Showing papers on "Turbulence published in 2003"

The Theory of Turbulent Jets

Abstract: This chapter contains sections titled: Theory of Free Turbulence, Prandtl's Old Theory of Free Turbulence, Application of Prandtl's Old Theory of Free Turbulence to Heat and Diffusion Problems, Theory of the Boundary Layer of a Two-Dimensional Turbulent Jet of Incompressible Fluid, Tollmien's Plane Turbulent Source, Tollmien's Axially Symmetric Turbulent Source, Distribution of Temperature and Constituent Concentration in the Main Region of a Jet According to Prandtl's Old Theory of Free Turbulence, Taylor's Free Turbulence Theory and Its Application, Prandtl's New Theory of Free Turbulence and Its Applications, Reichardt's Theory of Turbulent Mixing and Its Application, Determination of the Temperature Profile in a Jet on the Basis of the New Prandtl-Gortler Theory of Turbulence and Reichardt's Theory

The Spectrum of Turbulence

Abstract: The clustered distribution of interstellar matter raised C.F. von Weizsacker’s interest in turbulent flow with its nested vortex structures, its intermittent distribution of strongly active, dissipative turbulent bursts amidst more quiet regions, all this strongly fluctuating in time. Evidently many time scales are present, the smaller vortex structures circulating faster, being advected by the slower, larger ones. Also the spatial structures of the turbulent vortices or eddies display many scales. The prevailing impression of a turbulent flow field is its structural similarity on the various scales: zoomed smaller parts of the flow field look like larger ones, in a statistical sense. Such systems are properly described by power or scaling laws of the physical quantities of interest.

A generic length-scale equation for geophysical turbulence models

Abstract: A generalization of a class of differential length-scale equations typically used in second-order turbulence models for oceanic flows is suggested. Commonly used models, like the κ-e model and the Mellor-Yamada model, can be recovered as special cases of this generic model, and thus can be rationally compared. In addition, a method is proposed that yields a generalized framework for the calibration of the most frequently used class of differential length-scale equations. The generic model, calibrated with this method, exhibits a greater range of applicability than any of the traditional models. Stratified flows, plane mixing layers, and turbulence introduced by breaking surface waves are considered besides some classical test cases.

Particle-turbulence interactions in atmospheric clouds

Abstract: ▪ Abstract Turbulence is ubiquitous in atmospheric clouds, which have enormous turbulence Reynolds numbers owing to the large range of spatial scales present. Indeed, the ratio of energy-containing and dissipative length scales is on the order of 105 for a typical convective cloud, with a corresponding large-eddy Reynolds number on the order of 106 to 107. A characteristic trait of high-Reynolds-number turbulence is strong intermittency in energy dissipation, Lagrangian acceleration, and scalar gradients at small scales. Microscale properties of clouds are determined to a great extent by thermodynamic and fluid-mechanical interactions between droplets and the surrounding air, all of which take place at small spatial scales. Furthermore, these microscale properties of clouds affect the efficiency with which clouds produce rain as well as the nature of their interaction with atmospheric radiation and chemical species. It is expected, therefore, that fine-scale turbulence is of direct importance to the evolu...

Turbulent Boundary Layer in Compressible Fluids

Abstract: The continuity, momentum, and energy differential equations for turbulent flow of a compressible fluid are derived, and the apparent turbulent stresses and dissipation function are identified. A general formula for skin friction, including heat transfer to a flat plate, is developed for a thin turbulent boundary layer in compressible fluids with zero pressure gradient. Curves are presented giving skin-friction coefficients and heat-transfer coefficients for air for various wall-to-free-stream temperature ratios and free-stream Mach Numbers. In the special case when the boundary layer is insulated, this general formula yields skin-friction coefficients higher than those given by the von Karman wall-property compressible-fluid formula but lower than those given by the von Karman incompressible-fluid formula. Heat transfer from the boundary layer to the plate generally increases the friction and heat-transfer coefficients.

Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box

Abstract: High-resolution direct numerical simulations (DNSs) of incompressible homogeneous turbulence in a periodic box with up to 40963 grid points were performed on the Earth Simulator computing system. DNS databases, including the present results, suggest that the normalized mean energy dissipation rate per unit mass tends to a constant, independent of the fluid kinematic viscosity ν as ν→0. The DNS results also suggest that the energy spectrum in the inertial subrange almost follows the Kolmogorov k−5/3 scaling law, where k is the wavenumber, but the exponent is steeper than −5/3 by about 0.1.

Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications

Abstract: We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence Our study covers both gas-pressure-dominated (high β) and magnetic-pressure-dominated (low β) plasmas at different Mach numbers In addition, we present results for super-Alfvenic turbulence and discuss in what way it is similar to sub-Alfvenic turbulence We describe a technique of separating different magnetohydrodynamic modes (slow, fast and Alfven) and apply it to our simulations We show that, for both high- and low-β cases, Alfven and slow modes reveal a Kolmogorov k - 5 / 3 spectrum and scale-dependent Goldreich-Sridhar anisotropy, while fast modes exhibit a k - 3 / 2 spectrum and isotropy We discuss the statistics of density fluctuations arising from MHD turbulence in different regimes Our findings entail numerous astrophysical implications ranging from cosmic ray propagation to gamma ray bursts and star formation In particular, we show that the rapid decay of turbulence reported by earlier researchers is not related to compressibility and mode coupling in MHD turbulence In addition, we show that magnetic field enhancements and density enhancements are marginally correlated Addressing the density structure of partially ionized interstellar gas on astronomical-unit scales, we show that the viscosity-damped regime of MHD turbulence that we reported earlier for incompressible flows persists for compressible turbulence and therefore may provide an explanation for these mysterious structures

Small-scale hydrodynamics in lakes

Abstract: Recent small-scale turbulence observations allow the mixing regimes in lakes, reservoirs, and other enclosed basins to be categorized into the turbulent surface and bottom boundary layers as well as the comparably quiet interior. The surface layer consists of an energetic wave-affected thin zone at the very top and a law-of-the-wall layer right below, where the classical logarithmic-layer characteristic applies on average. Short-term current and dissipation profiles, however, deviate strongly from any steady state. In contrast, the quasi-steady bottom boundary layer behaves almost perfectly as a logarithmic layer, although periodic seiching modifies the structure in the details. The interior stratified turbulence is extremely weak, even though much of the mechanical energy is contained in baroclinic basin-scale seiching and Kelvin waves or inertial currents (large lakes). The transformation of large-scale motions to turbulence occurs mainly in the bottom boundary and not in the interior, where the local shear remains weak and the Richardson numbers are generally large.

Compressible Magnetohydrodynamic Turbulence: mode coupling, scaling relations, anisotropy, new regime and astrophysical implications

Abstract: We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas pressure dominated (high beta) and magnetically dominated (low beta) plasmas at different Mach numbers. In addition, we present results for superAlfvenic turbulence and discuss in what way it is similar to the subAlfvenic turbulence. We describe a technique of separating different magnetohydrodynamic (MHD) modes (slow, fast and Alfven) and apply it to our simulations. We show that, for both high and low beta cases, Alfven and slow modes reveal the Kolmogorov spectrum (index=-5/3) and scale-dependent Goldreich-Sridhar anisotropy, while fast modes exhibit spectrum with index=-3/2 and isotropy. We discuss the statistics of density fluctuations arising from MHD turbulence at different regimes. Our findings entail numerous astrophysical implications ranging from cosmic ray propagation to gamma ray bursts and star formation. In particular, we show that the rapid decay of turbulence reported by earlier researchers is not related to compressibility and mode coupling in MHD turbulence. In addition, we show that magnetic field enhancements and density enhancements are marginally correlated. Addressing the density structure of partially ionized interstellar gas on AU scales, we show that the new regime of MHD turbulence that we earlier reported for incompressible flows persists for compressible turbulence and therefore may provide an explanation for those mysterious structures.

