Showing papers in "Physics of Fluids in 2000"

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...

Quick deposition of a fluid on the wall of a tube

Abstract: We are interested in the amount of fluid left behind a drop moved inside a capillary tube. Long ago, Taylor showed that for very viscous liquids moved at small velocities, the film thickness is a monotonic increasing function of the capillary number. New data obtained with liquids of low viscosity are reported here and compared with Taylor’s law. Two successive effects are observed: above a threshold in capillary number, the film is thicker than a Taylor film; at a very high speed, the deposition law becomes a decreasing function of the drop velocity. Both behaviors are analyzed thanks to scaling arguments and shown to be consequences of inertia.

Numerical studies of flow over a circular cylinder at ReD=3900

Abstract: Flow over a circular cylinder at Reynolds number 3900 is studied numerically using the technique of large eddy simulation. The computations are carried out with a high-order accurate numerical method based on B-splines and compared with previous upwind-biased and central finite-difference simulations and with the existing experimental data. In the very near wake, all three simulations are in agreement with each other. Farther downstream, the results of the B-spline computations are in better agreement with the hot-wire experiment of Ong and Wallace [Exp. Fluids 20, 441–453 (1996)] than those obtained in the finite-difference simulations. In particular, the power spectra of velocity fluctuations are in excellent agreement with the experimental data. The impact of numerical resolution on the shear layer transition is investigated.

An approach to wall modeling in large-eddy simulations

Abstract: Channel flow with friction Reynolds number Reτ as high as 80 000 is treated by large-eddy simulation at a moderate cost, using the subgrid-scale model designed for detached-eddy simulations. It includes wall modeling, and was not adjusted for this flow. The grid count scales with the logarithm of the Reynolds number. Three independent codes are in fair agreement with each other. Reynolds-number variations and grid refinement cause trades between viscous, modeled, and resolved shear stresses. The skin-friction coefficient is too low, on the order of 15%. The velocity profiles contain a “modeled” logarithmic layer near the wall and some suggest a “resolved” logarithmic layer farther up, but the two layers have a mismatch of several units in U+.

Large-eddy simulation of a turbulent piloted methane/air diffusion flame (Sandia flame D)

Abstract: The Lagrangian Flamelet Model is formulated as a combustion model for large-eddy simulations of turbulent jet diffusion flames. The model is applied in a large-eddy simulation of a piloted partially premixed methane/air diffusion flame (Sandia flame D). The results of the simulation are compared to experimental data of the mean and RMS of the axial velocity and the mixture fraction and the unconditional and conditional averages of temperature and various species mass fractions, including CO and NO. All quantities are in good agreement with the experiments. The results indicate in accordance with experimental findings that regions of high strain appear in layer like structures, which are directed inwards and tend to align with the reaction zone, where the turbulence is fully developed. The analysis of the conditional temperature and mass fractions reveals a strong influence of the partial premixing of the fuel.

Modeling the splash of a droplet impacting a solid surface

Abstract: A numerical model is used to simulate the fingering and splashing of a droplet impacting a solid surface. A methodology is presented for perturbing the velocity of fluid near the solid surface at a time shortly after impact. Simulation results are presented of the impact of molten tin, water, and heptane droplets, and compared with photographs of corresponding impacts. Agreement between simulation and experiment is good for a wide range of behaviors. An expression for a splashing threshold predicts the behavior of the molten tin. The results of water and especially heptane, however, suggest that the contact angle plays an important role, and that the expression may be applicable only to impacts characterized by a relatively low value of the Ohnesorge number. Various experimental data of the number of fingers about an impacting droplet agree well with predictions of a previously published correlation derived from application of Rayleigh–Taylor instability theory.

Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories

Abstract: The turbulent Rayleigh–Taylor instability is investigated over a comprehensive range of fluid density ratio (R)1.3⩽R⩽50 [0.15⩽A=(R−1)/(R+1)⩽0.96] and different acceleration histories g(t) using the Linear Electric Motor. The mixing layer is diagnosed with backlit photography and laser-induced fluorescence. For a constant acceleration, the bubble (2) and spike (1) amplitudes are found to increase as hi=αiAgt2 with α2∼0.05±0.005 and α1∼α2RDα with Dα∼0.33±0.05. For temporally varying accelerations Ag(t)>0, this can be generalized to hi=2αiAS using S=[∫gdt]2/2 rather than the displacement Z=∫∫gdt′ dt. For impulsive accelerations, S remains constant during the coast phase and the amplitudes obey a power law hi∼tθi with θ2∼0.25±0.05 and θ1∼θ2RDθ with Dθ∼0.21±0.05. These values of Dα and Dθ compare favorably with numerical simulations and mix models. The average diameter at the mixing front for bubbles is found to increase as d2∼h2(1+A)/4 in qualitative agreement with “merger” models, but the associated dhi/dt i...

