Coherent structures: Comments on mechanisms

There is now overwhelming evidence that in most turbulent flows there exist regions moving with the flow where the velocity and vorticity have a characteristic structure. These regions are called coherent structures because within them the large-scale distributions of velocity and/or vorticity remain coherent even as these structures move through the flow and interact with other structures. Since the flow enters and leaves the bounding surfaces of these structures, a useful definition for coherent structures is that they are open volumes with distinctive large-scale vorticity distributions. Possible fruitful directions for the study of the dynamics of coherent structures are suggested. Most coherent structures research to data was concentrated on measurement and kinematical analysis; there is now a welcome move to examine the dynamics of coherent structures, by a variety of different methods. A few of them will be described

The structure of sheared turbulence near a plane boundary

An analysis is presented of how a plane boundary affects the structure of turbulence in a sheared free stream. A uniform-shear boundary layer (USBL) is formulated with slip velocity condition at the surface, and inhomogeneous rapid distortion theory is applied. The effects of blocking by the surface on the turbulence structure in USBL is compared with those in the shear-free boundary layer (SFBL). Shear produces highly anisotropic eddies elongated in the flow direction. The vertical velocity variance is reduced with shear at all heights, roughly in proportion to the reduction in the homogeneous value, but the shape of the profile remains unchanged only near the surface. The streamwise integral scales increase with shear, indicating elongation of the streamwise extent of eddies

Big whorls carry little whorls

The aim of the research was to explore the space-time structure of homogeneous turbulence by computing and then interpreting the two-point spectra and correlations of the velocity and pressure fields. Many of these statistics are of considerable practical importance. In particular, it is of interest to compare the different time and length integral scales and microscales for Eulerian and Lagrangian qualities, and to compare the space and time spectra

Aerothermal tests of a 12.5 percent cone at Mach 6.7 for various Reynolds numbers, angles of attack and nose shapes

The effects of free-stream unit Reynolds number, angle of attack, and nose shape on the aerothermal environment of a 3-ft basediameter, 12.5 deg half-angle cone were investigated in the Langley 8-foot high temperature tunnel at Mach 6.7. The average total temperature was 3300 R, the freestream unit Reynolds number ranged from 400,000 to 1,400,000 per foot, and the angle of attack ranged from 0 deg to 10 deg. Three nose configurations were tested on the cone: a 3-in-radius tip, a 1-in-radius tip on an ogive frustum, and a sharp tip on an ogive frustum. Surface-pressure and cold-wall heating-rate distributions were obtained for laminar, transitional temperature in the shock layer were obtained. The location of the start of transition moved forward both on windward and leeward sides with increasing free-stream Reynolds numbers, increasing angle of attack, and decreasing nose bluntness

Asymptotic Multi-Layer Analysis of Wind Over Unsteady Monochromatic Surface Waves

Asymptotic multi-layer analyses and computation of solutions for turbulent flows over steady and unsteady monochromatic surface wave are reviewed, in the limits of low turbulent stresses and small wave amplitude. The structure of the flow is defined in terms of asymptotically-matched thin-layers, namely the surface layer and a critical layer, whether it is elevated or immersed, corresponding to its location above or within the surface layer. The results particularly demonstrate the physical importance of the singular flow features and physical implications of the elevated critical layer in the limit of the unsteadiness tending to zero. These agree with the variational mathematical solution of Miles (1957) for small but finite growth rate, but they are not consistent physically or mathematically with his analysis in the limit of growth rate tending to zero. As this and other studies conclude, in the limit of zero growth rate the effect of the elevated critical layer is eliminated by finite turbulent diffusivity, so that the perturbed flow and the drag force are determined by the asymmetric or sheltering flow in the surface shear layer and its matched interaction with the upper region. But for groups of waves, in which the individual waves grow and decay, there is a net contribution of the elevated critical layer to the wave growth. Critical layers, whether elevated or immersed, affect this asymmetric sheltering mechanism, but in quite a different way to their effect on growing waves. These asymptotic multi-layer methods lead to physical insight and suggest approximate methods for analyzing higher amplitude and more complex flows, such as flow over wave groups.Comment: 20 page

