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Showing papers in "Physics of Fluids in 1990"


Journal ArticleDOI
TL;DR: In this paper, the geometry of solution trajectories for three first-order coupled linear differential equations can be related and classified using three matrix invariants for elementary three-dimensional flow patterns defined by instantaneous streamlines for flow at and away from no slip boundaries for both compressible and incompressible flow.
Abstract: The geometry of solution trajectories for three first‐order coupled linear differential equations can be related and classified using three matrix invariants. This provides a generalized approach to the classification of elementary three‐dimensional flow patterns defined by instantaneous streamlines for flow at and away from no‐slip boundaries for both compressible and incompressible flow. Although the attention of this paper is on the velocity field and its associated deformation tensor, the results are valid for any smooth three‐dimensional vector field. For example, there may be situations where it is appropriate to work in terms of the vorticity field or pressure gradient field. In any case, it is expected that the results presented here will be of use in the interpretation of complex flow field data.

1,727 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of turbulence on particle concentration fields and the modification of turbulence by particles has been investigated using direct numerical simulations of isotropic turbulence, where the particle motion was computed using Stokes' law of resistance and the particle volume fraction was negligible.
Abstract: The effect of turbulence on particle concentration fields and the modification of turbulence by particles has been investigated using direct numerical simulations of isotropic turbulence. The particle motion was computed using Stokes’ law of resistance and it was also assumed the particle volume fraction was negligible. For simulations in which the particles do not modify the turbulence field it was found that light particles collect preferentially in regions of low vorticity and high strain rate. For increased mass loading the particle field attenuated an increasing fraction of the turbulence energy. Examination of the spatial energy spectra showed that the fraction of turbulence kinetic energy in the high wave numbers was increased relative to the energy in the low wave numbers for increasing values of the mass loading. It was also found that the turbulence field was modified differently by light particles than by heavy particles because of the preferential collection of the light particles in low‐vorticity, high‐strain‐rate regions. Correlation coefficients between the second invariant of the deformation tensor and pressure showed little sensitivity to increased loading while correlations between enstrophy and pressure were decreased more by the light particles than by the heavy particles for increased mass loading.

610 citations


Journal ArticleDOI
TL;DR: A derivation of the convective diffusion equation for transport of a scalar quantity along a deforming interface is presented in this paper, where the direct contribution of interface deformation, giving rise to concentration variations as a result of local changes in interfacial area, is shown explicitly in a simple manner.
Abstract: A derivation of the convective‐diffusion equation for transport of a scalar quantity, e.g., surfactant, along a deforming interface is outlined. The direct contribution of interface deformation, giving rise to concentration variations as a result of local changes in interfacial area, is shown explicitly in a simple manner.

445 citations


Journal ArticleDOI
TL;DR: In this paper, a dilatation dissipation model for high Reynolds number compressible turbulence is introduced, which is predicated on the existence of shocklike structures embedded within energetic turbulent eddies.
Abstract: In this paper a concept of dilatation dissipation ed for high Reynolds number compressible turbulence is introduced. The concept is predicated on the existence of shocklike structures embedded within energetic turbulent eddies. A parametric expression for ed is found that contains calculable parameters of a turbulent field: turbulence energy and length scale, rms (turbulent) Mach number, and the kurtosis of the fluctuating velocity. The dilatation dissipation is incorporated in a second‐order closure model for compressible mixing layers and model predictions of mean and turbulence quantities are presented and, where possible, compared with experiments. It is shown that the model is capable of predicting the reduction of layer growth rates as a function of the convective Mach number Mc in accordance with Papamoschou–Roshko experiments; the computations are also shown to compare well with available measurements of Reynolds stresses at Mc=0.5–0.86. Finally, the physical implications of the new model and resu...

407 citations


Journal ArticleDOI
TL;DR: In this paper, it is shown that the stability of an elliptical flow is governed by an Ince equation and an analytical representation for a localized solution is given and establishes a direct link with previous computations and experiments.
Abstract: The three‐dimensional (3‐D) instability of a two‐dimensional (2‐D) flow with elliptical streamlines has been proposed as a generic mechanism for the breakdown of many 2‐D flows. A physical interpretation for the mechanism is presented together with an analytical treatment of the problem. It is shown that the stability of an elliptical flow is governed by an Ince equation. An analytical representation for a localized solution is given and establishes a direct link with previous computations and experiments.

322 citations


Journal ArticleDOI
TL;DR: In this paper, a theory is presented to describe the momentum transport properties of suspensions containing randomly placed, slender fibers, based on a diagrammatic representation of the multiple scattering expansion for the averaged Green's function as developed in the authors' previous work on the heat and mass transfer properties of fiber dispersions.
Abstract: A theory is presented to describe the momentum transport properties of suspensions containing randomly placed, slender fibers. The theory is based on a diagrammatic representation of the multiple scattering expansion for the averaged Green’s function as developed in the authors’ previous work on the heat and mass transfer properties of fiber dispersions [Phys. Fluids A 1, 3 (1989)]. The ‘‘best one‐body approximation’’ is used to calculate the wavenumber‐dependent, ensemble‐averaged stress for both aligned and isotropically oriented fiber dispersions. Both the dilute and semidilute concentration regimes are considered. The effective viscosity is calculated as a limit unit of the previously obtained wavenumber‐dependent properties. In the semidilute concentration regime the scaling form originally suggested by Batchelor [J. Fluid Mech. 46, 813 (1971)] is recovered for both orientation distributions and its relation to short range ‘‘screening’’ is discussed. Corrections to this result in a ‘‘semidilute expan...