A note on the overlap region in turbulent boundary layers

Abstract: Two independent experimental investigations of the behavior of turbulent boundary layers with increasing Reynolds number were recently completed. The experiments were performed in two facilities, the Minimum Turbulence Level (MTL) wind tunnel at Royal Institute of Technology (KTH) and the National Diagnostic Facility (NDF) wind tunnel at Illinois Institute of Technology (IIT). Both experiments utilized oil-film interferometry to obtain an independent measure of the wall-shear stress. A collaborative study by the principals of the two experiments, aimed at understanding the characteristics of the overlap region between the inner and outer parts of the boundary layer, has just been completed. The results are summarized here, utilizing the profiles of the mean velocity, for Reynolds numbers based on the momentum thickness ranging from 2500 to 27 000. Contrary to the conclusions of some earlier publications, careful analysis of the data reveals no significant Reynolds number dependence for the parameters desc...

Effect of preferential concentration on turbulent collision rates

Abstract: The effect of particle inertia on the interparticle collision rates of a turbulent aerosol was investigated recently by Sundaram and Collins (1997) using direct numerical simulation (DNS). They observed that for values of the particle Stokes number (here defined as the ratio of the particle response time to Kolmogorov time scale) near unity, the collision frequency was enhanced by between one and two orders of magnitude. This enhancement was attributed in part to the local enrichment of the particle concentration in low-vorticity regions of the flow due to the centrifuge effect commonly referred to as preferential concentration (Eaton and Fessler 1994). Sundaram and Collins (1997) showed that the correction factor for the collision kernel in a preferentially concentrated system is g(σ), where g(r) is the particle radial distribution function and σ is the collision diameter. This paper uses DNS, in combination with statistical analysis, to study the dependence of the radial distribution function on the tur...

Length scales of turbulence in stably stratified mixing layers

Abstract: Turbulence resulting from Kelvin–Helmholtz instability in layers of localized stratification and shear is studied by means of direct numerical simulation. Our objective is to present a comprehensive description of the turbulence evolution in terms of simple, conceptual pictures of shear–buoyancy interaction that have been developed previously based on assumptions of spatially uniform stratification and shear. To this end, we examine the evolution of various length scales that are commonly used to characterize the physical state of a turbulent flow. Evolving layer thicknesses and overturning scales are described, as are the Ozmidov, Corrsin, and Kolmogorov scales. These considerations enable us to provide an enhanced understanding of the relationships between uniform-gradient and localized-gradient models for sheared, stratified turbulence. We show that the ratio of the Ozmidov scale to the Thorpe scale provides a useful indicator of the age of a turbulent event resulting from Kelvin–Helmholtz instability.

Flow structure and modeling issues in the closure region of attached cavitation

Abstract: Particle image velocimetry (PIV) and high-speed photography are used to measure the flow structure at the closure region and downstream of sheet cavitation. The experiments are performed in a water tunnel of cross section 6.35×5.08 cm2 whose test area contains transparent nozzles with a prescribed pressure distribution. This study presents data on instantaneous and averaged velocity, vorticity and turbulence when the ambient pressure is reduced slightly below the cavitation inception level. The results demonstrate that the collapse of the vapor cavities in the closure region is the primary mechanism of vorticity production. When the cavity is thin there is no reverse flow downstream and below the cavitation, i.e., a reentrant flow does not occur. Instead, the cavities collapse as the vapor condenses, creating in the process hairpin-like vortices with microscopic bubbles in their cores. These hairpin vortices, some of which have sizes as much as three times the height of the stable cavity, dominate the flo...

Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method

Abstract: A spherical drop, placed in a second liquid of the same density, is subjected to shearing between parallel plates. The subsequent flow is investigated numerically with a volume-of-fluid (VOF) method. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds number. Our simulations compare well with previous theoretical, numerical, and experimental results. For capillary numbers greater than the critical value, the drop deforms to a dumbbell shape and daughter drops detach via an end-pinching mechanism. The number of daughter drops increases with the capillary number. The breakup can also be initiated by increasing the Reynolds number.

