Showing papers on "Turbulence published in 2000"

An Introduction to Combustion: Concepts and Applications

Abstract: Preface Preface to the Second Edition Preface to the First Edition 1: Introduction 2: Combustion and Thermochemistry 3: Introduction to Mass Transfer 4: Chemical Kinetics 5: Some Important Chemical Mechanisms 6: Coupling Chemical and Thermal Analyses of Reacting Systems 7: Simplifed Conversation Equations for Reacting Flows 8: Laminar Premixed Flames 9: Laminar Diffusion Flames 10: Droplet Evaporation and Burning 11: Introduction to Turbulent Flows 12: Turbulent Premixed Flames 13: Turbulent Nonpremixed Flames 14: Burning of Solids 15: Pollutant Emissions 16: Detonations Appendix A: Selected Thermodynamic Propertiesof Gases Comprising C-H-O-N System Appendix B: Fuel Properties Appendix C: Selected Properties of Air, Nitrogen, and Oxygen Appendix D: Diffusion Coefficients and Methodology for their Estimation Appendix E: Generalized Newton's Method for the Solution of Nonlinear Equations Appendix F: Computer Codes for Equilibrium Products of Hydrocarbon-Air Combustion

Vortex organization in the outer region of the turbulent boundary layer

Abstract: The structure of energy-containing turbulence in the outer region of a zero-pressure- gradient boundary layer has been studied using particle image velocimetry (PIV) to measure the instantaneous velocity fields in a streamwise-wall-normal plane. Experiments performed at three Reynolds numbers in the range 930 0) that occur on a locus inclined at 30–60° to the wall.In the outer layer, hairpin vortices occur in streamwise-aligned packets that propagate with small velocity dispersion. Packets that begin in or slightly above the buffer layer are very similar to the packets created by the autogeneration mechanism (Zhou, Adrian & Balachandar 1996). Individual packets grow upwards in the streamwise direction at a mean angle of approximately 12°, and the hairpins in packets are typically spaced several hundred viscous lengthscales apart in the streamwise direction. Within the interior of the envelope the spatial coherence between the velocity fields induced by the individual vortices leads to strongly retarded streamwise momentum, explaining the zones of uniform momentum observed by Meinhart & Adrian (1995). The packets are an important type of organized structure in the wall layer in which relatively small structural units in the form of three-dimensional vortical structures are arranged coherently, i.e. with correlated spatial relationships, to form much longer structures. The formation of packets explains the occurrence of multiple VITA events in turbulent ‘bursts’, and the creation of Townsend's (1958) large-scale inactive motions. These packets share many features of the hairpin models proposed by Smith (1984) and co-workers for the near-wall layer, and by Bandyopadhyay (1980), but they are shown to occur in a hierarchy of scales across most of the boundary layer.In the logarithmic layer, the coherent vortex packets that originate close to the wall frequently occur within larger, faster moving zones of uniform momentum, which may extend up to the middle of the boundary layer. These larger zones are the induced interior flow of older packets of coherent hairpin vortices that originate upstream and over-run the younger, more recently generated packets. The occurence of small hairpin packets in the environment of larger hairpin packets is a prominent feature of the logarithmic layer. With increasing Reynolds number, the number of hairpins in a packet increases.

Turbulence in plant canopies

Abstract: ▪ Abstract The single-point statistics of turbulence in the ‘roughness sub-layer’ occupied by the plant canopy and the air layer just above it differ significantly from those in the surface layer. The mean velocity profile is inflected, second moments are strongly inhomogeneous with height, skewnesses are large, and second-moment budgets are far from local equilibrium. Velocity moments scale with single length and time scales throughout the layer rather than depending on height. Large coherent structures control turbulence dynamics. Sweeps rather than ejections dominate eddy fluxes and a typical large eddy consists of a pair of counter-rotating streamwise vortices, the downdraft between the vortex pair generating the sweep. Comparison with the statistics and instability modes of the plane mixing layer shows that the latter rather than the boundary layer is the appropriate model for canopy flow and that the dominant large eddies are the result of an inviscid instability of the inflected mean velocity profi...

