Showing papers on "Turbulence published in 1980"

Estimates of the Local Rate of Vertical Diffusion from Dissipation Measurements

Abstract: Scaling of the turbulent energy equation suggests the balance of terms in the ocean is between turbulent production, dissipation and the loss to buoyancy. In this paper two models for the source of oceanic turbulence are considered; namely, production by the Reynolds stress working against a time variable mean shear, and the gravitational collapse of Kelvin-Helmholtz instabilities. Both of these shear instabilities are believed to be important in the ocean. Using values for the critical flux Richardson number and the measurements from studies of Kelvin-Helmholtz instabilities, the efficiency of turbulent mixing is shown to be comparable for the two models. Therefore, a general relationship between the dissipation rate and the buoyancy flux due to the small-scale turbulent velocity fluctuations is derived. The result is expressed as an upper bound on the value of the turbulent eddy coefficient for mass Kρ ⩽ 0.2ϵ/N2. Values of Kρ are calculated from recent oceanic measurements of energy dissipation...

Theory of Homogeneous Turbulence

Abstract: Publisher Summary This chapter presents an overview of the theory of homogeneous turbulence. Homogeneous isotropic turbulence is an idealized concept of turbulence, assumed to be governed by a statistical law that is invariant under arbitrary translation (homogeneity), rotation, or reflection (isotropy) of the coordinate system. This is an idealization of real turbulent motions, which are observed in nature or produced in a laboratory, and generally have much more complicated structures. This idealization was first introduced by Taylor to the theory of turbulence and used to reduce the formidable complexity of the statistical expression of turbulence, and thus make the subject feasible for theoretical treatment. Turbulence combines the difficulty of a strongly nonlinear dynamical system with that of a nonconservative system. The presence of energy dissipation due to viscosity deprives turbulence of the opportunity of being in a thermal equilibrium state. In this chapter, concepts of quasi-normality of large-scale motions are explained. A brief discussion on zero cumulant approximation and modified zero cumulant approximation is presented. Turbulence of other dimensions is also explained.

Two-dimensional turbulence

Abstract: The theory of two-dimensional turbulence is reviewed and unified, and some hydrodynamic and plasma applications are considered. The topics covered include some equations of incompressible hydrodynamics, absolute statistical equilibrium, spectral transport of energy and enstrophy, turbulence on the surface of a rotating sphere, turbulent diffusion, MHD turbulence, and two-dimensional superflow. Finally, an attempt is made to assess the status and future of the principal research topics which have been discussed.

Improved Subgrid-scale Models for Large-Eddy Simulation

Abstract: The paper analyzes models for subgrid-scale turbulence. The analysis indicates that there is sufficient information in the resolved scales to determine some characteristics of the complete flow field. The kinetic energy of the small-scale motions can be decomposed into two parts: one results from the large scales and is correlated with them, and the other part is uncorrelated which leads to a two-component eddy-viscosity model. The 'production equals dissipation' argument does not apply to the small scales in the decay of turbulence because it does not account for the uncorrelated component. The exchange between the large and small scales takes place mainly between the smallest scales of the former and the largest scales of the latter; this argument is the basis of a new model shown to be superior to the Smagorinsky model (1963).

Natural Transition of Boundary Layers—The Effects of Turbulence, Pressure Gradient, and Flow History

Abstract: Natural transition of boundary layers is investigated for a flat plate in a low-speed wind tunnel with free-stream turbulence intensities ranging from 0.3 to 5 per cent, and with pressure-gradient ...

Transition to turbulence in plane Poiseuille and plane Couette flow

Abstract: Direct numerical solutions of the three-dimensional time-dependent Navier-Stokes equations are presented for the evolution of three-dimensional finite-amplitude disturbances of plane Poiseuille and plane Couette flows. Spectral methods using Fourier series and Chebyshev polynomial series are used. It is found that plane Poiseuille flow can sustain neutrally stable two-dimensional finite-amplitude disturbances at Reynolds numbers larger than about 2800. No neutrally stable two-dimensional finite-amplitude disturbances of plane Couette flow were found.Three-dimensional disturbances are shown to have a strongly destabilizing effect. It is shown that finite-amplitude disturbances can drive transition to turbulence in both plane Poiseuille flow and plane Couette flow at Reynolds numbers of order 1000. Details of the resulting flow fields are presented. It is also shown that plane Poiseuille flow cannot sustain turbulence at Reynolds numbers below about 500.

