Showing papers on "Turbulence published in 1972"

A First Course in Turbulence

Abstract: Keywords: turbulence ; transport ; contraintes ; transport ; couche : limite ; ecoulement ; tourbillon ; energie Reference Record created on 2005-11-18, modified on 2016-08-08

Turbulent Transport of Momentum and Heat

Abstract: This chapter contains sections titled: The Reynolds equations, Elements of the kinetic theory of gases, Estimates of the Reynolds stress, Turbulent heat transfer, Turbulent shear flow near a rigid wall

Spectral Characteristics of Surface-Layer Turbulence

Abstract: The behaviour of spectra and cospectra of turbulence in the surface layer is described within the framework of similarity theory using wind and temperature fluctuation data obtained in the 1968 AFCRL Kansas experiments. With appropriate normalization, the spectra and cospectra are each reduced to a family of curves which spread out according to z/L at low frequencies but converge to a single universal curve in the inertial subrange. The paper compares these results with data obtained by other investigators over both land and water. Spectral constants for velocity and temperature are determined and the variability in the recent estimates of the constants is discussed. The high-frequency behaviour is consistent with local isotropy. In the inertial subrange, where the spectra fall as n−5/3, the cospectra fall faster: uω and ωθ as n−7/3, and uθ, on the average, as n−5/2. The 4/3 ratio between the transverse and longitudinal spectral levels is observed at wavelengths of the order of the height above ground under unstable conditions and at wavelengths of the order of L/10 under stable conditions. This lower isotropic limit is shown to be governed by the combined effects of shear and buoyancy on small-scale eddies.

Mathematical Models of turbulence

Abstract: Keywords: turbulence ; melange ; modeles : mathematiques ; mecanique des : fluides Reference Record created on 2005-11-18, modified on 2016-08-08

Numerical Investigation of Neutral and Unstable Planetary Boundary Layers

Abstract: Results of numerical integrations are presented for a neutrally stratified planetary boundary layer containing a passive scalar, and for three unstable cases with upward heat flux. The air is assumed unsaturated. A total of either 16,000 or 32,000 grid points was used in a three-dimensional region with length and width several times the height of the boundary layer. A key result is the irrelevance of the neutral height scale, u*/f, and its replacement by the height zi of the inversion base which confines the convective mixing when m and only for the two slightly unstable cases were the vertical velocity eddies distinctly elongated as in Ekman-layer theories. At large instabilities it is shown how the friction velocity u/* loses its influence upon the turbulence intensifies and a convective velocity wale becomes important. Vertical profiles of mean wind, potential tempe...

The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments

Abstract: The dynamical equations governing small amplitude wave disturbances in turbulent shear flows are derived. These equations require additional equations or assumptions about the wave-induced fluctuations in the turbulence Reynolds stresses before a closed system can be obtained. Some simple closure models are proposed, and the results of calculations using these models are presented. When the predictions are compared with our data for channel flow, we find it essential that these oscillations in the Reynolds stresses be included in the model. A simple eddy-viscosity representation serves surprisingly well in this respect.

The wall region in turbulent shear flow

Abstract: Hot-film measurements in a fully developed channel flow have been made in an attempt to gain more insight into the process of Reynolds stress production. The background for this effort is the observation of a certain sequence of events (deceleration, ejection and sweep) in the wall region of turbulent flows by Corino (1965) and Corino & Brodkey (1969). The instantaneous product signal uv was classified according to the sign of its components u and v, and these classified portions were then averaged to obtain their contributions to the Reynolds stress . The signal was classified into four categories; the two main ones were that with u negative and v positive, which can be associated with the ejection-type motion of Corino & Brodkey (1969), and that with u positive and v negative, associated with the sweep-type motion. It was found that over the wall region investigated, 3·5 [les ] y [les ] 100, these two types of motion give rise to a stress considerably greater than the total Reynolds stress. Two other types of motion, (i) u negative, v negative, corresponding to low-speed fluid deflected towards the wall, and (ii) u positive, v positive, corresponding to high-speed fluid reflected outwards from the wall, were found to account for the ‘excess’ stress produced by the first two categories, which give contributions of opposite sign.The autocorrelations of the classified portions of uv were obtained to determine the relative time scales of these four types of motion. The positive stress producing motions (u 0 and u > 0, v 0, v > 0). It was further surmised that turbulent energy dissipation is associated with the Reynolds stress producing motions, since these result in localized shear regions in which the dissipation is several orders of magnitude greater than the average dissipation at the wall.