Shape and Structure, from Engineering to Nature

Abstract: 1. Natural form, questioning, and theory 2. Mechanical structure 3. Thermal structure 4. Heat trees 5. Fluid trees 6. Ducts and rivers 7. Turbulent structure 8. Convective trees 9. Structure in power systems 10. Structure in time: rhythm 11. Transportation and economics structure 12. Shapes with constant resistance About the author Author index Subject index.

A thickened flame model for large eddy simulations of turbulent premixed combustion

Abstract: A subgrid scale model for large eddy simulations of turbulent premixed combustion is developed and validated. The approach is based on the concept of artificially thickened flames, keeping constant the laminar flame speed sl0. This thickening is simply achieved by decreasing the pre-exponential factor of the chemical Arrhenius law whereas the molecular diffusion is enhanced. When the flame is thickened, the combustion–turbulence interaction is affected and must be modeled. This point is investigated here using direct numerical simulations of flame–vortex interactions and an efficiency function E is introduced to incorporate thickening effects in the subgrid scale model. The input parameters in E are related to the subgrid scale turbulence (velocity and length scales). An efficient approach, based on similarity assumptions, is developed to extract these quantities from the resolved velocity field. A specific operator is developed to exclude the dilatational part of the velocity field from the estimation of...

Electron temperature gradient driven turbulence

Abstract: Collisionless electron-temperature-gradient-driven (ETG) turbulence in toroidal geometry is studied via nonlinear numerical simulations To this aim, two massively parallel, fully gyrokinetic Vlasov codes are used, both including electromagnetic effects Somewhat surprisingly, and unlike in the analogous case of ion-temperature-gradient-driven (ITG) turbulence, we find that the turbulent electron heat flux is significantly underpredicted by simple mixing length estimates in a certain parameter regime (ŝ∼1, low α) This observation is directly linked to the presence of radially highly elongated vortices (“streamers”) which lead to very effective cross-field transport The simulations therefore indicate that ETG turbulence is likely to be relevant to magnetic confinement fusion experiments

Passive Scalars in Turbulent Flows

Abstract: ▪ Abstract Passive scalar behavior is important in turbulent mixing, combustion, and pollution and provides impetus for the study of turbulence itself. The conceptual framework of the subject, strongly influenced by the Kolmogorov cascade phenomenology, is undergoing a drastic reinterpretation as empirical evidence shows that local isotropy, both at the inertial and dissipation scales, is violated. New results of the complex morphology of the scalar field are reviewed, and they are related to the intermittency problem. Recent work on other aspects of passive scalar behavior—its spectrum, probability density function, flux, and variance—is also addressed.

Analysis and interpretation of instantaneous turbulent velocity fields

Abstract: Methods of analyzing and interpreting velocity-field data (both two- and three-dimensional) to understand the kinematics, dynamics, and scales of turbulence are discussed. Reynolds decomposition and vorticity are traditionally used; however, several other methods, including Galilean (constant convection velocity) and LES decompositions (low-pass filtering), in conjunction with critical-point analysis of the local velocity gradient tensor, reveal more about the structure of turbulence. Once the small-scale structures have been identified, it is necessary to assess their importance to the overall dynamics of the turbulence by visualizing the motions they induce and the stresses they impose both on other small-scale vortices and on the larger-scale field.

On coherent-vortex identification in turbulence

Abstract: The identification issue of coherent vortices is investigated on the basis of direct numerical simulation (DNS) and large-eddy simulations (LES) of turbulent flows. It is first shown that the pressure Laplacian is positive within a low-pressure tube of small cross section enclosed by convex isobaric surfaces in a uniform-density flow. Since this quantity is related to the second invariant Q of ∇ u , the Q criterion (region where Q is positive) is a necessary condition for the existence of such tubes. This eduction scheme is compared to other classical methods in incompressible simulations of isotropic turbulence: a mixing layer, a channel flow and a backward-facing step. Q-isosurfaces turn out to display very nice coherent vortices. This criterion is also used in combination with a conditional sampling method to discuss the characteristics of quasi-longitudinal vortices in a manipulated channel flow. The contribution of near-wall vortical structures to velocity and vorticity fluctuations is clearly isolat...

