Showing papers on "Turbulence published in 1996"

A Lagrangian dynamic subgrid-scale model of turbulence

Abstract: The dynamic model for large-eddy simulation of turbulence samples information from the resolved velocity field in order to optimize subgrid-scale model coefficients. When the method is used in conjunction with the Smagorinsky eddy-viscosity model, and the sampling process is formulated in a spatially local fashion, the resulting coefficient field is highly variable and contains a significant fraction of negative values. Negative eddy viscosity leads to computational instability and as a result the model is always augmented with a stabilization mechanism. In most applications the model is stabilized by averaging the relevant equations over directions of statistical homogeneity. While this approach is effective, and is consistent with the statistical basis underlying the eddy-viscosity model, it is not applicable to complex-geometry inhomogeneous flows. Existing local formulations, intended for inhomogeneous flows, are most commonly stabilized by artificially constraining the coefficient to be positive. In this paper we introduce a new dynamic model formulation, that combines advantages of the statistical and local approaches. We propose to accumulate the required averages over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to in-homogeneous flows in complex geometries. We analyse direct numerical simulation data to document the effects of such averaging on the Smagorinsky coefficient. The characteristic Lagrangian time scale over which the averaging is performed is chosen based on measurements of the relevant Lagrangian autocorrelation functions, and on the requirement that the model be purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are slightly superior to those of the spatially (planar) averaged dynamic model. The relationship between the model and vortical structures in isotropic turbulence, as well as ejection events in channel flow, is investigated. Computational overhead is kept small (about 10% above the CPU requirements of the spatially averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.

New Trends in Large-Eddy Simulations of Turbulence

Abstract: The paper presents large-eddy simulation (LES) formalism, along with the various subgrid-scale models developed since Smagorinsky’s model. We show how Kraichnan’s spectral eddy viscosity may be implemented in physical space, yielding the structure-function model. Recent developments of this model that allow the eddy viscosity to be inhibited in transitional regions are discussed. We present a dynamic procedure, where a double filtering allows one to dynamically determine the subgrid-scale model constants. The importance of backscatter effects is discussed. Alternatives to the eddy-viscosity assumption, such as scale- similarity models, are considered. Pseudo-direct simulations in which numerical diffusion replaces subgrid transfers are mentioned. Various applications of LES to incompressible and compressible turbulent flows are given, with an emphasis on the generation of coherent vortices

Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy

Abstract: This paper argues that the active turbulence and coherent motions near the top of a vegetation canopy are patterned on a plane mixing layer, because of instabilities associated with the characteristic strong inflection in the mean velocity profile. Mixing-layer turbulence, formed around the inflectional mean velocity profile which develops between two coflowing streams of different velocities, differs in several ways from turbulence in a surface layer. Through these differences, the mixing-layer analogy provides an explanation for many of the observed distinctive features of canopy turbulence. These include: (a) ratios between components of the Reynolds stress tensor; (b) the ratio K H /K M of the eddy diffusivities for heat and momentum; (c) the relative roles of ejections and sweeps; (d) the behaviour of the turbulent energy balance, particularly the major role of turbulent transport; and (e) the behaviour of the turbulent length scales of the active coherent motions (the dominant eddies responsible for vertical transfer near the top of the canopy). It is predicted that these length scales are controlled by the shear length scale L s = U(h)/U′(h) (where h is canopy height, U(z) is mean velocity as a function of height z, and U′ = dU/dz). In particular, the streamwise spacing of the dominant canopy eddies Λ x = mL s , with m = 8.1. These predictions are tested against many sets of field and wind-tunnel data. We propose a picture of canopy turbulence in which eddies associated with inflectional instabilities are modulated by larger-scale, inactive turbulence, which is quasi-horizontal on the scale of the canopy.