Turbulence in Accretion Disks: Vorticity Generation and Angular Momentum Transport via the Global Baroclinic Instability

Abstract: In this paper we present the global baroclinic instability as a source for vigorous turbulence leading to angular momentum transport in Keplerian accretion disks. We show by analytical considerations and three-dimensional radiation-hydrodynamic simulations that, in particular, protoplanetary disks have a negative radial entropy gradient, which makes them baroclinic. Two-dimensional numerical simulations show that a baroclinic flow is unstable and produces turbulence. These findings are tested for numerical effects by performing a simulation with a barotropic initial condition, which shows that imposed turbulence rapidly decays. The turbulence in baroclinic disks transports angular momentum outward and creates a radially inward-bound accretion of matter. Potential energy is released, and excess kinetic energy is dissipated. Finally, the reheating of the gas supports the radial entropy gradient, forming a self-consistent process. We measure accretion rates in our two-dimensional and three-dimensional simulations of = -10-9 to -10-7 M? yr-1 and viscosity parameters of ? = 10-4 to 10-2, which fit perfectly together and agree reasonably with observations. The turbulence creates pressure waves, Rossby waves, and vortices in the (R, )-plane of the disk. We demonstrate in a global simulation that these vortices tend to form out of little background noise and to be long-lasting features, which have already been suggested to lead to the formation of planets.

Traveling waves in pipe flow

Abstract: A family of three-dimensional traveling waves for flow through a pipe of circular cross section is identified. The traveling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at Reynolds numbers as low as 1250. All states are immediately unstable. Their dynamical significance is that they provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.

Mixing efficiency in stratified shear flows

Abstract: ▪ Abstract The issue of the physical mechanism(s) that control the efficiency with which the density field in stably stratified fluid is mixed by turbulent processes has remained enigmatic. Similarly enigmatic has been an explanation of the numerical value of ∼0.2, which is observed to characterize this efficiency experimentally. We review recent work on the turbulence transition in stratified parallel flows that demonstrates that this value is not only numerically predictable but also that it is expected to be a nonmonotonic function of the Richardson number that characterizes preturbulent stratification strength. This value of the mixing efficiency appears to be characteristic of the late-time behavior of the turbulent flow that develops after an initially laminar shear flow has undergone the transition to turbulence through an intermediate instability of Kelvin-Helmholtz type.

Simulations of small-scale turbulent dynamo

Abstract: We report an extensive numerical study of the small-scale turbulent dynamo at large magnetic Prandtl numbers Pm. A Pm scan is given for the model case of low-Reynolds-number turbulence. We concentrate on three topics: magnetic-energy spectra and saturation levels, the structure of the field lines, and the field-strength distribution. The main results are (1) the folded structure (direction reversals at the resistive scale, field lines curved at the scale of the flow) persists from the kinematic to the nonlinear regime; (2) the field distribution is self-similar and appears to be lognormal during the kinematic regime and exponential in the saturated state; and (3) the bulk of the magnetic energy is at the resistive scale in the kinematic regime and remains there after saturation, although the spectrum becomes much shallower. We propose an analytical model of saturation based on the idea of partial two-dimensionalization of the velocity gradients with respect to the local direction of the magnetic folds. The model-predicted spectra are in excellent agreement with numerical results. Comparisons with large-Re, moderate-Pm runs are carried out to confirm the relevance of these results. New features at large Re are elongation of the folds in the nonlinear regime from the viscous scale to the box scale and the presence of an intermediate nonlinear stage of slower-than-exponential magnetic-energy growth accompanied by an increase of the resistive scale and partial suppression of the kinetic-energy spectrum in the inertial range. Numerical results for the saturated state do not support scale-by-scale equipartition between magnetic and kinetic energies, with a definite excess of magnetic energy at small scales. A physical picture of the saturated state is proposed.