Suppression of turbulence and transport by sheared flow

Abstract: The role of stable shear flow in suppressing turbulence and turbulent transport in plasmas and neutral fluids is reviewed. Localized stable flow shear produces transport barriers whose extensive and highly successful utilization in fusion devices has made them the primary experimental technique for reducing and even eliminating the rapid turbulent losses of heat and particles that characterize fusion-grade plasmas. These transport barriers occur in different plasma regions with disparate physical properties and in a range of confining configurations, indicating a physical process of unusual universality. Flow shear suppresses turbulence by speeding up turbulent decorrelation. This is a robust feature of advection whenever the straining rate of stable mean flow shear exceeds the nonlinear decorrelation rate. Shear straining lowers correlation lengths in the direction of shear and reduces turbulent amplitudes. It also disrupts other processes that feed into or result from turbulence, including the linear instability of important collective modes, the transport-producing correlations between advecting fluid and advectants, and large-scale spatially connected avalanchelike transport events. In plasmas, regions of stable flow shear can be externally driven, but most frequently are created spontaneously in critical transitions between different plasma states. Shear suppression occurs in hydrodynamics and represents an extension of rapid-distortion theory to a long-time-scale nonlinear regime in two-dimensional stable shear flow. Examples from hydrodynamics include the emergence of coherent vortices in decaying two-dimensional Navier-Stokes turbulence and the reduction of turbulent transport in the stratosphere.

Fluid mechanics in the driven cavity

Abstract: This review pertains to the body of work dealing with internal recirculating flows generated by the motion of one or more of the containing walls. These flows are not only technologically important, they are of great scientific interest because they display almost all fluid mechanical phenomena in the simplest of geometrical settings. Thus corner eddies, longitudinal vortices, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same closed geometry. This facilitates the comparison of results from experiment, analysis, and computation over the whole range of Reynolds numbers. Considerable progress has been made in recent years in the understanding of three-dimensional flows and in the study of turbulence. The use of direct numerical simulation appears very promising.

Flow structure in depth-limited, vegetated flow

Abstract: Aquatic vegetation controls the mean and turbulent flow structure in channels and coastal regions and thus impacts the fate and transport of sediment and contaminants. Experiments in an open-channel flume with model vegetation were used to better understand how vegetation impacts flow. In particular, this study describes the transition between submerged and emergent regimes based on three aspects of canopy flow: mean momentum, turbulence, and exchange dynamics. The observations suggest that flow within an aquatic canopy may be divided into two regions. In the upper canopy, called the “vertical exchange zone”, vertical turbulent exchange with the overlying water is dynamically significant to the momentum balance and turbulence; and turbulence produced by mean shear at the top of the canopy is important. The lower canopy is called the “longitudinal exchange zone” because it communicates with surrounding water predominantly through longitudinal advection. In this region turbulence is generated locally by the canopy elements, and the momentum budget is a simple balance of vegetative drag and pressure gradient. In emergent canopies, only a longitudinal exchange zone is present. When the canopy becomes submerged, a vertical exchange zone appears at the top of the canopy and deepens into the canopy as the depth of submergence increases.

An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows

Abstract: Some new developments of explicit algebraic Reynolds stress turbulence models (EARSM) are presented. The new developments include a new near-wall treatment ensuring realizability for the individual stress components, a formulation for compressible flows, and a suggestion for a possible approximation of diffusion terms in the anisotropy transport equation. Recent developments in this area are assessed and collected into a model for both incompressible and compressible three-dimensional wall-bounded turbulent flows. This model represents a solution of the implicit ARSM equations, where the production to dissipation ratio is obtained as a solution to a nonlinear algebraic relation. Three-dimensionality is fully accounted for in the mean flow description of the stress anisotropy. The resulting EARSM has been found to be well suited to integration to the wall and all individual Reynolds stresses can be well predicted by introducing wall damping functions derived from the van Driest damping function. The platform for the model consists of the transport equations for the kinetic energy and an auxiliary quantity. The proposed model can be used with any such platform, and examples are shown for two different choices of the auxiliary quantity.