Structure of the reynolds stress near the wall

Abstract: Experimental studies of the flow field near the wall in a turbulent boundary layer using hot-wire probes are reported. Measurements of the product uv are studied using the technique of conditional sampling with a large digital computer to single out special events (bursting) when large contributions to turbulent energy and Reynolds stress occur. The criterion used to determine when the product uv is sampled is that the streamwise velocity at the edge of the sublayer should have attained a certain value. With this simple criterion we find that 60% of the contribution to is made during only 55% of the total time.

Experiments on the flow past spheres at very high Reynolds numbers

Abstract: The present work is concerned with the flow past spheres in the Reynolds number range 5 × 104 [les ] Re [les ] 6 × 106. Results are reported for the case of a smooth surface. The total drag, the local static pressure and the local skin friction distribution were measured at a turbulence level of about 0·45%. The present results are compared with other available data as far as possible. Information is obtained from the local flow parameters on the positions of boundary-layer transition from laminar to turbulent flow and of boundary-layer separation. Finally the dependence of friction forces on Reynolds number is pointed out.

Experiments on a Turbulent Jet in a Cross Flow

Abstract: Experiments on turbulent circular jets issuing into cross flow from both heated and unheated jets

Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow.

Abstract: Experiments on fully developed turbulent flow in a channel which is rotating at a steady rate about a spanwise axis are described. The Coriolis force components in the region of two-dimensional mean flow affect both local and global stability. Three stability-related phenomena were observed or inferred: (1) the reduction (increase) of the rate of wall-layer streak bursting in locally stabilized (destabilized) wall layers; (2) the total suppression of transition to turbulence in a stabilized layer; (3) the development of large-scale roll cells on the destabilized side of the channel by growth of a Taylor-Gortler vortex instability. Local effects of rotational stabilization, such as reduction of the turbulent stress in wall layers, can be related to the local Richardson number in a simple way. This paper not only investigates this effect, but also, by methods of flow visualization, exposes some of the underlying structure changes caused by rotation.-

The reattachment and relaxation of a turbulent shear layer

Abstract: Existing experiments on the low-speed flow downstream of steps and fences, and some new measurements downstream of a backward-facing step, are used to demonstrate the complicated nature of the flow in the reattachment region and its effect on the slow non-monotonic return of the shear layer to the ordinary boundary-layer state. A key feature of the flow is found to be the splitting of the shear layer at reattachment, where part of the flow is deflected upstream into the recirculating flow region to supply the entrainment; the part of the flow that continues downstream suffers a pronounced decrease in eddy length scale, evidently because the larger eddies are torn in two. This phenomenon will occur in all cases where a shear layer reattaches after a prolonged region of separation, either at low speed or in supersonic flow. For simplicity, the discussion in the present paper is confined to low-speed flows.

Measurements of magnetotail plasma flow made with Vela 4B

Abstract: The flow of plasma in the earth's magnetotail has been measured with an electrostatic analyzer on Vela 4B at geocentric distances of ∼18 RE. The analyzer on the rotating (64-sec period) satellite measures proton energy spectra from 79 ev to 19 kev, and the plasma, flow is detected and measured by the substantial spin modulation that it often causes in the measured proton fluxes. The satellite's spin axis is kept directed radially outward along a radius vector from the earth, and so the analyzer, whose aperture is in the satellite's equatorial plane, most effectively senses flows in the direction perpendicular to the radius vector. Some results of the measurements are that (1) plasma flow speeds of several hundred km/sec are frequently measured in the plasma sheet, particularly during substorms, and these sometimes approach 1000 km/sec; however, evident flow in a given direction seldom persists for more than a few minutes; (2) these rapid substorm-related flows are usually directed generally sunward; (3) flow in the anti-sunward (tailward) direction is observed early in some substorms as the plasma sheet thins down; this may suggest the formation of a neutral line at geocentric distances <18 RE;, (4) the magnetotail is separated from the surrounding magnetosheath by a boundary layer a few thousand kilometers thick in which magnetosheath-like flow occurs but at reduced particle density and velocity; and (5) averaging of all flow measurements made in the plasma, sheet over many months does not reveal any distinct pattern of flow either sunward or anti-sunward; an average of the flows observed during periods of a few minutes of clearly evident flow, however, does reveal a flow in the general direction of the sun. It appears that the plasma sheet may often be in turbulent motion with turbulence-cell dimensions no greater than a few RE.