Adjustment of a turbulent boundary layer to a canopy of roughness elements

Abstract: Am odel is developed for the adjustment of the spatially averaged time-mean flow of ad eep turbulent boundary layer over small roughness elements to a canopy of larger three-dimensional roughness elements. Scaling arguments identify three stages of the adjustment. First, the drag and the finite volumes of the canopy elements decelerate air parcels; the associated pressure gradient decelerates the flow within an impact region upwind of the canopy. Secondly, within an adjustment region of length of order Lc downwind of the leading edge of the canopy, the flow within the canopy decelerates substantially until it comes into a local balance between downward transport of momentum by turbulent stresses and removal of momentum by the drag of the canopy elements. The adjustment length, Lc ,i s proportional to(i) the reciprocal of the roughness density (defined to be the frontal area of canopy elements per unit floor area) and (ii) the drag coefficient of individual canopy elements. Further downstream, within a roughness-change region ,t hecanopy is shown to affect the flow above as if it were a change in roughness length, leading to the development of an internal boundary layer. A quantitative model for the adjustment of the flow is developed by calculating analytically small perturbations to a logarithmic turbulent velocity profile induced by the drag due to a sparse canopy with L/Lc � 1, where L is the length of the canopy. These linearized solutions are then evaluated numerically with a nonlinear correction to account for the drag varying with the velocity. A further correction is derived to account for the finite volume of the canopy elements. The calculations are shown to agree with experimental measurements in a fine-scale vegetation canopy, when the drag is more important than the finite volume effects, and a canopy of coarse-scale cuboids, when the finite volume effects are of comparable importance to the drag in the impact region. An expression is derived showing how the effective roughness length of the canopy, z eff 0 ,i s related to the drag in the canopy. The value of z eff varies smoothly with fetch through the adjustment region from the roughness length of the upstream surface to the equilibrium roughness length of the canopy. Hence, the analysis shows how to resolve the unphysical flow singularities obtained with previous models of flow over sudden changes in surface roughness.

Evaluation of the turbulence model influence on the numerical simulations of unsteady cavitation

Abstract: Unsteady cavitation in a Venturi-type section was simulated by two-dimensional computations of viscous, compressible, and turbulent cavitating flows. The numerical model used an implicit finite volume scheme (based on the SIMPLE algorithm) to solve Reynolds-averaged Navier-Stokes equations, associated with a barotropic vapor/liquid state law that strongly links the density variations to the pressure evolution. To simulate turbulence effects on cavitating flows, four different models were implemented (standard $k-\varepsilon$ RNG; modified $k-\varepsilon$ RNG; $k-\omega$ with and without compressibility effects), and numerical results obtained were compared to experimental ones. The standard models $k-\varepsilon$ RNG and $k-\omega$ without compressibility effects lead to a poor description of the self-oscillation behavior of the cavitating flow. To improve numerical simulations by taking into account the influence of the compressibility of the two-phase medium on turbulence, two other models were implemented in the numerical code: a modified $k-\varepsilon$ model and the $k-\omega$ model including compressibility effects. Results obtained concerning void ratio, velocity fields, and cavitation unsteady behavior were found in good agreement with experimental ones. The role of the compressibility effects on turbulent two-phase flow modeling was analyzed, and it seemed to be of primary importance in numerical simulations.

Digital Particle Image Velocimetry

Abstract: Development of aerospace airframes and propulsion systems depends on the accurate simulation of these components in their normal operating environment. Measurement of velocity fields is of critical importance in these aerodynamic studies in order to both verify the external flow field and also to determine the performance of these components/systems in the flow field. Quantitative flow field measurements were initially obtained in aerodynamic studies using Pitot static probes, which were suitable for measuring the time-average or low frequency response flow field properties at a single point in the flow.1 Hot wire anemometry proved to be a significant improvement over pitot probes by providing high frequency response velocity measurements.1 Adding more wires enabled multi-component flow measurements. By their design, hot wires are very fragile and easily damaged by foreign objects or particles in the flow. While able to provide continuous records of flow fluctuations, hot wire anemometers only perform reliably in low turbulence flows. Similar to pitot probes, hot wire anemometers were invasive and disturbed the flow field under study. The first non-invasive point velocity measurement technique was Laser Doppler Velocimetry (LDV), which used a crossed pair of laser beams to measure the velocity of seed particles entrained in the flow.1

Direct numerical simulations of turbulent channel flow with transverse square bars on one wall

Abstract: Direct numerical simulations have been carried out for a fully developed turbulent channel flow with a smooth upper wall and a lower wall consisting of square bars separated by a rectangular cavity. A wide range of of the Clauser roughness function reflects that of the form drag.