On the decay of homogeneous isotropic turbulence

Abstract: Decaying homogeneous, isotropic turbulence is investigated using a phenomenological model based on the three-dimensional turbulent energy spectra. We generalize the approach first used by Comte-Bellot and Corrsin [J. Fluid Mech. 25, 657 (1966)] and revised by Saffman [J. Fluid Mech. 27, 581 (1967); Phys. Fluids 10, 1349 (1967)]. At small wave numbers we assume the spectral energy is proportional to the wave number to an arbitrary power. The specific case of power 2, which follows from the Saffman invariant, is discussed in detail and is later shown to best describe experimental data. For the spectral energy density in the inertial range we apply both the Kolmogorov −5/3 law, E(k)=Ce2/3k−5/3, and the refined Kolmogorov law by taking into account intermittency. We show that intermittency affects the energy decay mainly by shifting the position of the virtual origin rather than altering the power law of the energy decay. Additionally, the spectrum is naturally truncated due to the size of the wind tunnel tes...

Splashing impact of a single drop onto very thin liquid films

Abstract: Liquid films with thicknesses on the order of 1 mm were commonly used for the study of drop impingement onto a wetted surface. This is because films thinner than 1 mm are difficult to generate and measure due to capillary meniscus. In this work a novel method to produce thin films of well-defined thickness has been developed. Also a reliable process with minimum uncertainty to determine film thickness was proposed. New splashing phenomena were observed for drop impact onto thin films. It is found that the critical splash level (the threshold Weber number) is insensitive to film thickness for a given solid surface if the film is sufficiently thin. It is also shown that the critical splash level increases with liquid viscosity.

The anisotropy of the small scale structure in high Reynolds number (Rλ∼1000) turbulent shear flow

Abstract: The postulate of local isotropy (PLI) is tested in a wind tunnel uniform shear flow in which the Reynolds number is varied over the range 100⩽Rλ⩽1, 100(6.7×102⩽Rl⩽6.3×104). The high Rλ is achieved by using an active grid [Mydlarski and Warhaft, J. Fluid Mech. 320, 331 (1996)] in conjunction with a shear generator. We focus on the increments of the longitudinal velocity fluctuations in the direction of the mean shear. PLI requires that odd order moments of these quantities approach zero as Rλ→∞. Confirming the lower Reynolds number measurements of Garg and Warhaft [Phys. Fluids 10, 662 (1998)], we show that the skewness of ∂u/∂y decreases as Rλ−0.5 (with a value of 0.2 at Rλ∼1000). Although the decrease is slower than classical scaling arguments suggest, the result is consistent with PLI, indicating a negligible value at high Rλ. However, the normalized fifth moment, 〈(∂u/∂y)5〉/〈(∂u/∂y)2〉5/2, is of order 10, and shows no diminution with Reynolds number, while the normalized seventh moment increases with Rλ...

The coalescence cascade of a drop

Abstract: When a drop is deposited gently onto the surface of a layer of the same liquid, it sits momentarily before coalescing into the bottom layer. High-speed video imaging reveals that the coalescence process is not instantaneous, but rather takes place in a cascade where each step generates a smaller drop. This cascade is self-similar and we have observed up to six steps. The time associated with each partial coalescence scales with the surface tension time scale. The cascade will, however, not proceed ad infinitum due to viscous effects, as the Reynolds number of the process is proportional to the square root of the drop diameter. Viscous effects will therefore begin to be important for the very smallest drops. This cascade is very similar to the one observed previously by Charles and Mason [J. Colloid Sci. 15, 105 (1960)] for two immiscible liquids, where one of the liquids replaces the air in our setup.

Turbulent boundary layer control utilizing the Lorentz force

Abstract: Direct numerical simulations (DNS) of a turbulent channel flow at low Reynolds number (Reτ=100,200,400, where Reτ is the Reynolds number based on the wall-shear velocity and channel half-width) are carried out to examine the effectiveness of using the Lorentz force to reduce skin friction. The Lorentz force is created by embedding electrodes and permanent magnets in the flat surface over which the flow passes. Both open-loop and closed-loop control schemes are examined. For open-loop control, both temporally and spatially oscillating Lorentz forces in the near-wall region are tested. It is found that skin-friction drag can be reduced by approximately 40% if a temporally oscillating spanwise Lorentz force is applied to a Reτ=100 channel flow. However, the power to generate the required Lorentz force is an order of magnitude larger than the power saved due to the reduced drag. Simulations were carried out at higher Reynolds numbers (Reτ=200,400) to determine whether efficiency, defined as the ratio of the p...