Viscous coupling of shear-free turbulence across nearly flat fluid interfaces

The interactions between shear-free turbulence in two regions (denoted as + and − on either side of a nearly flat horizontal interface are shown here to be controlled by several mechanisms, which depend on the magnitudes of the ratios of the densities, ρ+/ρ−, and kinematic viscosities of the fluids, μ+/μ−, and the root mean square (r.m.s.) velocities of the turbulence, u0+/u0−, above and below the interface. This study focuses on gas–liquid interfaces so that ρ+/ρ− ≪ 1 and also on where turbulence is generated either above or below the interface so that u0+/u0− is either very large or very small. It is assumed that vertical buoyancy forces across the interface are much larger than internal forces so that the interface is nearly flat, and coupling between turbulence on either side of the interface is determined by viscous stresses. A formal linearized rapid-distortion analysis with viscous effects is developed by extending the previous study by Hunt & Graham (J. Fluid Mech., vol. 84, 1978, pp. 209–235) of shear-free turbulence near rigid plane boundaries. The physical processes accounted for in our model include both the blocking effect of the interface on normal components of the turbulence and the viscous coupling of the horizontal field across thin interfacial viscous boundary layers. The horizontal divergence in the perturbation velocity field in the viscous layer drives weak inviscid irrotational velocity fluctuations outside the viscous boundary layers in a mechanism analogous to Ekman pumping. The analysis shows the following. (i) The blocking effects are similar to those near rigid boundaries on each side of the interface, but through the action of the thin viscous layers above and below the interface, the horizontal and vertical velocity components differ from those near a rigid surface and are correlated or anti-correlated respectively. (ii) Because of the growth of the viscous layers on either side of the interface, the ratio uI/u0, where uI is the r.m.s. of the interfacial velocity fluctuations and u0 the r.m.s. of the homogeneous turbulence far from the interface, does not vary with time. If the turbulence is driven in the lower layer with ρ+/ρ− ≪ 1 and u0+/u0− ≪ 1, then uI/u0− ~ 1 when Re (=u0−L−/ν−) ≫ 1 and R = (ρ−/ρ+)(v−/v+)1/2 ≫ 1. If the turbulence is driven in the upper layer with ρ+/ρ− ≪ 1 and u0+/u0− ≫ 1, then uI/u0+ ~ 1/(1 + R). (iii) Nonlinear effects become significant over periods greater than Lagrangian time scales. When turbulence is generated in the lower layer, and the Reynolds number is high enough, motions in the upper viscous layer are turbulent. The horizontal vorticity tends to decrease, and the vertical vorticity of the eddies dominates their asymptotic structure. When turbulence is generated in the upper layer, and the Reynolds number is less than about 106–107, the fluctuations in the viscous layer do not become turbulent. Nonlinear processes at the interface increase the ratio uI/u0+ for sheared or shear-free turbulence in the gas above its linear value of uI/u0+ ~ 1/(1 + R) to (ρ+/ρ−)1/2 ~ 1/30 for air–water interfaces. This estimate agrees with the direct numerical simulation results from Lombardi, De Angelis & Bannerjee (Phys. Fluids, vol. 8, no. 6, 1996, pp. 1643–1665). Because the linear viscous–inertial coupling mechanism is still significant, the eddy motions on either side of the interface have a similar horizontal structure, although their vertical structure differs

Effects of vertical vibration on hopper flows of granular material

The discharge of granular material from a hopper subject to vertical sinusoidal oscillations was investigated using experiments and discrete element computer simulations. With the hopper exit closed, side-wall convection cells are observed, oriented such that particles move up along the inclined walls of the hopper and down at the center line. The convection cells are a result of the granular bed dilation during free fall and the subsequent interaction with the hopper walls. The mass discharge rate for a vibrating hopper scaled by the discharge rate without vibration reaches a maximum value at a dimensionless velocity amplitude just greater than 1. Further increases in the velocity decrease the discharge rate. The decrease occurs due to a decrease in the bulk density of the discharging material when vibration is applied

Investigation of real-gas and viscous effects on the aerodynamic characteristics of a 40 deg half-cone with suggested correlations for the shuttle orbiter

Parameters were evaluated that might be used to correlate shuttle orbiter aerodynamic data to be used in extrapolating from wind-tunnel to flight conditions. Preliminary calculations indicate that the lee-side forces will have an insignificant influence on the aerodynamic characteristics of the orbiter for moderate angle-of-attack entries; therefore, this work is focused on phenomena which have an overriding influence on windward forces, namely, real-gas (equilibrium and nonequilibrium) and viscous-interaction effects. Analytically determined flow fields previously obtained on 40 deg blunted cones were used as a data source to evaluate various correlation parameters. Inviscid effects were found to be the dominant contributor to the aerodynamic coefficients in the altitude range of 64 to 76.2 km. The most suitable correlation of the aerodynamic forces on these cones is based on local dynamic pressure and local Mach number

Self similarity of two point correlations in wall bounded turbulent flows

The structure of turbulence at a height y from a wall is affected by the local mean shear at y, by the direct effect of the wall on the eddies, and by the action of other eddies close to or far from the wall. Some researchers believe that a single one of these mechanisms is dominant, while others believe that these effects have to be considered together. It is important to understand the relative importance of these effects in order to develop closure models, for example for the dissipation or for the Reynolds stress equation, and to understand the eddy structure of cross correlation functions and other measures. The specific objective was to examine the two point correlation, R sub vv, of the normal velocity component v near the wall in a turbulent channel flow and in a turbulent boundary layer. The preliminary results show that even in the inhomogeneous turbulent boundary layer, the two-point correlation function may have self similar forms. The results also show that the effects of shear and of blocking are equally important in the form of correlation functions for spacing normal to the wall. But for spanwise spacing, it was found that the eddy structure is quire different in these near flows. So any theory for turbulent structure must take both these effects into account