Many routes to turbulent convection

Abstract: Using automated laser-Doppler methods we have identified four distinct sequences of instabilities leading to turbulent convection at low Prandtl number (2·5–5·0), in fluid layers of small horizontal extent. Contour maps of the structure of the time-averaged velocity field, in conjunction with high-resolution power spectral analysis, demonstrate that several mean flows are stable over a wide range in the Rayleigh number R, and that the sequence of time-dependent instabilities depends on the mean flow. A number of routes to non-periodic motion have been identified by varying the geometrical aspect ratio, Prandtl number, and mean flow. Quasi-periodic motion at two frequencies leads to phase locking or entrainment, as identified by a step in a graph of the ratio of the two frequencies. The onset of non-periodicity in this case is associated with the loss of entrainment as R is increased. Another route to turbulence involves successive subharmonic (or period doubling) bifurcations of a periodic flow. A third route contains a well-defined regime with three generally incommensurate frequencies and no broadband noise. The spectral analysis used to demonstrate the presence of three frequencies has a precision of about one part in 104 to 105. Finally, we observe a process of intermittent non-periodicity first identified by Libchaber & Maurer at lower Prandtl number. In this case the fluid alternates between quasi-periodic and non-periodic states over a finite range in R. Several of these processes are also manifested by rather simple mathematical models, but the complicated dependence on geometrical parameters, Prandtl number, and mean flow structure has not been explained.

Vortex pairing in a circular jet under controlled excitation. Part 1. General jet response

Abstract: Hot-wire and flow visualization studies were performed in three air jets subjected to pure-tone excitation The instability, vortex roll-up, and transition to the controlled excitation were investigated The conditions most favorable to vortex parting were determined as a function of the excitation Strouhal number, the Reynolds number, and the initial shear-layer state; it was shown that the rolled-up vortex rings undergo pairing under 'the shear layer mode', and the 'jet-column mode' when the Strouhal numbers based on the initial shear-layer momentum thickness are 0012 and 085, respectively Coherent ring-like vortical structures could be educed to the end of the potential core; however, the paired vortex becomes weaker with increasing downstream distances The transverse transport of 'u' momentum by the coherent structures was much larger during the pairing process than in regions where a single vortex is studied

A wind-tunnel study of turbulent flow close to regularly arrayed rough surfaces

Abstract: Recent observations of flux-gradient anomalies in atmospheric flow close to forests, and similar rough surfaces, prompted a wind-tunnel investigation in which cross-wire anemometry was used to study the vertical development and horizontal variability of adiabatic flow over five regularly arrayed rough surfaces, encompassing a 32-fold range of roughness concentration λ. The roughness elements were cylinders, 6 mm in both height and diameter. Below a layer in which the velocity profile is semi-logarithmic, two surface influences upon the mean velocity field can be distinguished: wake diffusion and horizontal inhomogeneity. The wake diffusion effect causes non-dimensional vertical velocity gradients to be smaller than in the semi-logarithmic region; at least for elements with aspect ratios l/h ≲ 1, it is governed by the transverse dimension l of the roughness elements, and is observed when z > h + 1.5l (where z is height above the underlying surface, and h is the height of the roughness elements). A simple diffusivity model successfully describes the horizontally averaged velocity profiles in the region of wake influence, despite conceptual disadvantages. The horizontal inhomogeneity of the flow is negligible when z > h + D (D being the inter-element spacing), and does not entirely mask the wake diffusion effect except over very sparsely roughened surfaces (λ ≲ 0.02). A criterion for negligibility of both effects, and hence for applicability of conventional turbulent diffusivity theory for momentum, is z > h + 1.5D. These results are compared with atmospheric data, and indicate that wake diffusion may well cause some underestimation of the zero-plane displacement d over typical vegetated surfaces.