Drop deformation, breakup, and coalescence with compatibilizer

Abstract: The effect of copolymers on the breakup and coalescence of polybutadiene (PB) drops in polydimethylsiloxane (PDMS) is studied using a four-roll mill flow cell. Copolymers are produced at the interface by a reaction between functionalized homopolymers. They reduce the interfacial tension and thus enhance breakup; they also inhibit coalescence of drops. Under the conditions of our experiments, the latter effect is much more significant than the former. For example, the addition of copolymer sufficient to reduce the interfacial tension by only 3% relative to the bare interface value is found to reduce the critical capillary number Cac for coalescence by a factor of 6. The critical capillary number for coalescence in the absence of copolymer is also measured for the first time. It is found to scale with the drop radius a as Cac∼a−0.82±0.03 and with the viscosity ratio λ as Cac∼λ−0.41±0.06.

Steady free-surface thin film flows over topography

Abstract: We consider the slow motion of a thin viscous film flowing over a topographical feature (trench or mound) under the action of an external body force. Using the lubrication approximation, the equations of motion simplify to a single nonlinear partial differential equation for the evolution of the free surface in time and space. It is shown that the problem is governed by three dimensionless parameters corresponding to the feature depth, feature width and feature steepness. Quasi-steady solutions for the free surface are reported for a wide range of these parameters. Our computations reveal that the free surface develops a ridge right before the entrance to the trench or exit from the mound and that this ridge can become large for steep substrate features of significant depth. Such capillary ridges have also been observed in the contact line motion over a planar substrate where the buildup of pressure near the contact line is responsible for the ridge. For flow over topography, the ridge formation is a manifestation of the effect of the capillary pressure gradient induced by the substrate curvature. In addition, the minimum film thickness is always found near the concave corner of the feature. Both the height of the ridge and the minimum film thickness are found to be strongly dependent on both the profile depth and steepness. Finally, it is found that either finite feature width or a significant vertical component of gravity can suppress these effects in a way that is made quantitative and which allows the operative physical mechanism to be explained.

Pore-scale simulation of dispersion

Abstract: Tracer dispersion has been simulated in three-dimensional models of regular and random sphere packings for a range of Peclet numbers. A random-walk particle-tracking (PT) method was used to simulate tracer movement within pore-scale flow fields computed with the lattice-Boltzmann (LB) method. The simulation results illustrate the time evolution of dispersion, and they corroborate a number of theoretical and empirical results for the scaling of asymptotic longitudinal and transverse dispersion with Peclet number. Comparisons with nuclear magnetic resonance (NMR) spectroscopy experiments show agreement on transient, as well as asymptotic, dispersion rates. These results support both NMR findings that longitudinal dispersion rates are significantly lower than reported in earlier experimental literature, as well as the fact that asymptotic rates are observed in relatively short times by techniques that employ a uniform initial distribution of tracers, like NMR.

On weakly nonlinear modulation of waves on deep water

Abstract: We propose a new approach for modeling weakly nonlinear waves, based on enhancing truncated amplitude equations with exact linear dispersion. Our example is based on the nonlinear Schrodinger (NLS) equation for deep-water waves. The enhanced NLS equation reproduces exactly the conditions for nonlinear four-wave resonance (the “figure 8” of Phillips) even for bandwidths greater than unity. Sideband instability for uniform Stokes waves is limited to finite bandwidths only, and agrees well with exact results of McLean; therefore, sideband instability cannot produce energy leakage to high-wave-number modes for the enhanced equation, as reported previously for the NLS equation. The new equation is extractable from the Zakharov integral equation, and can be regarded as an intermediate between the latter and the NLS equation. Being solvable numerically at no additional cost in comparison with the NLS equation, the new model is physically and numerically attractive for investigation of wave evolution.