Hot-Wire Anemometry: Principles and Signal Analysis

Abstract: Hot-wire anemometry (HWA) is one of the basic measuring techniques used by research scientists and engineers working in fluid mechanics. It is applicable to a wide variety of flows from studies of atmospheric phenomena to investigations of supersonic flows. HWA is an indirect measuring technique based on the heat transfer from a sensing element and for this reason is very sensitive to ambient variations in the temperature. The use of HWA is therefore not usually recommended for the measurement of mean flow properties. However, owing to the fast response and good spatial resolution of the technique, it is irreplaceable for investigations of rapidly varying flows and especially turbulence. Different modes of operation of the hot-wires permit measurements of velocity, temperature and concentration at a modest price and effort which makes the technique attractive and profitable in many situations. In spite of tremendous developments of other measuring techniques over the past two decades, particularly optical techniques such as laser-Doppler anemometry (LDA) or particle image velocimetry (PIV), HWA retains a number of distinct advantages which ensure its present and future use. Hans Bruun has written a comprehensive book which provides a state-of-the-art survey on developments and use of HWA. In many details the book complements the classical monographs of Corrsin (1963), Melnik and Weske (1967) and the more recent contributions to the subject from Perry (1982) and Lomas (1986). The author approaches the subject in an easy to read, straightforward manner, starting with the basic principles of HWA. He avoids putting much effort into describing the electronic arrangements or compensation networks, concentrating on the heat transfer considerations and the time/space resolution capabilities of HWA for turbulence measurements. The author proceeds with a general introduction to the velocity measurements. The material is informative and introduces topics such as the response equations used for HWA signal interpretation and methods for data acquisition, processing and presentation. Separate chapters are devoted to one-, two- and three-component velocity measurements. The author continues at considerable length with all necessary information about HWA for conducting measurements, including probe design and manufacture, aerodynamic effects of prongs and probe support, calibration techniques and signal interpretation. The emphasis is placed on methods which have been successfully used in turbulence research in the past. Temperature effects and measurements of the temperature fluctuations are presented in chapter 7. A good account is given of the methods for correcting hot-wire readings for drift in the ambient fluid temperature. The text also covers the resistance-wire method for measurements of the instantaneous temperature fluctuations. The author dedicates a separate chapter to hot-wire techniques used for investigating reverse flows and near-wall flows. The pulsed and flying hot-wire techniques as well as the split film probes are discussed in detail. A brief account is also given of other interesting attempts to extend the applicability of HWA to flows of high turbulence intensity. This chapter ends with an extensive analysis of near-wall hot-wire measurements and the determination of the wall shear stress. The author summarizes in a separate chapter successful extensions of the HWA technique beyond conventional applications. The material covered includes the determination of the void-fraction and turbulence properties in two-phase flows, evaluation of concentration fluctuations in gas mixtures and turbulence measurements in compressible flows. Vorticity measurements are discussed in chapter 10. These are of special importance to turbulence modelling since the vorticity is directly related to the turbulent dissipation rate. Modelling of the transport equation for this quantity seems to be the weakest link in the existing turbulence models used for engineering applications (CFD). This is good discussion of instantaneous velocity gradient measurements in turbulent flows and a good description of basic and more recent complex hot-wire configurations used for the vorticity measurements. The last two chapters deal with conditional sampling and time series analysis of turbulence fluctuations. There is plenty of interesting material related to processing and averaging signals measured in periodic flows, intermittency measurements and identification of coherent structures in turbulent flows. The closing chapter provides a useful survey of conventional statistical analysis of random signals in amplitude and phase domains. The list of the references at the end provides a complete overview of virtually all important studies related to HWA published to date. This is an excellent book written in a clear and readable style suitable for students, research scientists and engineers. The text is well supported by mathematical analysis and, whenever necessary, with adequate illustrations and diagrams. I highly recommend the book to everyone working in the field of experimental fluid mechanics. It should be obligatory reading for students involved in turbulence measurements. J Jovanovic References Corrsin S. 1963 Turbulence: experimental methods Handbook of Physics vol 8.2 (Berlin: Springer) pp 523 - 90 Melnik W L and Weske J R 1967 Advances in hot-wire anemometry Proc. Int. Symp. on Hot Wire Anemometry (Department of Aerospace Engineering, University of Maryland) Perry A E 1982 Hot-Wire Anemometry (Oxford: Clarendon Press) Lomas C G 1986 Fundamentals of Hot-Wire Anemometry (Cambridge: Cambridge University Press)