On the equations of fully fluidized granular materials

Abstract: Equations for fully fluidized granular materials are proposed and are solved in a simple case. In fully fluidized granular materials, the granular particles slip or collide with each other and energy is dissipated. In describing the energy dissipation process characteristic to granular materials, a measure of random motion of granular particles is introduced as a new internal variable. We derive the constitutive equations by using a simple kinematical model of the collision of particles. The set of equations for fully fluidized granular materials obtained has properties similar to the equations that describe turbulence. For reasonable assumptions, these equations predict the results of Bagnold, namely that the shear and normal stress depend upon the square of the velocity gradient. In case of steady one-dimensional gravity flow the calculated flow profiles resemble experimental ones.

Selective decay hypothesis at high mechanical and magnetic reynolds numbers

Abstract: Implications of certain applications of turbulence theory to two-dimensional turbulence and magnetohydrodynamic flow are discussed. It is shown that the use of the Navier-Stokes equation (NSE) for measurements of turbulent fluctuations has been effective only for three-dimensional flows. For two-dimensional flows, used for the study of large-scale motions in the atmosphere or ocean, enstrophy is cascaded to high wave numbers and dissipated at a finite rate even at infinite Re. MHD flows are numerically calculated for the two-dimensional case and analytically for the three-dimensional case, for which discrepancies in the relative rates of energy and cross helicity decay lead to a recommendation that numerical calculations for the three-dimensional case be carried out to determine the precise decayed states.

Investigation of a Reattaching Turbulent Shear Layer: Flow Over a Backward-Facing Step

Abstract: The paper studies incompressible flow over a backward-facing step in order to investigate the flow characteristics in the separated shear layer, the reattachment zone, and the redeveloping boundary layer after reattachment. It is shown that turbulent intensities and shear stress reach maxima in the reattachment zone, followed by rapid decay near the surface after reattachment. In addition, it is found that downstream of reattachment, the flow returns very slowly to the structure of an ordinary turbulent boundary layer.

The transition to aperiodic behavior in turbulent systems

Abstract: Some systems achieve aperiodic temporal behavior through the production of successive half subharmonics. A recursive method is presented here that allows the explicit computation of this aperiodic behavior from the initial subharmonics. The results have a character universal over specific systems, so that all such transitions are characterized by noise of a universal internal similarity.

On the calculation of turbulent heat transport downstream from an abrupt pipe expansion

Abstract: A numerical study is reported of flow and heat transfer in the separated flow region created by an abrupt pipe expansion Computations employed an adaptation of the TEACH-2E computer program with the standard model of turbulence Emphasis is given to the simulation, from both a physical and numerical viewpoint, of the region in the immediate vicinity of the wall where turbulent transport gives way to molecular conduction and diffusion Wall resistance laws or wall functions used to bridge this near-wall region are based on the idea that, beyond the viscous sublayer, the turbulent length scale is universal, increasing linearly with distance from the wall Predictions of expermental data for a diameter ratio of 054 show generally encouraging agreement with experiment At a diameter of 043 different trends are discernible between measurement and calculation though this appears to be due to effects unconnected with the wall region studied

Baroclinic instability and geostrophic turbulence

Abstract: I examine the geostrophic turbulence field in equilibrium with a horizontally uniform mean zonal flow driven by solar heating. The equilibrium mean vertical shear is highly supercritical, and the turbulence field has its maximum in kinetic energy at wavenumbers smaller than the wavenumbers of fastest growth predicted by linear stability theory. Wavenumber spectra obtained by averaging lengthy numerical integrations of the two-level quasi-geostrophic equations agree well with the predictions of a simple Markovian turbulence model. Analysis of the turbulence model suggests that the most energetic wavenumbers equilibrate from scattering of the temperature perturbations into higher wavenumbers by the barotropic adverting field. In the higher unstable wavenumbers, including the most supercritical, linear instability is offset chiefly by local rotations of the unstable structures by larger, more energetic eddies.