Elastic turbulence in a polymer solution flow

Abstract: Turbulence is a ubiquitous phenomenon that is not fully understood. It is known that the flow of a simple, newtonian fluid is likely to be turbulent when the Reynolds number is large (typically when the velocity is high, the viscosity is low and the size of the tank is large). In contrast, viscoelastic fluids such as solutions of flexible long-chain polymers have nonlinear mechanical properties and therefore may be expected to behave differently. Here we observe experimentally that the flow of a sufficiently elastic polymer solution can become irregular even at low velocity, high viscosity and in a small tank. The fluid motion is excited in a broad range of spatial and temporal scales, and we observe an increase in the flow resistance by a factor of about twenty. Although the Reynolds number may be arbitrarily low, the observed flow has all the main features of developed turbulence. A comparable state of turbulent flow for a newtonian fluid in a pipe would have a Reynolds number as high as 10(5) (refs 1, 2). The low Reynolds number or 'elastic' turbulence that we observe is accompanied by significant stretching of the polymer molecules, resulting in an increase in the elastic stresses of up to two orders of magnitude.

A turbulence scheme allowing for mesoscale and large‐eddy simulations

Abstract: The paper describes the turbulence scheme implemented in the Meso-NH community research model, and reports on some validation studies. Since the model is intended to perform both large-eddy and mesoscale simulations, we have developed a full three-dimensional scheme, based on the original method of Redelsperger and Sommeria. A prognostic equation for the turbulent kinetic energy is used, together with conservative variables for moist non-precipitating processes. A particularity of the scheme is the use of variable turbulent Prandtl and Schmidt numbers, consistently derived from the complete set of second-order turbulent-moment equations. The results of three idealized boundary-layer simulations allowing detailed comparisons with other large-eddy simulation (LES) models are discussed, and lead to the conclusion that the model is performing satisfactorily. The vertical flux and gradient computation can be run in isolation from the rest of the scheme, providing an efficient single-column parametrization for the mesoscale configuration of the model, if an appropriate parametrization of the eddy length-scale is used. The mixing-length specification is then the only aspect of the scheme which differs from the LES to the mesoscale configuration, and the numerical constants used for the closure terms are the same in both configurations. The scheme is run in single-column mode for the same three cases as above, and a comparison of single-column and LES results again leads to satisfactory results. It is believed that this result is original, and is due to the proper formulation of the parametrized mixing length and of the turbulent Prandtl and Schmidt numbers. In fact, a comparison of the parametrized mixing length with the length-scale of the energy-containing eddies deduced by spectral analysis of the LES shows interesting similarity.

The Anisotropy of Magnetohydrodynamic Alfvénic Turbulence

Abstract: We perform direct three-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size 2π threaded by strong uniform magnetic fields. We use a pseudospectral code with hyperviscosity and hyperdiffusivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale independent. We discuss why this is not the true scaling law and how the curvature of large-scale magnetic fields affects the power spectrum and leads to the wrong conclusion. When we correct for this effect, we find that the anisotropy of eddies depends on their size: smaller eddies are more elongated than larger ones along local magnetic field lines. The results are consistent with the scaling law ∥ ~ recently proposed by Goldreich & Sridhar. Here ∥ (and ⊥) are wavenumbers measured relative to the local magnetic field direction. However, we see some systematic deviations that may be a sign of limitations to the model or our inability to fully resolve the inertial range of turbulence in our simulations.