Patterns in the ocean: Ocean processes and marine population dynamics

Abstract: We present solutions for nutrient transfer to osmotrophs in the full range of flow regimes for which solutions have been published, and we extend some of those solutions to new parameter domains and flow environments. These regimes include stagnant water; steady, unitorm flow arising from swimming or sinking; steady shear flows; and fluctuating shear from dissipation of turbulence, as well as the combined effects of turbulence-induced shear and swimming or sinking. Solutions for nutrient fluxes cannot be carried over from one flow regime to another. In all cases, however, mass transfer increases with cell size and with flow velocity. Cell shape becomes particularly important at high flow velocities. For steady, uniform flow arising from sinking or swimming, we find asymptotic analytic and numerical solutions from the engineering literature superior to those in more common use within oceanography. These engineering solutions suggest flow effects an order of magnitude smaller than commonly supposed. A cell radius near 20 Ilm is needed before swimming or sinking can be expected to increase the flux of nutrients, such as nitrate or phosphate, substantially (by ~50%) over the stagnant-water case. We find sound asymptotic solutions for the case oflinear shear and supplement them with numerical solutions of our own to cover the range of cell sizes and shear rates of interest for phytoplankton. We extend them further to cover viscous shears from dissipating turbulence for cells smaller than the Kolmogorov scale (order of 1-6mm in the ocean). Our analysis suggests turbulence effects an order of magnitude greater than previously postulated, with a cell size of 60~lm needed to experience substantial gain. Cell rotation, whether induced by the propulsion mechanism in swimming or passively by shear across the cell perimeter, will reduce the rate of nutrient transfer relative to a non-rotating cell unless the axis of rotation parallels the direction of flow. Although in calm water dinoflagellates by swimming are able to increase nutrient uptake, in strong turbulence they may not be able to maintain a rotational axis parallel to the direction of swimming or the direction of shear, resulting in a relative reduction in flux. Conversely, large chains of diatoms and filamentous cyanobacteria that span the radius of the smallest vortices are best able to take advantage of turbulence. Despite these deductions from a diversity of analytic and numerical solutions, unequivocal data to test the contribution of advection to nutrient acquisition by phytoplankton are scarce owing, in large part, to the inability to visualize, record and thus mimic fluid motions in the vicinities of cells in natural flows.

Dominant two‐dimensional solar wind turbulence with implications for cosmic ray transport

Abstract: Two new methods for distinguishing two-dimensional (2D) turbulence from slab turbulence are applied to Helios magnetometer data. Two-component models with varying slab and 2D ingredients are considered. Both methods indicate that solar wind magnetic turbulence possesses a dominant (∼85 % by energy) 2D component. The presence of such a large 2D component provides a natural solution to the long-standing problem of “too small” cosmic ray mean free paths derived from quasilinear scattering theory when using the slab model.

Numerical models for two-phase turbulent flows

Abstract: Numerical models for turbulent fluid-particle flows are reviewed. The two approaches typically used for modelling the dispersed (particle) phase are the trajectory and two-fluid formulations, while volume- averaged models are most common for the continuous (fluid) phase. The review is structured according to the turbulence models used for the continuous phase: turbulence energy-dissipation models, large- eddy simulations, direct numerical simulations, and discrete vortex models. The applications of these models to simulate particle dispersion due to fluid turbulence and the adjustments to the models to account for the modulation of the carrier phase turbulence by the particles are addressed.