Predictability of Turbulent Flows

Abstract: The test-field model of turbulence is used to compute the growth of prediction error for inertial-range turbulence in both three and two dimensions. It is found that initial uncertainty in high wavenumbers spreads through the entire inertial range according to a similarity behavior. For the energy inertial range, the time required for error to reach wavenumber k from very high wavenumbers is t=Aϵ−1/3k−2/3, where ϵ is the rate of energy transfer per unit mass and A≈10 in three dimensions or A≈2.5 in two dimensions. For the enstrophy inertial range in two dimensions the time for error to propagate from k′ down to k≪k′ (k and k′ both in the inertial range) is t≈4η−1/2{[ln(k′/ k1)]2/3−[ln(k/ k1)]2/3}, where η is the rate of enstrophy transfer and k1 marks the bottom of the enstrophy inertial range. Error growth is also computed for a two-dimensional spectrum that fits the energy spectrum of planetary waves in the atmosphere. An initial state determined with a horizontal resolution feasible with a sat...

Fully developed asymmetric flow in a plane channel

Abstract: The paper presents the results of a detailed experimental examination of fully developed asymmetric flow between parallel planes. The asymmetry was introduced by roughening one of the planes while the other was left smooth; the ratio of the shear stresses at the two surfaces was typically about 4:1.The main emphasis of the research has been on establishing the turbulence structure, particularly in the central region of the channel where the two dissimilar wall flows (generated by the smooth and rough surfaces) interact. Measurements have included profiles of all non-zero double and triple velocity correlations; spectra of the same correlations at several positions in the channel; skewness and flatness factors; and lateral two-point space correlations of the streamwise velocity fluctuation.The region of greatest interaction is characterized by strong diffusional transport of turbulent shear stress and kinetic energy from the rough towards the smooth wall region, giving rise, inter alia, to an appreciable separation between the planes of zero shear stress and maximum mean velocity. The profiles of length scales of the larger-scale motion are, in contrast to the turbulent velocity field, nearly symmetric. Moreover, it appears that at high Reynolds numbers the small-scale motion may in many respects be treated as isotropic.

Experiments on the nonlinear stages of free-shear-layer transition

Abstract: An experimental study is made of the instability and transition of a laminar free shear layer by sound excitation. Primary emphasis is placed on the nonlinear stages of transition. Transition from laminar instability to turbulent breakdown covers approximately five wavelengths of downstream distance. The instability has six distinct regions of behaviour : a region of exponential growth described by linear theory; a nonlinear region where critical-layer effects are important, and harmonics and subharmonics are generated; a region of finite amplitude equilibration of the fundamental mode; a region of finite amplitude triggered sub-harmonic instabilities; a region of three-dimensional longitudinal vortex formation; and a final region of weak secondary instabilities and turbulent breakdown.

Mechanism by Which a Two‐Dimensional Roughness Element Induces Boundary‐Layer Transition

Abstract: An experimental investigation of the effect of two‐dimensional roughness elements on boundary‐layer transition is described. Primary emphasis is given to the nature of disturbances within the recovery zone, i.e., that region in the immediate downstream of the roughness where the mean flow has been distorted by the presence of the roughness. Detailed measurements of mean velocity distributions, of disturbance spectra, and intensity, growth, and decay of disturbances at discrete frequencies were made for a range of unit Reynolds numbers. The measurements demonstrate that the behavior can best be understood by considering wave‐type disturbances, and that the basic mechanism by which a two‐dimensional roughness element induces earlier transition to turbulent flow is by the destabilizing influence of the flow within the recovery zone. Comparison with the behavior expected from stability theory supports this conclusion.

An in vivo study of aortic flow disturbances

Abstract: The general nature of flow-disturbances and turbulence in fluid flows, and the special features which may govern their appearance in unsteady flows, are considered. A hot-film anemometer system, modified for use within arteries, has been used to examine flow disturbances in the aorta. Results suggested that the extent of flow-disturbances may be influenced by both peak flow velocity and pulse-rate, expressed in terms of the relevant fluid dynamic parameters. Possible underlying mechanisms are discussed, and power spectra for laminar and highly disturbed aortic velocity waveforms presented.