Flat plate streaming potential investigations: Hydrodynamics and electrokinetic equivalency

Abstract: The accurate measurement of streaming potentials in either capillaries or flat plate systems requires Poiseuille flow, i.e., flow must be steady, incompressible, laminar, and established. The established flow stipulation is rarely addressed yet it is of critical importance. Our findings suggest that while the onset of turbulence causes no abrupt change in the streaming potential, flow must be established throughout at least 90% of the flow field for accurate streaming potential measurement. The development of a flat plate flow system based on (1 × 25 × 75) mm plates is discussed in light of the hydrodynamic requirements. The electrokinetic equivalency between plates and capillaries of the same material is discussed and the small discrepancy is attributed to surface roughness and possible differences in surface chemical composition. The flat plate system offers substantial advantages over capillaries in that both surface treatments and analyses via a variety of quantitative techniques are greatly facilitated.

Threshold windspeeds for sand on Mars: Wind tunnel simulations

Abstract: Wind friction threshold speeds for particle movement were determined in a wind tunnel operating at martian surface pressure with a 95 percent CO2 and 5 percent air atmosphere. The relationship between friction speed and free-stream velocity is extended to the critical case for Mars of momentum thickness Reynolds numbers between 425 and 2000. It is determined that the dynamic pressure required to initiate saltation is nearly constant for pressures between 1 bar and 4 mb for atmospheres of both air and CO2.

Open Channel Flow with Suspended Sediments

Abstract: Characteristics of open channel flow with suspended sediments were theoretically investigated introducing a theory based on the Monin-Obukhov length First, a velocity distribution equation based on the theory showed a good agreement with the measured velocity distribution Second, the hydraulic resistance and the distribution of suspended sediment concentration observed in experiments were explained theoretically Third, a transport rate formula for suspended sediments, in which classical equations were included as a particular case, was obtained; and this formula, in cooperation with a reference concentration derived in the present study, showed agreement with experimental results Finally, the critical condition for deposition of suspended particles and the collapse of turbulence were derived and verified by experiments

Convection in a rotating layer: a simple case of turbulence.

Abstract: Convection in a layer heated from below and rotating about a vertical axis exhibits a unique phenomenon in fluid dynamics in that the small-amplitude motion is governed by random effects in both its spatial and its time dependence. A simple theoretical description of the phenomenon is compared with laboratory observations. A more detailed mathematical description appears to be feasible because of the weakly nonlinear nature of the problem.

Vortex pairing in a circular jet under controlled excitation. Part 2. Coherent structure dynamics

Abstract: The coherent structure dynamics in the near field of a circular jet has been experimentally explored by inducing ‘stable’ vortex pairing through controlled excitation (see Zaman & Hussain 1980) and applying phase-averaging techniques. Hot-wire measurements were made in a 7·62 cm air jet with laminar exit boundary layer at the Reynolds number ReD = 3·2 × 104, excited at the Strouhal number StD = 0·85. At a particular phase during the pairing process, spatial distributions of the phase-average longitudinal and lateral velocity perturbations (〈u)〉, 〈v〉), vorticity, streamlines, the coherent and background Reynolds stresses and turbulence intensities have been educed. These data have been obtained for four different locations occupied by the vortices at the same phase (preceding, during, and following the pairing event), in the region 0 < x/D < 5. Spatial distributions of these measures at four successive phases during the pairing process are also educed in an attempt to further understand the vortex-pairing dynamics. The flow physics is discussed on the basis of measurements over the physical extent of the vortical structures, phase-locked to specific phases of the pairing event and thus do not involve use of the Taylor hypothesis.The computed pseudostream functions at particular phases are compared with the corresponding streamlines drawn by the method of isoclines. Transition of the vortices is examined on the basis of vorticity diffusion, the superimposed random fluctuation field intensities and Reynolds stress and phase-locked circumferential correlation measurements. The peak vorticity drops rapidly owing to transition and interaction of the vortices during pairing but, farther downstream, the decay can be attributed to destruction of the coherent vorticity by the background turbulence Reynolds stress, especially at the locations of the latter's ‘saddle points’. Controlled excitation enhances the initial circumferential coherence of the vortical structures, but is ineffective in delaying turbulent breakdown near the end of the potential core; the breakdown appears to occur through evolution of the circumferential lobe structures. The coherent structure Reynolds stress is found to be much larger than the background turbulence Reynolds stress for 0 < x/D [lsim ] 3, but these two are comparable near the end of the jet potential core. The zone average of the coherent structure Reynolds stress over the cross-section of the merging vortex pair is much larger than that over a single vortical structure either before or after the completion of pairing. During the pairing process, such average correlations are found to be the largest at an early phase of the process while entrainment, turbulent breakdown as well as rapid diffusion of vorticity occur at a later phase. The regions of alternate positive and negative coherent Reynolds stresses associated with the structures and their interactions help explain ‘negative production’.