Three-dimensional wake transition

Abstract: It is now well-known that the wake transition regime for a circular cylinder involves two modes of small-scale three-dimensional instability (modes “A” and “B”; Williamson, 1988), depending on the regime of Reynolds number (Re), although almost no understanding of the physical origins of these instabilities, or indeed their effects on near wake formation, have hitherto been made clear. There is now some strong interest in this problem, coming not only from experiment, but also from Direct Numerical Simulation, where, in some cases, these modes A and B have been found clearly (Thompson & Hourigan, 1996; Zhang et al., 1995; Henderson, 1995; Mittal & Balachandar, 1996). Much of the recent surge of activity concerning the wake transition and development of turbulence in wakes has been addressed comprehensively in a review paper. Williamson (1996a).

The structure and development of a wing-tip vortex

Abstract: Experiments have been performed on the tip vortex trailing from a rectangular NACA 0012 half-wing. Preliminary studies showed the vortex to be insensitive to the introduction of a probe and subject only to small wandering motions. Meaningful velocity measurements could therefore be made using hot-wire probes.Detailed analysis of the effects of wandering was performed to properly reveal the flow structure in the core region and to give confidence in measurements made outside the core. A theory has been developed to correct mean-velocity profiles for the effects of wandering and to provide complete quantitative estimates of its amplitude and contributions to Reynolds stress fields. Spectral decomposition was found to be the most effective method of separating these contributions from velocity fluctuations due to turbulence.Outside the core the flow structure is dominated by the remainder of the wing wake which winds into an ever-increasing spiral. There is no large region of axisymmetric turbulence surrounding the core and little sign of turbulence generated by the rotational motion of the vortex. Turbulence stress levels vary along the wake spiral in response to the varying rates of strain imposed by the vortex. Despite this complexity, the shape of the wake spiral and its turbulent structure reach an approximately self-similar form.On moving from the spiral wake to the core the overall level of velocity fluctuations greatly increases, but none of this increase is directly produced by turbulence. Velocity spectra measured at the vortex centre scale in a manner that implies that the core is laminar and that velocity fluctuations here are a consequence of inactive motion produced as the core is buffeted by turbulence in the surrounding spiral wake. Mean-velocity profiles through the core show evidence of a two-layered structure that dies away with distance downstream.

Towards better uncertainty estimates for turbulence statistics

Abstract: Methods for calculating the statistical uncertainty associated with the sampling of random processes such as those which occur in turbulence research are given. In particular, formulas based on normal distribution assumptions and on any general distribution shape are given for means, variances, Reynolds stresses, correlation coefficients, homogeneous and mixed turbulent triple products and fourth order turbulence moments. In addition, two resampling algorithms, the “bootstrap” and “jackknife”, are presented and compared using actual turbulence data. The availability of these methods will allow turbulence data to be presented with statistical uncertainty error bars on all turbulence quantities.

On the onset of high-Reynolds-number grid-generated wind tunnel turbulence

Abstract: Using an active grid devised by Makita (1991), shearless decaying turbulence is studied for the Taylor-microscale Reynolds number, Rλ, varying from 50 to 473 in a small (40 × 40 cm2 cross-section) wind tunnel. The turbulence generator consists of grid bars with triangular wings that rotate and flap in a random way. The value of Rλ is determined by the mean speed of the air (varied from 3 to 14 m s–1) as it passes the rotating grid, and to a lesser extent by the randomness and rotation rate of the grid bars. Our main findings are as follows. A weak, not particularly well-defined scaling range (i.e. a power-law dependence of both the longitudinal (u) and transverse (v) spectra, F11(k1) and F22(k1) respectively, on wavenumber k1) first appears at Rλ ∼ 50, with a slope, n1, (for the u spectrum) of approximately 1.3. As Rλ was increased, n1 increased rapidly until Rλ ∼ 200 where n ∼ 1.5. From there on the increase in n1 was slow, and even by Rλ = 473 it was still significantly below the Kolmogorov value of 1.67. Over the entire range, 50 [les ] Rλ [les ] 473, the data were well described by the empirical fit: . Using a modified form of the Kolmogorov similarity law: F11(k1) = C1*e2/3k1–5/3(k 1η)5/3–n1 where e is the turbulence energy dissipation rate and η is the Kolmogorov microscale, we determined a linear dependence between n1 and C1*: C1* = 4.5 – 2.4n1. Thus for n1 = 5/3 (which extrapolation of our results suggests will occur in this flow for Rλ ∼ 104), C1* = 0.5, the accepted high-Reynolds-number value of the Kolmogorov constant. Analysis of the p.d.f. of velocity differences Δu(r) and Δv(r) where r is an inertial subrange interval, conditional dissipation, and other statistics showed that there was a qualitative difference between the turbulence for Rλ 200 (strong turbulence). For the latter, the p.d.f.s of Δu(r) and Δv(r) had super Gaussian tails and the dissipation (both of the u and v components) conditioned on Δu(r) and Δv(r) was a strong function of the velocity difference. For Rλ 200 are consistent with the predictions of the Kolmogorov refined similarity hypothesis (and make a distinction between the dynamical and kinematical contributions to the conditional statistics). They have much in common with similar statistics done in shear flows at much higher Rλ, with which they are compared.

