration structure even at very high Reynolds numbers. In particular, it is demonstrated that increasing mean shear tends to reduce small-scale spatial intermittency in the concentration fluctuations (viz., the higher the mean shear, the more space-filling and less singular the associated local dissipation rate of concentration variance becomes).

Effects of molecular diffusivities on counter-gradient scalar and momentum transfer in strongly stable stratification

The effects of molecular diffusivities of heat and mass on the counter-gradient scalar and momentum transfer in strongly stable stratification are experimentally investigated in unsheared and sheared stratified water mixing-layer flows downstream of turbulence-generating grids. Experiments are carried out in two kinds of stably stratified water flows. In the case of thermal stratification, the difference between the turbulent fluxes of an active scalar (heat with the Prandtl number of Pr ≈ 6) and a passive scalar (mass with the Schmidt number of Sc ≈ 600) is investigated. In the case of salt stratification, the effects of the molecular diffusion of the active scalar (salt) with a very high Schmidt number of Sc ≈ 600 on the counter-gradient scalar transfer is studied. Comparisons of the effects of molecular diffusivities are also made between thermally stratified water and air (Pr ≈ 0.7) flows. Further, the effects of mean shear on the counter-gradient scalar and momentum transfer are investigated for both stratified cases. Instantaneous temperature, concentration and streamwise and vertical velocities are simultaneously measured using a combined technique with a resistance thermometer, a laser-induced fluorescence method, and a laser-Doppler velocimeter with high spatial resolution. Turbulent scalar fluxes, joint probability density functions, and cospectra are estimated.The results of the first case show that both active heat and passive mass develop counter-gradient fluxes but that the counter-gradient flux of passive mass is about 10% larger than that of active heat, mostly due to molecular diffusion effects at small scales. The counter-gradient scalar transfer mechanism in stable stratification can be explained by considering the relative balance between the available potential energy and the turbulent kinetic energy as in Schumann (1987). In thermally and salt-stratified water mixing-layer flows with the active scalars of high Prandtl and Schmidt numbers, the buoyancy-induced motions with finger-like structures first contribute to the counter-gradient scalar fluxes at small scales, and then the large-scale motions, which bring fluid back to its original levels, generate the counter-gradient fluxes at large scales. The contribution of the small-scale motions to the counter-gradient fluxes in stratified water flows is quite different from that in stratified air flows. The higher Prandtl or Schmidt number of the active scalar generates both the stronger buoyancy effects and the longer time-oscillation period of the counter-gradient scalar fluxes. The time-oscillation occurs at large scales but the counter-gradient fluxes at small scales persist without oscillating. The mean shear acts to reduce the counter-gradient scalar and momentum transfer at large scales, and therefore the counter-gradient fluxes in sheared stratified flows can be seen only in very strong stratification. The behaviour of the counter-gradient momentum flux in strong stratification is quite similar to that of the counter-gradient scalar flux.

Effects of Mean Shear on Homogeneous Turbulence. Turbulence Statistics and Turbulence Models.

The effects of mean shear enforced on decaying isotropic turbulence have been investigated by numerical experiments with the direct numerical simulation (DNS) of Navier-Stokes equations. In flows rapidly distorted from isotropy, it is important to elucidate the behavior of turbulent quantities, in particular, the pressure-strain correlations contributing to the origin of the anisotropic state. The pressure-strain term in the Reynolds stress equations becomes positive only in the spanwise velocity fluctuations, and hence turbulence energy is extracted from components in both streamwise and shear directions. The redistribution process as well as the anisotropic behavior of turbulence statistics are accurately evaluated with a linear analysis based on the rapid distortion theory. Furthermore, from the assessment of turbulence models for pressure-strain correlations using the present DNS data, it is found that none of the existing models represent the energy sink from the shear direction except for a model using the Langevin equation, and the destruction of the Reynolds shear stress is described rather well using a classical linear model.