The critical velocity in pipeline flow of slurries

Abstract: In slurry transport, the critical velocity is defined as the minimum velocity demarcating flows in which the solids form a bed at the bottom of the pipe (bed load flows) from fully suspended flow. An analysis based on balancing the energy required to suspend the particles with that derived from dissipation of an appropriate fraction of the turbulent eddies is used to develop a correlation for prediction of the critical velocity. Comparison of the results with available experimental critical velocity data, relating to a rather wide variety of slurry systems, confirms that the present correlation does a superior job of prediction than all previously proposed critical velocity correlations.

Reynolds number dependence of skewness and flatness factors of turbulent velocity derivatives

Abstract: The influence of fluctuations in the rate of local turbulent energy dissipation on higher‐order structure functions for small separation distances r and on moments of turbulent velocity derivatives is examined using the hypotheses of Kolmogoroff and Obukhov for the probability density and variance of the dissipation fluctuations. The predicted variation of the skewness and flatness factors with Rλ represents the available experimental data fairly well over a relatively wide range of Rλ when the constant μ introduced in the variance hypothesis is suitably chosen. The predicted variation of S with K fits the data very well. The present analysis breaks down for moments of sufficiently high order probably due to basic shortcomings of the hypotheses.

Measurements of dissipation rate and some other characteristics of turbulent plane and circular jets

Abstract: The mean rate of dissipation e is measured along the axes of a plane jet and three circular jets, covering good ranges of the jet Reynolds number Ujd/ν and the downstream distance x. The data confirm the universal relations, derived from requirements of self‐preservation, between e and x, for both the circular jet and the plane jet. For either type of jet, the turbulence Reynolds number Rλ and the local Reynolds number Rc (based on local velocity and length scales) are found to be related as Rλ∼2.3Rc1/2.

Temperature fluctuations and scales in grid-generated turbulence

Abstract: To study the mixing of a passive scalar in nearly isotropic turbulence, experiments have been made in isotropically mixed thermal fields with thermal mesh size Mθ (a) equal to the momentum mesh size M, (b) larger than M (obtained by heating only alternate rods of the turbulence generating grid), and (c) smaller than M. This last condition was achieved by inserting a fine heating screen with Mθ M was an increase in the relative intensity of temperature fluctuations compared with the Mθ = M case, and a marginal increase in their decay rate; contrary to expectation, the ratio R of temperature to velocity integral scales in the region of approximate homogeneity did not differ from that corresponding to Mθ = M. In heated screen experiments, the relative decay rate was independent of Mθ/M and ΔT. For the three locations of the heating screen used in these experiments, the decay rate was also independent of the relative distance xs of the heating screen from the turbulence generating grid; however, larger xs was associated with larger relative intensity of fluctuations. To a first approximation, the ratio R approached unity according to the empirical relation R = 1 − A exp [− αxθ/(UT0)], where xθ is downstream distance measured from the heating screen, and T0 is a characteristic turbulence decay time scale at x0 = 0. It was also verified that the skewness of the streamwise temperature derivative is approximately zero sufficiently downstream of the heating screen. Where the present study overlaps with previous measurements, an extensive comparison reveals several points of agreement as well as departure.