Large-eddy simulation of turbulent confined coannular jets

Abstract: Large-eddy simulation (LES) was used to study mixing of turbulent, coannular jets discharging into a sudden expansion. This geometry resembles that of a coaxial jet-combustor, and the goal of the calculation was to gain some insight into the phenomena leading to lean blow-out (LBO) in such combustion devices. This is a first step in a series of calculations, where the focus is on the fluid dynamical aspects of the mixing process in the combustion chamber. The effects of swirl, chemical reactions and heat release were not taken into account. Mixing of fuel and oxidizer was studied by tracking a passive scalar introduced in the central jet. The dynamic subgrid-scale (DM) model was used to model both the subgrid-scale stresses and the subgrid-scale scalar flux. The Reynolds number was 38000, based on the bulk velocity and diameter of the combustion chamber. Mean velocities and Reynolds stresses are in good agreement with experimental data. Animated results clearly show that intermittent pockets of fuel-rich fluid (from the central jet) are able to cross the annular jet, virtually undiluted, into the recirculation zone. Most of the fuel-rich fluid is, however, entrained into the recirculation zone near the instantaneous reattachment point. Fuel trapped in the recirculation zone is, for the most part, entrained back into the step shear layer close to the base of the burner.

Flow hydrodynamics in tidal marsh canopies

Abstract: The transport of particulate and dissolved matter on the surface of coastal marshes is controlled by the hydrodynamic characteristics of over-marsh flows. High-frequency (5 Hz) in situ measurements of flow speed were collected in Spartina alternijlora, Juncus roemerianus, and Di:-tichlis spicata canopies using hot-film anemometry sensor arrays. These data indicate that mean flow speed, turbulence intensity, and the shape of the vertical speed profile are influenced by variations in plant morphology and stem density. Mean flow speed and turbulence intensity are inversely related to stem density and to distance from the creek edge. Flow energies decrease by about one order of magnitude when flows encounter the vegetated marsh surface and continue to decrease as vegetation density increa,ses. Turbulent flow energy also decays exponentially with increasing distance from the creek edge. Reductions in flow speed coupled with energy decay provide a hydrologic mechanism for sediment deposition patterns commonly observed in marsh systems. Suspended matter transport is also affected by plant-flow interactions. Vertical flow structure is strongly influenced by canopy morphology (plant type and plant shape). Plant-flow interactions result in vertical speed profiles whose shapes deviate from the logarithmic profile typical in free-stream conditions and in the development of transitional flow regimes (i.e. neither laminar nor fully turbulent).

The velocity field of the turbulent very near wake of a circular cylinder

Abstract: Hot-wire measurements were conducted in the very near wake (x/d⩽10) of a circular cylinder at a Reynolds number based on cylinder diameter, Re d of 3900. Measurements of the streamwise velocity component with the use of single sensor hot-wire probes were found to be inaccurate for such flowfields where high flow angles are present. An X-array probe provided detailed streamwise and lateral velocity component statistics. Frequency spectra of these two velocity components are also presented. Measurements with a 4-sensor hot-wire probe confirmed that the very near wake region is dominantly two-dimensional, thus validating the accuracy of the present X-array data.

Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate

Abstract: It is well known that subgrid models such as Smagorinsky's cannot be used for the spatially growing simulation of the transition to turbulence of flat-plate boundary layers, unless large-amplitude perturbations are introduced at the upstream boundary: they are over-dissipative, and the flow simulated remains laminar. This is also the case for the structure-function model (SF) of Metais & Lesieur (1992). In the present paper we present a sequel to this model, the filtered-structure-function (FSF) model. It consists of removing the large-scale fluctuations of the field before computing its second-order structure function. Analytical arguments confirm the superiority of the FSF model over the SF model for large-eddy simulations of weakly unstable transitional flows. The FSF model is therefore used for the simulation of a quasi-incompressible (M∞ = 0.5) boundary layer developing spatially over an adiabatic flat plate, with a low level of upstream forcing. With the minimal resolution 650 × 32 × 20 grid points covering a range of streamwise Reynolds numbers Rex1 e [3.4 × 105, 1.1 × 106], transition is obtained for 80 hours of time-processing on a CRAY 2 (whereas DNS of the whole transition takes about ten times longer). Statistics of the LES are found to be in acceptable agreement with experiments and empirical laws, in the laminar, transitional and turbulent parts of the domain. The dynamics of low-pressure and high-vorticity distributions is examined during transition, with particular emphasis on the neighbourhood of the critical layer (defined here as the height of the fluid travelling at a speed equal to the phase speed of the incoming Tollmien–Schlichting waves). Evidence is given that a subharmonic-type secondary instability grows, followed by a purely spanwise (i.e. time-independent) mode which yields peak-and-valley splitting and transition to turbulence. In the turbulent region, flow visualizations and local instantaneous profiles are provided. They confirm the presence of low- and high-speed streaks at the wall, weak hairpins stretched by the flow and bursting events. It is found that most of the vorticity is produced in the spanwise direction, at the wall, below the high-speed streaks. Isosurfaces of eddy viscosity confirm that the FSF model does not perturb transition much, and acts mostly in the vicinity of the hairpins.

MHD Turbulence Revisited

Abstract: Kraichnan (1965) proposed that MHD turbulence occurs as a result of collisions between oppositely directed Alfv\'en wave packets. Recent work has generated some controversy over the nature of non linear couplings between colliding Alfv\'en waves. We find that the resolution to much of the confusion lies in the existence of a new type of turbulence, intermediate turbulence, in which the cascade of energy in the inertial range exhibits properties intermediate between those of weak and strong turbulent cascades. Some properties of intermediate MHD turbulence are: (i) in common with weak turbulent cascades, wave packets belonging to the inertial range are long lived; (ii) however, components of the strain tensor are so large that, similar to the situation in strong turbulence, perturbation theory is not applicable; (iii) the breakdown of perturbation theory results from the divergence of neighboring field lines due to wave packets whose perturbations in velocity and magnetic fields are localized, but whose perturbations in displacement are not; (iv) 3--wave interactions dominate individual collisions between wave packets, but interactions of all orders $n\geq 3$ make comparable contributions to the intermediate turbulent energy cascade; (v) successive collisions are correlated since wave packets are distorted as they follow diverging field lines; (vi) in common with the weak MHD cascade, there is no parallel cascade of energy, and the cascade to small perpendicular scales strengthens as it reaches higher wave numbers; (vii) For an appropriate weak excitation, there is a natural progression from a weak, through an intermediate, to a strong cascade.