Decaying turbulence in an active-grid-generated flow and comparisons with large-eddy simulation

Abstract: Measurements of nearly isotropic turbulence downstream of an active grid are performed as a high-Reynolds-number (Re λ ≃720) update of the Comte-Bellot & Corrsin data set. Energy spectra at four downstream distances from the grid, ranging from x/M = 20 to x/M = 48, are measured and documented for subsequent initialization of, and comparison with, large-eddy simulations (LES). Data are recorded using an array of four X-wire probes which enables measurement of filtered velocities, filtered in the streamwise (using Taylor's hypothesis) and cross-stream directions. Different filter sizes are considered by varying the separation between the four probes. Higher-order statistics of filtered velocity are quantified by measuring probability density functions, and hyper-flatness and skewness coefficients of two-point velocity increments. The data can be used to study the ability of LES to reproduce both spectral and higher-order statistics of the resolved velocity field. In this study, the Smagorinsky, dynamic Smagorinsky, and dynamic mixed nonlinear models are considered. They are implemented in simulations of decaying isotropic turbulence using a pseudospectral code with initial conditions that match the measured energy spectra at x/ M = 20

Noise Investigation of a High Subsonic, Moderate Reynolds Number Jet Using a Compressible Large Eddy Simulation

Abstract: This study investigates the noise radiated by a subsonic circular jet with a Mach number of 0.9 and a Reynolds number of 65000 computed by a compressible Large Eddy Simulation (LES). First, it demonstrates the feasibility of using LES to predict accurately both the flow field and the sound radiation on a domain including the acoustic field. Mean flow parameters, turbulence intensities, velocity spectra and integral length scales are in very good agreement with experimental data. The noise generated by the jet, provided directly by the simulation, is also consistent with measurements in terms of sound pressure spectra, levels and directivity. The apparent location of the sound sources is at the end of the potential core in accordance with some experimental observations at similar Reynolds numbers and Mach numbers. Second, the noise generation mechanisms are discussed in an attempt to connect the flow field with the acoustic field. This study shows that for the simulated moderate Reynolds number jet, the predominant sound radiation in the downstream direction is associated with the breakdown of the shear layers in the central jet zone.

Local Magnetohydrodynamic Models of Layered Accretion Disks

Abstract: Using numerical MHD simulations, we have studied the evolution of the magnetorotational instability (MRI) in stratified accretion disks in which the ionization fraction (and therefore resistivity) varies substantially with height. This model is appropriate to dense, cold disks around protostars or dwarf nova systems, which are ionized by external irradiation of cosmic rays or high-energy photons. We find that the growth and saturation of the MRI occurs only in the upper layers of the disk where the magnetic Reynolds number exceeds a critical value; in the midplane the disk remains quiescent. The vertical Poynting flux into the "dead" central zone is small; however, velocity fluctuations in the dead zone driven by the turbulence in the active layers generate a significant Reynolds stress in the midplane. When normalized by the thermal pressure, the Reynolds stress in the midplane never drops below about 10% of the value of the Maxwell stress in the active layers, even though the Maxwell stress in the dead zone may be orders of magnitude smaller than this. Significant mass mixing occurs between the dead zone and active layers. Fluctuations in the magnetic energy in the active layers can drive vertical oscillations of the disk in models in which the ratio of the column density in the dead zone to that in the active layers is less than 10. These results have important implications for the global evolution of a layered disk; in particular, there may be residual mass inflow in the dead layer. We discuss the effects that dust in the disk may have on our results.