Detached-Eddy Simulations past a circular cylinder

Abstract: The flow is calculated with laminar separation (LS) at Reynolds numbers 50,000 and 140,000, and with turbulent separation (TS) at140,000 and 3 × 106. The TS cases are effectively tripped, but compared with untripped experiments at very high Reynolds numbers. The finest grid has about 18,000 points in each of 56 grid planes spanwise; the resolution is far removed from Direct Numerical Simulations, and the turbulence model controls the separation if turbulent. The agreement is quite good for drag, shedding frequency, pressure, and skin friction. However the comparison is obscured by large modulations of the vortex shedding and drag which are very similar to those seen in experiments but also, curiously, durably different between cases especially of the LS type. The longest simulations reach only about 50 shedding cycles. Disagreement with experimental Reynolds stresses reaches about 30%, and the length of the recirculation bubble is about double that measured. The discrepancies are discussed, as are the effects of grid refinement, Reynolds number, and a turbulence-model curvature correction. The finest grid does not give the very best agreement with experiment. The results add to the validation base of the Detached-Eddy Simulation (DES) technique for smooth-surface separation. Unsteady Reynolds-averaged simulations are much less accurate than DES for LS cases, but very close for TS cases. Cases with a more intricate relationship between transition and separation are left for future study.

Electron temperature gradient turbulence.

Abstract: The first toroidal, gyrokinetic, electromagnetic simulations of small scale plasma turbulence are presented. The turbulence considered is driven by gradients in the electron temperature. It is found that electron temperature gradient (ETG) turbulence can induce experimentally relevant thermal losses in magnetic confinement fusion devices. For typical tokamak parameters, the transport is essentially electrostatic in character. The simulation results are qualitatively consistent with a model that balances linear and secondary mode growth rates. Significant streamer-dominated transport at long wavelengths occurs because the secondary modes that produce saturation become weak in the ETG limit.

A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer

Abstract: A scale-dependent dynamic subgrid-scale model for large-eddy simulation of turbulent flows is proposed. Unlike the traditional dynamic model, it does not rely on the assumption that the model coefficient is scale invariant. The model is based on a second test-filtering operation which allows us to determine from the simulation how the coefficient varies with scale. The scale-dependent model is tested in simulations of a neutral atmospheric boundary layer. In this application, near the ground the grid scale is by necessity comparable to the local integral scale (of the order of the distance to the wall). With the grid scale and/or the test-filter scale being outside the inertial range, scale invariance is broken. The results are compared with those from (a) the traditional Smagorinsky model that requires specification of the coefficient and of a wall damping function, and (b) the standard dynamic model that assumes scale invariance of the coefficient. In the near-surface region the traditional Smagorinsky and standard dynamic models are too dissipative and not dissipative enough, respectively. Simulations with the scale-dependent dynamic model yield the expected trends of the coefficient as a function of scale and give improved predictions of velocity spectra at different heights from the ground. Consistent with the improved dissipation characteristics, the scale-dependent model also yields improved mean velocity profiles.

Simulations of Incompressible MHD Turbulence

Abstract: We simulate incompressible MHD turbulence in the presence of a strong background magnetic field. Our major conclusions are: 1) MHD turbulence is most conveniently described in terms of counter propagating shear Alfven and slow waves. Shear Alfven waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfven waves, as does a passive scalar. 2) MHD turbulence is anisotropic with energy cascading more rapidly along k_perp than along k_parallel, where k_perp and k_parallel refer to wavevector components perpendicular and parallel to the local magnetic field. Anisotropy increases with increasing k_perp. 3) MHD turbulence is generically strong in the sense that the waves which comprise it suffer order unity distortions on timescales comparable to their periods. Nevertheless, turbulent fluctuations are small deep inside the inertial range compared to the background field. 4) Decaying MHD turbulence is unstable to an increase of the imbalance between the flux of waves propagating in opposite directions along the magnetic field. 5) Items 1-4 lend support to the model of strong MHD turbulence by Goldreich & Sridhar (GS). Results from our simulations are also consistent with the GS prediction gamma=2/3. The sole notable discrepancy is that 1D power law spectra, E(k_perp) ~ k_perp^{-alpha}, determined from our simulations exhibit alpha ~ 3/2, whereas the GS model predicts alpha = 5/3.