Air Bubble Entrainment in Free-Surface Turbulent Shear Flows

Abstract: In high velocity water flows, large quantities of air bubbles are entrained at the free-surfaces. Practical applications are found in Chemical, Civil, Environmental, Mechanical, Mining and Nuclear Engineering. Air-water flows are observed in small-scale as well as large-scale flow situations. E.g., thin circular jets used as mixing devices in chemical plants (Qw ~ 0.001 L/s, diameter ~ 1 mm), and spillway flows (Qw > 10,000 m3/s, flow thickness over 10 m). In each case, however, the interactions between the entrained air bubbles and the turbulence field are significant. This monograph investigates the "air bubble entrainment in free-surface turbulent shear flows". It develops an analysis of the air entrainment processes in free-surface flows. The air-water flows are investigated as homogeneous mixtures with variable density. The variations of fluid density result from the non-uniform air bubble distributions and the turbulent diffusion process. Several types of air-water free-surface flows are studied : plunging jet flows (Part II), open channel flows (Part III), and turbulent water jets discharging into air (Part IV). Each configuration can be characterised as a high-velocity free-surface flow with turbulent shear layer and large air bubble content. Experimental observations confirm the conceptual idea that the air-water mixture behaves as a homogeneous compressible fluid. The monograph presents numerous and recent experimental investigations with mean velocities up to 57 m/s and mean air contents up to 70%. The analysis of experimental studies provides new information on the air-water flow field : air bubble distributions, air-water velocity profiles, air bubble sizes and bubble-turbulence interactions. The results show a strong similarity between all the flow patterns. In each case the distributions of air concentration (i.e. void fraction) can be approximated by a simple advective diffusion theory. New analysis is developed for each flow configuration and compared successfully with model and prototype data. The velocity distributions in air-water flows have the same shape as for monophase flows. However the presence of air bubbles modifies some turbulence characteristics while the turbulence controls the mechanism of bubble breakup. The book presents new useful information for design engineers and research-and-development scientists who need a better understanding of the fluid mechanics of air-water flows. Both qualitative and quantitative information are provided. In some cases the limits of our knowledge are pointed out. The book consists of five parts. Part I introduces the topic and its relevance, develops a dimensional analysis and discusses the air-water gas transfer process. In each subsequent part, the distributions of air content and air-water velocity are described. The results are grouped as : plunging jet flows (Part II), open channel flows (Part III) and high-velocity water jets discharging into the atmosphere (Part IV). In Part V, an analogy between the various types of air-water flows is developed. In the appendices, tables of physical and chemical properties of fluids are provided in appendix A. The report presents results expressed in SI Units. A table of unit conversions is given in appendix B. Estimates of bubble rise velocity are discussed in appendix C. Appendix D develops sound celerity calculations in two-phase flows. Appendices E, G, H and I present complete calculations of the air bubble diffusion process. Boundary layer characteristics and jet trajectory calculations are detailed in appendices F and J respectively. Appendix K defines bubble size distribution characteristic parameters. Observations by LEONARDO DA VINCI are recounted in appendix L. 'Errare Humanum Est'. Appendix M presents a correction form. Readers who find an error or mistake are welcome to record the error on the page and to send a copy to the author. At the beginning of the book, the reader will find the table of contents, a list of symbols, a glossary and an album of colourful photographs of 'white waters'.

Two-layer approximate boundary conditions for large-eddy simulations

Abstract: A new method to model the effect of the solid boundaries on the rest of the flowfield in large-eddy simulations is proposed The filtered Navier-Stokes equations are solved up to the first computational point From there to the wall, a simplified set of equations is solved, and an estimate of the instantaneous wall shear stress required to impose boundary conditions is obtained Computations performed for the plane channel, square duct, and the rotating channel flow cases gave improved results compared with existing models The additional computing time required by the model is on the order of 10-15% of the overall computing time The mean flow quantities and low-order statistics, which are of primary interest in engineering calculations, are in very good agreement with the reference data available in the literature

Evolution of turbulent magnetic fluctuation power with heliospheric distance

Abstract: On the basis of transport theories appropriate to a radially expanding solar wind, new results for the evolution of the energy density in solar wind fluctuations at MHD scales are derived. The models, which represent a departure from the well-known WKB description, include the effects of “mixing”, driving by stream-stream interactions (compression and shear) and interstellar pick-up ions as well as non-isotropic MHD turbulence. Magnetometer data from Voyager 1 and 2 and Pioneer 11 are compared to the turbulence-based models and close agreement is found between theory and data for a reasonable choice of parameters.