Anisotropy of turbulence in stably stratified mixing layers

Abstract: Direct numerical simulations of turbulence resulting from Kelvin–Helmholtz instability in stably stratified shear flow are used to study sources of anisotropy in various spectral ranges. The set of simulations includes various values of the initial Richardson and Reynolds numbers, as well as Prandtl numbers ranging from 1 to 7. We demonstrate that small-scale anisotropy is determined almost entirely by the spectral separation between the small scales and the larger scales on which background shear and stratification act, as quantified by the buoyancy Reynolds number. Extrapolation of our results suggests that the dissipation range becomes isotropic at buoyancy Reynolds numbers of order 105, although we cannot rule out the possibility that small-scale anisotropy persists at arbitrarily high Reynolds numbers, as some investigators have suggested. Correlation-coefficient spectra reveal the existence of anisotropic flux reversals in the dissipation subrange whose magnitude decreases with increasing Reynolds number. The scalar concentration field tends to be more anisotropic than the velocity field. Estimates of the dissipation rates of kinetic energy and scalar variance based on the assumption of isotropy are shown to be accurate for buoyancy Reynolds numbers greater than O(102). Such estimates are therefore reliable for use in the interpretation of most geophysical turbulence data, but may give misleading results when applied to smaller-scale flows.

On the prediction of gas–solid flows with two-way coupling using large eddy simulation

Abstract: The purpose of this paper is to examine the feasibility of large eddy simulation (LES) for predicting gas–solid flows in which the carrier flow turbulence is modified by momentum exchange with particles. Several a priori tests of subgrid-scale (SGS) turbulence models are conducted utilizing results from direct numerical simulation (DNS) of a forced homogeneous isotropic turbulent flow with the back effect of the particles modeled using the point-force approximation. Properties of the subgrid-scale field are computed by applying Gaussian filters to the DNS database. Similar to the behavior observed in single-phase flows, a priori test results show that, while the local energy flux is inaccurately estimated, the overall SGS dissipation is reasonably predicted using the conventional Smagorinsky model and underestimated using the Bardina scale-similarity model. Very good agreement between model predictions and DNS results are measured using closures whose coefficients are computed using the resolved field, the so-called dynamic subgrid models, with the mixed model yielding more accurate predictions than the dynamic Smagorinsky model. A priori test results are then confirmed in actual LES calculations used to investigate the sensitivity of the predictions to mesh refinement. The LES was performed at infinite turbulent Reynolds number and for a range of particle response times and mass loadings. Grid resolution in the LES was varied from 323 to 963 collocation points, with particle sample sizes of 885 000 for each response time. LES predictions of the flow with two-way coupling are independent of mesh refinement when using the dynamic mixed model and when the particle relaxation time becomes larger than the characteristic time scale of the unresolved fluid turbulent field.

Analysis of discretization in the direct simulation Monte Carlo

Abstract: We propose a continuous-time formulation of the direct simulation Monte Carlo that allows the evaluation of the transport coefficient dependence on the time step through the use of the Green–Kubo theory. Our results indicate that the error exhibits quadratic dependence on the time step, and that for time steps of the order of one mean free time the error is of the order of 5%. Our predictions for the transport coefficients are in good agreement with numerical experiments. The calculation of the cell size dependence, first obtained by Alexander et al. [Phys. Fluids 10, 1540 (1998)], is reviewed and a correction is pointed out.

Effects of shallowness on the development of free-surface mixing layers

Abstract: The development of two shallow mixing layers with different water depths is analyzed experimentally by means of laser Doppler anemometry. The experiments show that bottom friction plays an important role in the growth of the mixing layer width and in the strength and dimensions of the large quasi two-dimensional turbulence structures therein. It is found in this study that the initial growth rate of both mixing layers is similar to what has been found for deep water plane mixing layers. Further downstream the reduction of the growth rate can be ascribed to the decrease of the velocity difference between the two ambient streams in combination with the suppression of the growth of the large turbulence structures. In the most shallow mixing layer considered, the influence of the bottom friction is dominant, impeding the further growth of the mixing layer width. It is demonstrated that the reduced mixing layer growth is related to a loss of coherence in the large turbulence structures. This loss of coherence also reduces the characteristic length-scale that establishes the lateral mixing of matter and momentum in the mixing layer. Eventually the water depth becomes the dominant length scale that determines the characteristic motion of the turbulence in that case. From the energy density spectra of the turbulence fluctuations and from the phase relation between the two velocity components in the horizontal plane it is concluded that large structures contribute most to the exchange of momentum in the mixing layer and thus to the Reynolds-stresses.