Turbulent convection at very high Rayleigh numbers

Abstract: Turbulent convection occurs when the Rayleigh number (Ra)--which quantifies the relative magnitude of thermal driving to dissipative forces in the fluid motion--becomes sufficiently high. Although many theoretical and experimental studies of turbulent convection exist, the basic properties of heat transport remain unclear. One important question concerns the existence of an asymptotic regime that is supposed to occur at very high Ra. Theory predicts that in such a state the Nusselt number (Nu), representing the global heat transport, should scale as Nu proportional to Ra(beta) with beta = 1/2. Here we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (10(6) < or = Ra < or = 10(7)), using cryogenic helium gas as the working fluid. Our data, over the entire range of Ra, can be described to the lowest order by a single power-law with scaling exponent beta close to 0.31. In particular, we find no evidence for a transition to the Ra(1/2) regime. We also study the variation of internal temperature fluctuations with Ra, and probe velocity statistics indirectly.

The structure and fluid mechanics of turbidity currents: a review of some recent studies and their geological implications

Abstract: Summary The literature on the structure and behaviour of gravity currents is reviewed, with emphasis on some recent studies, and with particular attention to turbidity currents, though reference is also made to comparable behaviour in pyroclastic flows. Questions of definition are discussed, in particular the distinction between dense currents, which may deposit en masse, and more dilute currents. High-density dispersions may exist as a discrete, independently moving layer beneath a more dilute flow, as the basal part of a continuous density distribution or possibly as a transient depositional layer. Existing theory appears inadequate to explain the behaviour of some high-density dispersions. Surge-type currents are contrasted with quasi-steady currents, which may be generated by a variety of mechanisms including direct feed by rivers in flood. Such fluvially generated currents provide one means of generating currents with reversing buoyancy. Geologically significant turbidity currents are impractical for direct study owing to their large scale and (often) destructive nature. Small-scale laboratory currents offer a wealth of insights into turbidity current behaviour. This paper summarizes recent experimental studies that focus on the physical structure of gravity currents, with emphasis on the velocity and turbulence structure, the vertical density distribution and the stability of stratification. Preliminary quantification of the turbulence structure (including controls on turbulent entrainment, turbulent kinetic energy, Reynolds stresses and turbulence production) has been facilitated by recent technological developments that have allowed the measurement of instantaneous fluctuations in both velocity and concentration. Laboratory models, however, generally involve substantial simplification, and require compromises in some parameters to achieve adequate scaling of the parameters of most interest. Mathematical modelling also provides important insights into turbidity current behaviour. We discuss various approaches to modelling, ranging from simple hydraulic equations to systems of partial differential equations that explicitly treat conservation of momentum, fluid and sediment mass, and turbulent kinetic energy. The application for which the model is designed (i.e. to calculate mean head velocity or to create an instantaneous two-dimensional contour plot of downstream velocity in a current) determines the complexity of the mathematical model required. The behaviour of suspension currents around topography is complex and depends upon the relative height of the topography, and upon the density and velocity structure of the current. Many interactions with topography are well described by the internal Froude number, Fri. Both reflection and deflection of currents may occur on the upstream side of topography, depending upon Fri. On the downstream side of topography, flow separation, lee waves or hydraulic jumps may occur.

The mixing transition in turbulent flows

Abstract: Data on turbulent mixing and other turbulent-flow phenomena suggest that a (mixing) transition, originally documented to occur in shear layers, also occurs in jets, as well as in other flows and may be regarded as a universal phenomenon of turbulence. The resulting fully-developed turbulent flow requires an outer-scale Reynolds number of Re = U[delta]/v [greater, similar] 1–2 × 104, or a Taylor Reynolds number of ReT = u[prime prime or minute] [lambda]T/v [greater, similar] 100–140, to be sustained. A proposal based on the relative magnitude of dimensional spatial scales is offered to explain this behaviour.