Structural evolution of intermittency and anisotropy at different scales analyzed using three-dimensional wavelet transforms

The three-dimensional Mexican hat wavelet transform is used as a Fourier-spectral space filter to study (1) the process by which the nonlinearities in the equations of motion create intermittent regions of concentrated vorticity and (2) the process by which isotropic turbulence becomes anisotropic by mean shear. In the first study, the three-dimensional wavelet transform is applied to direct numerical simulations of the transition from Gaussian initial conditions to isotropic turbulence. During this transition, the initially noncoherent vorticity field is transformed by the Navier–Stokes nonlinearities into coherent regions of concentrated vorticity. Analysis of the wavelet-transformed enstrophy field suggests (a) that small scales are always more intermittent than large scales, (b) that the level of intermittency at the small scales grows more rapidly than at the large scales, and most importantly (c) that the structural development of turbulence at different scales is correlated both with the evolution of global statistical measures that dominate at those scales (energy and dissipation rate) and with the evolution of the energy and dissipation-rate (or enstrophy) spectra. In the second study, the three-dimensional wavelet transform is applied to simulations of the transition from isotropic to homogeneous but anisotropic shear-dominated turbulence. It is found that the effect of mean shear on large scales is very different from the effect of shear on small scales. Enstrophy structures rotate continuously to the mean flow direction with time at all scales, while the structures are elongated by mean strain rate dominantly in the principal strain-rate direction. Small scales elongate more rapidly than large scales. However, scales both smaller and larger than the enstrophy peak had lower inclination angles relative to the mean flow direction. Furthermore, the anisotropic structure of the enstrophy field at scales smaller than the peak in the enstrophy spectrum is dominantly ‘‘rodlike,’’ whereas large-scale structure is more ‘‘disklike.’’

Post-stenotic core flow behavior in pulsatile flow and its effects on wall shear stress

Arteries of several species, including man, tend to adjust their diameters such that the mean wall shear stress is in the range of 10–20 dynes cm −2. Additionally, intimal thickening in the human carotid bifurcation correlates well with the reciprocal of wall shear stress as determined in model studies. The correlation indicates that wherever the local mean wall shear stress exceeds approximately 10 dynes cm −2, the artery tends to be spared from intimal thickening. However, it is not known whether mean shear stress, i.e. the time-averaged value, or the instantaneous shear stress is the appropriate correlative variable. Each of these variables suggests different mechanisms for the reaction of the artery wall to its hemodynamic environment. It is therefore important to devise means by which the effects of mean shear and pulsatile shear can be separated in the study of atherogenesis. The present investigation examines the post-stenotic flow field in Plexiglas ™ models under pulsatile conditions approximating those in the aortas of the cynomolgus monkey, an animal often employed in atherogenesis research. Behavior of the core flow and its effects on wall shear stress are studied for stenoses of 75 and 90% area reductions using laser velocimetry. The results show that the post-stenotic field contains regions in which the mean wall shear stress is low, but the pulsatile excursions are large. A preliminary comparison of the present results with data available from a separate animal study suggests that intimal thickening in the neighborhood of a coarctation in the aorta of the cynomolgus monkey correlates better with the reciprocal of the maximum of the absolute value of pulsatile wall shear than with the reciprocal of the mean shear. This suggests that atherosclerotic intimal thickening requires that the wall shear stress must be low throughout the pulsatile cycle, not simply low in the mean sense. The present model studies provide a basis for the design of in vivo experiments which can test hypotheses relating wall shear to atherosclerotic intimal thickening.

Particle Dispersion and Mixing of Conservative Properties in an Eddy-Resolving Model

We examine the diffusive behavior of the flow field in an eddy-resolving, primitive equation circulation model. Analysis of fluid particle trajectories illustrates the transport mechanisms, which are leading to uniform tracer and potential vorticity distributions in the interior of the subtropical thermocline. In contrast to the assumption of weak mixing in recent analytical theories, the numerical model indicates the alternative of tracer and potential vorticity homogenization on isopycnal surfaces taking place in a nonideal fluid with strong, along-isopycnal eddy mixing. The eastern, ventilated portion of the gyre appears to be sufficiently homogeneous to allow the concept of an eddy diffusivity to apply. A break in a random walk behavior of particle statistics occurs after about 100 days when along-flow dispersion sharply increases, indicative of mean shear effects. During the first months of particle spreading, eddy dispersal and mean advection are of similar magnitude. Eddy kinetic energy is of O(60–80 cm2 s−2) in the model thermocline, comparable to the pool of weak eddy intensity found in the eastern parts of the subtropical oceans. Eddy diffusivity in the model thermocline (Kxx = 8 × 107, Kyy = 3 × 107 cm2 s−1) seems to be higher by a factor of about 3 than oceanic values estimated for these area. Below the thermocline, model diffusivity decreases substantially and becomes much more anisotropic, with particle dispersal preferentially in the zonal direction. The strong nonisotropic behavior, prominent also in all other areas of water eddy intensity, appears as the major discrepancy when compared with the observed behavior of SOFAR floats and surface drifters in the ocean.