On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence

Abstract: The objective of the present study is to analyze our recent direct numerical simulation (DNS) results to explain in some detail the main physical mechanisms responsible for the modification of isotropic turbulence by dispersed solid particles. The details of these two-way coupling mechanisms have not been explained in earlier publications. The present study, in comparison to the previous DNS studies, has been performed with higher resolution (Reλ=75) and considerably larger number (80 million) of particles, in addition to accounting for the effects of gravity. We study the modulation of turbulence by the dispersed particles while fixing both their volume fraction, φv=10−3, and mass fraction, φm=1, for three different particles classified by the ratio of their response time to the Kolmogorov time scale: microparticles, τp/τk≪1, critical particles, τp/τk≈1, large particles, τp/τk>1. Furthermore, we show that in zero gravity, dispersed particles with τp/τk=0.25 (denoted here as “ghost particles”) modify the spectra of the turbulence kinetic energy and its dissipation rate in such a way that keeps the decay rate of the turbulence energy nearly identical to that of particle-free turbulence, and thus the two-way coupling effects of these ghost particles would not be detected by examining only the temporal behavior of the turbulence energy of the carrier flow either numerically or experimentally. In finite gravity, these ghost particles accumulate, via the mechanism of preferential sweeping resulting in the stretching of the vortical structures in the gravitational direction, and the creation of local gradients of the drag force which increase the magnitudes of the horizontal components of vorticity. Consequently, the turbulence becomes anisotropic with a reduced decay rate of turbulence kinetic energy as compared to the particle-free case.

Homotopy of exact coherent structures in plane shear flows

Abstract: Three-dimensional steady states and traveling wave solutions of the Navier–Stokes equations are computed in plane Couette and Poiseuille flows with both free-slip and no-slip boundary conditions. They are calculated using Newton’s method by continuation of solutions that bifurcate from a two-dimensional streaky flow then by smooth transformation (homotopy) from Couette to Poiseuille flow and from free-slip to no-slip boundary conditions. The structural and statistical connections between these solutions and turbulent flows are illustrated. Parametric studies are performed and the parameters leading to the lowest onset Reynolds numbers are determined. In all cases, the lowest onset Reynolds number corresponds to spanwise periods of about 100 wall units. In particular, the rigid-free plane Poiseuille flow traveling wave arises at Reτ=44.2 for Lx+=273.7 and Lz+=105.5, in excellent agreement with observations of the streak spacing. A simple one-dimensional map is proposed to illustrate the possible nature of ...

Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell

Abstract: Numerical experiments are conducted to study high-Rayleigh-number convective turbulence (Ra ranging from 2 × 10 6 up to 2 × 10 11 ) in a Γ = 1/2 aspect-ratio cylindrical cell heated from below and cooled from above and filled with gaseous helium (Pr = 0.7). The numerical approach allows three-dimensional velocity, vorticity and temperature fields to be analysed. Furthermore, several numerical probes are placed within the fluid volume, permitting point-wise velocity and temperature time series to be extracted. Taking advantage of the data accessibility provided by the direct numerical simulation the flow dynamics has been explored and separated into its mean large-scale and fluctuating components, both in the bulk and in the boundary layer regions

Liquid flow in microchannels: experimental observations and computational analyses of microfluidics effects

Abstract: Experimental observations of liquid microchannel flows are reviewed and results of computer experiments concerning channel entrance, wall slip, non-Newtonian fluid, surface roughness, viscous dissipation and turbulence effects on the friction factor are discussed. The experimental findings are classified into three groups. Group I emphasizes 'flow instabilities' and group II points out 'viscosity changes' as the causes of deviations from the conventional flow theory for macrochannels. Group III caters to studies that did not detect any measurable differences between micro- and macroscale fluid flow behaviors. Based on numerical friction factor analyses, the entrance effect should be taken into account for any microfluidic system. It is a function of channel length, aspect ratio and the Reynolds number. Non-Newtonian fluid flow effects are expected to be important for polymeric liquids and particle suspension flows. The wall slip effect is negligible for liquid flows in microconduits. Significant surface roughness effects are a function of the Darcy number, the Reynolds number and cross-sectional configurations. For relatively low Reynolds numbers, Re < 2000, onset to turbulence has to be considered important because of possible geometric non-uniformities, e.g., a contraction and/or bend at the inlet to the microchannel. Channel-size effect on viscous dissipation turns out to be important for conduits with Dh < 100 µm.