A linear process in wall-bounded turbulent shear flows

Abstract: A linear process in wall-bounded turbulent shear flows has been investigated through numerical experiments. It is shown that the linear coupling term, which enhances non-normality of the linearized Navier–Stokes system, plays an important role in fully turbulent—and hence, nonlinear —flows. Near-wall turbulence is shown to decay without the linear coupling term. It is also shown that near-wall turbulence structures are not formed in their proper scales without the nonlinear terms in the Navier–Stokes equations, thus indicating that the formation of the commonly observed near-wall turbulence structures are essentially nonlinear, but the maintenance relies on the linear process. Other implications of the linear process are also discussed.

Direct numerical simulation of turbulent thermal boundary layers

Abstract: In this paper, a method of generating realistic turbulent temperature fluctuations at a computational inlet is proposed and direct numerical simulations of turbulent thermal boundary layers developing on a flat plate with isothermal and isoflux wall boundary conditions are carried out. Governing equations are integrated using a fully implicit fractional-step method with 352×64×128 grids for the Reynolds number of 300, based on the free-stream velocity and the inlet momentum thickness, and the Prandtl number of 0.71. The computed Stanton numbers for the isothermal and isoflux walls are in good agreement with power-law relations without transient region from the inlet. The mean statistical quantities including root-mean-square temperature fluctuations, turbulent heat fluxes, turbulent Prandtl number, and skewness and flatness of temperature fluctuations agree well with existing experimental and numerical data. A quadrant analysis is performed to investigate the coherence between the velocity and temperature...

Optimal perturbations for boundary layers subject to stream-wise pressure gradient

Abstract: Configurations of perturbation velocity which optimally excite an algebraic growth mechanism in the Falkner–Skan boundary layer are studied using a direct–adjoint technique. The largest transient amplification is obtained by stream-wise oriented vortices, in agreement with previous results for the Blasius boundary layer. Adverse pressure gradient is found to increase the resulting growth, the reverse is true for accelerated flows. It is shown that optimally excited algebraic mechanisms are capable of competition with optimally excited Tollmien–Schlichting waves in super-critical flows before succumbing to viscous damping. Disturbances optimized for maximal amplification over shorter periods are generally oblique and can experience significant transient growth; it is argued that they should not be dismissed when searching for rapidly growing perturbations which may preferentially induce early transition. Optimal disturbances transform into streaks downstream of their inception, attesting to the ubiquity of these flow structures.

A vortex-based model for the subgrid flux of a passive scalar

Abstract: A model for the flux of a passive scalar by the subgrid motions in the large-eddy simulation of turbulent flow is proposed within the framework of the stretched-vortex subgrid stress model. The model is based on an analytical solution for the winding of a scalar field by an elemental subgrid vortex. This gives a tensor gradient-diffusion expression for the local flux of the scalar with subgrid turbulent diffusivity which depends upon the subgrid energy, the local cell size, and the vortex orientation in space. The scalar-flux subgrid model is tested by comparison of the results of 323 large-eddy simulation of passive-scalar transport by forced isotropic turbulence in the presence of a mean scalar gradient, with the direct-numerical simulation results of Overholt and Pope [Phys. Fluids 8, 2128 (1996)]. The present large-eddy simulation results predict that at large Taylor–Reynolds numbers, the ratio of the scalar variance to the squared product of the scalar gradient with the dissipation length of the turbulence, is asymptotic to a nearly constant value c[prime]2/(alpha1 Lepsilon)2[approximate]0.36.

Scott Russell’s wave generator

Abstract: In this paper we study the dynamics of a system consisting of a heavy box sinking vertically into water. The classic configuration is due to Scott Russell who used the sinking box in 1844 to illustrate the formation of a solitary wave in a long rectangular tank. We use a combination of computer simulation and experiment to clarify details of the wave formation and the dynamics of the sinking box. We find that as the box sinks the water is heaved up to form both the solitary wave and a reverse plunging wave which forms a vortex. This vortex follows the wave down the tank. The computer simulation uses the particle method smoothed particle hydrodynamics (SPH) which allows us to follow the formation of the waves and the dynamics of the box. The simulation results are in satisfactory agreement with the experiments. We derive scaling relations for the velocity of the box and for the amplitude of the solitary wave. These scaling relations are in reasonable agreement with the experiments and the simulations.