Mechanism by which a two-dimensional roughness element induces boundary-layer transition: roughness induced transition

Abstract: An experimental investigation of the effect of two-dimensional roughness elements on boundary layer transition is described. Primary emphasis is given to the nature of disturbances within the recovery zone, i.e., that region in the immediate downstream of the roughness where the mean flow has been distorted by the presence of the roughness. Detailed measurements of mean velocity distributions, of disturbance spectra, and intensity, growth, and decay of disturbances at discrete frequencies were made for a range of unit Reynolds number. The measurements demonstrate that the behavior can best be understood by considering wave-type disturbances, and that the basic mechanism by which a two-dimensional roughness element induces earlier transition to turbulent flow is by the destabilizing influence of the flow within the recovery zone. Comparison with the behavior expected from stability theory supports this conclusion.

An experimental study of the velocity distribution and transition to turbulence in the aorta

Abstract: The development and evaluation of a hot-film probe, suitable for use within arteries and operated with a commercial constant-temperature anemometer and linearizcr, is described. The performance of the system in the recording of arterial velocity wave forms is described, and instantaneous and time-averaged velocity profiles constructed from measurements in the thoracic aorta of dogs are presented. The profiles were blunt, with boundary layers estimated to be less than 2 mm thick throughout the cycle, and significant skews were observed, the explanation for which appears to lie in the influence of local geometry on the flow. A preliminary study of flow disturbances in the aorta based on visual observation of instantaneous velocity wave forms and frequency spectrum analysis is reported. The occurrence of flow disturbances and turbulence is shown to be related to peak Reynolds number and the frequency parameter α. The possible roles of free-stream disturbances and boundary-layer transition in generating these disturbances are discussed.

Time Scales and Correlations in a Turbulent Boundary Layer

Abstract: Space‐time correlations with large streamwise separation were obtained in a turbulent boundary layer with a zero‐pressure gradient. The auto and cross correlations of the velocities u and υ with streamwise spatial separation distances up to 20 boundary layer thicknesses revealed a difference in their structure and decay rate. Using conditional averaging techniques, the velocity product, uυ, was sampled in both the turbulent and nonturbulent zones. Further conditional sampling led to an average picture of the velocities in the interfacial bulges. Near the wall the space‐time correlation results are consistent with the idea of retarded fluid being ejected outward from the wall region and influencing the intermittent region.

Galloping Oscillations of Prismatic Structures

Abstract: Galloping oscillations can arise above a certain onset wind velocity with lateral force coefficient A 1 > 0 (unstable cross sections) and also at A 1 ≤ 0 (stable cross sections). In the latter case, an initial disturbance is also necessary to trigger the vibrations. This triggering disturbance must be larger than the unstable amplitude, proportional to structural damping, and in some cases must be able to decrease with increasing wind velocity. The onset velocities are higher with A 1 ≤ 0 and are directly proportional to structural damping in all cases. Turbulence can drastically change the aeroelastic stability of prismatic bodies. With rectangular cross sections of 2/1 the tendency to galloping instability from zero position decreases with increasing turbulence intensity and can vanish at intensities of 8% or so. On the contrary, prisms of 1/2, stable in the smooth flow, can become unstable in the turbulent flow and their tendency to galloping oscillations increases with turbulence intensity.

The Hemodynamic Importance of the Geometry of Bifurcations in the Circle of Willis (Glass Model Studies)

Abstract: The critical Reynolds number, Rec, at which turbulence developed in glass model bifurcations was measured with an Evans blue indicator for bifurcations with a branch/trunk area ratio of unity, and bifurcation angles of 45°, 90°, 135°, and 180°. The Rec dropped from 2,500 in a straight tube to 1,200 in the 180° bifurcation. Further drops occured with pulsatile flow (if the mean flow rate was used to calculate the velocity). Three sizes of aneurysms at the apex of the 90° bifurcation lowered the Rec at small bifurcations, and less in the 180° ones. The curves for steady and pulsatile flow crossed at 135°. We did qualitative, but not quantitative, assessments of axial stream impingement on the apex of the bifurcation in the site of aneurysm formation, and of boundary layer separation and vortex shedding at the lateral angles. Both appeared to vary with the angle of the bifurcation and the Reynolds number. We also studied flow profiles in glass models of anterior cerebral-anterior communicating artery bifurca...