Review of Lagrangian Stochastic Models for Trajectories in the Turbulent Atmosphere

Abstract: We review the theoretical basis for, and the advantages of, random flight models for the trajectories of tracer particles in turbulence. We then survey their application to calculate dispersion in the principal types of atmospheric turbulence (stratified, vertically-inhomogeneous, Gaussian or non-Gaussian turbulence in the surface layer and above), and show that they are especially suitable for some problems (e.g., quantifying ground emissions).

High-density turbidity currents; are they sandy debris flows?

Abstract: Conventionally, turbidity currents are considered as fluidal flows in which sediment is supported by fluid turbulence, whereas debris flows are plastic flows in which sediment is supported by matrix strength, dispersive pressure, and buoyant lift. The concept of high-density turbidity current refers to high-concentration, commonly nonturbulent, flows of fluids in which sediment is supported mainly by matrix strength, dispersive pressure, and buoyant lift. The conventional wisdom that traction carpets with entrained turbulent clouds on top represent high-density turbidity currents is a misnomer because traction carpets are neither fluidal nor turbulent. Debris flows may also have entrained turbulent clouds on top. The traction carpet/debris flow and the overriding turbulent clouds are two separate entities in terms of flow rheology and sediment-support mechanism. In experimental and theoretical studies, which has linked massive sands and floating clasts to high-density turbidity currents, the term "high-density turbidity current" has actually been used for laminar flows. In alleviating this conceptual problem, sandy debris flow is suggested as a substitute for high-density turbidity current. Sandy debris flows represent a continuous spectrum of processes between cohesive and cohesionless debris flows. Commonly they are rheologically plastic. They may occur with or without entrained turbulent clouds on top. Their sediment-support mechanisms include matrix strength, dispersive pressure, and buoyant lift. They are characterized by laminar flow conditions, a moderate to high grain concentration, and a low to moderate mud content. Although flows evolve and transform during the course of transport in density-stratified flows, the preserved features in a deposit are useful to decipher only the final stages of deposition. At present, there are no established criteria to decipher transport mechanisms from the depositional record.

Turbulent nature of refractive-index variations in biological tissue.

Abstract: Phase-contrast microscopy shows that the structure of the refractive-index inhomogeneities in a variety of mammalian tissues resembles that of frozen turbulence. Viewed over a range of scales, the spectrum of index variations exhibits a power-law behavior for spatial frequencies spanning at least a decade (0.5–5 μm−1) and has an outer scale in the range of 4–10 μm, above which correlations are no longer seen. The observed structure function fits the classical Kolmogorov model of turbulence. These observations are fundamental to understanding light propagation in tissue and may provide clues about how tissues develop and organize.

Experiments on particle—turbulence interactions in the near–wall region of an open channel flow: implications for sediment transport

Abstract: A high-speed video system was used to study the interaction between sediment particles and turbulence in the wall region of an open channel flow with both smooth and transitionally rough beds. In smooth flows, particles immersed within the viscous sublayer were seen to accumulate along low-speed wall streaks; apparently due to the presence of quasi-streamwise vortices in the wall region. Larger particles did not tend to group along streaks, however their velocity was observed to respond to the streaky structure of the flow velocity in the wall region. In transitionally rough flows particle sorting was not observed. Coherent flow structures in the form of shear layers typically observed in the near-wall region interacted with sediment particles lying on the channel bottom, resulting in the particles being entrained into suspension. Although there has been some speculation that this process would not be effective in entraining particles totally immersed in the viscous sublayer, the results obtained demonstrate the opposite. The entrainment mechanism appears to be the same independent of the roughness condition of the bottom wall, smooth or transitionally rough. In the latter case, however, hiding effects tend to preclude the entrainment of particles with sizes finer than that of the roughness elements. The analysis of particle velocity during entrainment shows that the streamwise component tends to be much smaller than the local mean flow velocity, while the vertical component tends to be much larger than the local standard deviation of the vertical flow velocity fluctuations, which would indicate that such particles are responding to rather extreme flow ejection events.