The influence of mean shear on unsteady aperture flow, with application to acoustical diffraction and self-sustained cavity oscillations

This paper discusses the linearized theory of unsteady flow through a two-dimensional aperture in a thin plate in the presence of a grazing mean flow on one side of the plate. The mean shear layer is modelled by a vortex sheet, and it is predicted that at low mean-flow Mach numbers there is a transfer of energy from the mean flow to the disturbed motion of the vortex sheet provided (i) the Kutta condition is imposed at the leading edge of the aperture, resulting in the unsteady shedding of vorticity from the edge, and (ii) the width of the aperture 2s satisfies ½ < 2s/λ < 1.1, where λ is the hydrodynamic wavelength of the disturbance on the vortex sheet within the aperture. The theory is used to examine the effect of mean shear on the diffraction of sound by a perforated screen, and to predict the spontaneous excitation and suppression of self-sustained oscillations in a wall-cavity beneath a nominally steady mean flow. In the latter case support for the proposed theory is provided by a favourable comparison of theoretical results with experimental data available in the literature.

On the stability of fine-scaled turbulent free shear flows

A theoretical model has been developed to investigate the stability of a disturbance in an incompressible turbulent shear flow dominated by turbulence scales that are small with respect to the cross-stream dimension of the flow. The approach utilizes the ‘phase average’ concept to derive the differential equations governing the mechanics of a potential flow disturbance. Turbulence closure is effected at second order. The result is an Orr–Sommerfeld-type equation with complications introduced by the turbulence model. Integration of the linear eigenvalue problem for a wake disturbance leads to the result that the critical eddy-viscosity-based Reynolds number is markedly increased by decreasing the turbulence scale. The viscoelastic behaviour of background turbulence, further complicated by the effects of mean shear, appears to provide stabilization and is discussed in some detail.

Lagrangian Statistics from Numerically Integrated Turbulent Shear Flow

Lagrangian turbulence statistics were obtained from a three-dimensional numerical model of plane Poiseuille flow at large Reynolds number. Single-particle Lagrangian correlations were computed and compared with Eulerian space correlations. Although the curves were not self-similar, a dimensionless scale ratio defined at the e-folding time was comparable to Eulerian-Lagrangian scale ratios found in the literature. The numerically obtained mean-square particle displacements exhibited correct short- and long-time behavior. Mean-square particle separations were analyzed, and two-particle Lagrangian velocity correlations taken at the same time were more persistent than Lagrangian autocorrelations. A semiempirical functional form was constructed for the two-particle velocity correlations which yielded two-particle distance correlations in good agreement with those of the numerical model. The effect of mean shear on downstream separation was examined. Results indicate a t3 or steeper dependence for downstream mean-square separation 〈(xa − xb)2〉, with strong shear and Reynolds stress. Batchelor's similarity law, namely, that 〈(xaj − xbj)2〉 ∝ εt3 in directions not controlled by shear, is postulated for the direction of shear when shear generates ε. This postulate was tested numerically and found to be consistent.

Sound Field Within a Region of Anisotropic Turbulence

The pressure fluctuations within a region of anisotropic turbulence are considered, taking into account the effect of mean shear. Expressions for the pressure correlation function, mean-square pressure, mean-square-pressure-gradient, and certain integral moments of the correlation function are given for the general anisotropic case in the form of single space integrals over velocity correlation functions. As an example, a model of turbulence with oriented vorticity interacting with a uniform mean shear is treated. The relation of the associated pressure correlation-function-moments to the acoustic driving force to be anticipated on a plate bounding a turbulent flow is discussed. This work was supported by the Wright Air Development Center under Contract AF 33(616)-2331.