Direct numerical simulation of'short' laminar separation bubbles with turbulent reattachment

Abstract: Direct numerical simulation of the incompressible Navier–Stokes equations is used to study flows where laminar boundary-layer separation is followed by turbulent reattachment forming a closed region known as a laminar separation bubble. In the simulations a laminar boundary layer is forced to separate by the action of a suction profile applied as the upper boundary condition. The separated shear layer undergoes transition via oblique modes and [Lambda]-vortex-induced breakdown and reattaches as turbulent flow, slowly recovering to an equilibrium turbulent boundary layer. Compared with classical experiments the computed bubbles may be classified as ‘short’, as the external potential flow is only affected in the immediate vicinity of the bubble. Near reattachment budgets of turbulence kinetic energy are dominated by turbulence events away from the wall. Characteristics of near-wall turbulence only develop several bubble lengths downstream of reattachment. Comparisons are made with two-dimensional simulations which fail to capture many of the detailed features of the full three-dimensional simulations. Stability characteristics of mean flow profiles are computed in the separated flow region for a family of velocity profiles generated using simulation data. Absolute instability is shown to require reverse flows of the order of 15–20%. The three-dimensional bubbles with turbulent reattachment have maximum reverse flows of less than 8% and it is concluded that for these bubbles the basic instability is convective in nature.

Approximate Wall Boundary Conditions in the Large-Eddy Simulation of High Reynolds Number Flow

Abstract: The near-wall regions of high Reynolds numbers turbulent flows must be modelled to treat many practical engineering and aeronautical applications. In this review we examine results from simulations of both attached and separated flows on coarse grids in which the near-wall regions are not resolved and are instead represented by approximate wall boundary conditions. The simulations use the dynamic Smagorinsky subgrid-scale model and a second-order finite-difference method. Typical results are found to be mixed, with acceptable results found in many cases in the core of the flow far from the walls, provided there is adequate numerical resolution, but with poorer results generally found near the wall. Deficiencies in this approach are caused in part by both inaccuracies in subgrid-scale modelling and numerical errors in the low-order finite-difference method on coarse near-wall grids, which should be taken into account when constructing models and performing large-eddy simulation on coarse grids. A promising new method for developing wall models from optimal control theory is also discussed.

A weak turbulence theory for incompressible MHD

Abstract: We derive a weak turbulence formalism for incompressible MHD. Three-wave interactions lead to a system of kinetic equations for the spectral densities of energy and helicity. We find energy spectra solution of the kinetic equations. The constants of the spectra are computed exactly and found to depend on the amount of correlation between the velocity and the magnetic field. Comparison with several numerical simulations and models is also made.

Velocity Modification of H I Power Spectrum

Abstract: The distribution of atomic hydrogen in the Galactic plane is usually mapped using the Doppler shift of 21 cm emission line, and this causes the modification of the observed emission spectrum. We calculate the emission spectrum in velocity slices of data (channel maps) and derive its dependence on the statistics of velocity and density fields. We find that, (1) if the density spectrum is steep, i.e., n < -3, the large k asymptotics of the emissivity spectrum are dominated by the velocity fluctuations; and (2) the velocity fluctuations make the emission spectra shallower, provided that the data slices are sufficiently thin. In other words, turbulent velocity creates small-scale structure that can erroneously be identified as clouds. The effect of thermal velocity is very similar to the change of the effective slice thickness, but the difference is that, while an increase of the slice thickness increases the amplitude of the signal, the increase of the turbulent velocity leaves the measured intensities intact while washing out fluctuations. The contribution of fluctuations in warm H I is suppressed relative to those in the cold component when the velocity channels used are narrower than the warm H I thermal velocity and small angular scale fluctuations are measured. We calculate how the spectra vary with the change of velocity slice thickness and show that the observational 21 cm data is consistent with the explanation that the intensity fluctuations within individual channel maps are generated by turbulent velocity fields. As the thickness of velocity slices increases, density fluctuations begin to dominate emissivity. This allows us to disentangle velocity and density statistics. The application of our technique to Galactic and SMC data reveals spectra of density and velocity with power law indexes close to -11/3. This is a Kolmogorov index, but the explanation of the spectrum as due to the Kolmogorov-type cascade faces substantial difficulties. We generalize our treatment for the case of a statistical study of turbulence inside individual clouds. The mathematical machinery developed is applicable to other emission lines.