318 citations


Journal ArticleDOI
TL;DR: In this paper, the energy transfer from the eddy-damped quasinormal Markovian (EDQNM) theory of turbulence at low Reynolds numbers was investigated. But the results of the simulation were not as good as those obtained by direct numerical simulations.
Abstract: Detailed computations were made of energy transfer among the scales of motion in incompressible turbulent fields at low Reynolds numbers generated by direct numerical simulations. It was observed that although the transfer resulted from triad interactions that were nonlocal in k space, the energy always transferred locally. The energy transfer calculated from the eddy‐damped quasinormal Markovian (EDQNM) theory of turbulence at low Reynolds numbers is in excellent agreement with the results of the numerical simulations. At high Reynolds numbers the EDQNM theory predicts the same transfer mechanism in the inertial range that is observed at low Reynolds numbers, i.e., predominantly local transfer caused by nonlocal triads. The weaker, nonlocal energy transfer is from large to small scales at high Reynolds numbers and from small to large scales at low Reynolds numbers.

263 citations


Journal ArticleDOI
TL;DR: In this article, the effects of compressibility on the turbulence field were studied experimentally to explore the effect of high-Reynolds-number compressible free shear layers.
Abstract: High-Reynolds-number compressible free shear layers were studied experimentally to explore the effects of compressibility on the turbulence field. A reduction in both the level and the lateral extent of turbulence fluctuations with increasing convective Mach number (Mc) (reported earlier for Mc of 0.51 and 0.64) is much higher at Mc of 0.86. The higher-order moments of turbulence fluctuations such as skewness and flatness show that the intermittency due to the excursion of large-scale structures into the free streams at the edge of shear layers was significantly reduced (both in the level and the extent) due to increased Mc.

245 citations


Journal ArticleDOI
TL;DR: In this paper, the traditional Smagorinsky subgrid-scale viscosity (CSλ)2S has been supplemented by the addition of stochastic backscatter.
Abstract: The traditional Smagorinsky subgrid‐scale viscosity (CSλ)2S has been supplemented by the addition of stochastic backscatter. The random acceleration is derived from a vector potential Cb‖S δt‖3/2(λ/δt)2g. Here S is the local strain rate, λ is the grid resolution length scale, δt is the time step, and g is a unit random Gaussian. It is found that values CS=0.2 for the Smagorinsky constant and Cb=0.4 for the backscatter constant give a robust calculation of the two‐dimensional shear mixing layer with the observed growth rate and with realistic emergence of random coherent eddy structures.

245 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical simulation of the first dipole rebound from the wall agrees with experimental visualizations, and each rebound is associated with the detachment of a secondary vorticity layer from a wall, these layers merge, and at a value of Reynolds number Re=1600, form a new dipole.
Abstract: Accurate numerical simulations of vortex dipoles impinging on flat boundaries have revealed interesting new features. In the case of free‐slip boundaries the dipole does not rebound from the wall. In the case of nonslip walls rebounding occurs and complex interactions of secondary and tertiary vortices appear. The numerical simulation of the first dipole rebound from the wall agrees with experimental visualizations. Numerical experiments extending in time beyond the real experiments show multiple rebounding. Each rebound is associated with the detachment of a secondary vorticity layer from the wall, these layers merge, and at a value of Reynolds number Re=1600, form a new dipole. This dipole has sufficient circulation to induce on itself a motion in the opposite direction to the motion of the initial dipole.

241 citations


Journal ArticleDOI
TL;DR: The fluid-dynamic and solid-body interactions among a suspension of perfectly elastic particles settling in a viscous gas are studied in this paper, where the particle velocity distribution and averages of the fluid and particle velocities are derived.
Abstract: The fluid‐dynamic and solid‐body interactions among a suspension of perfectly elastic particles settling in a viscous gas are studied. The Reynolds number of the particles, Re≡ρfUa/μ, is small but their Stokes number St≡mŪ/(6πμa2) is large, indicating that particle inertia and viscous forces in the fluid are important. Here, ρf is the density of the fluid, m is the mass of a particle, U is the average velocity of the particles, a is their radius, and μ is the fluid viscosity. Equations for the particle velocity distribution and averages of the fluid and particle velocities are derived. For very large Stokes numbers, St≫φ−3/2, where φ is the particle volume fraction, solid‐body collisions lead to a nearly Maxwellian velocity distribution. On the other hand, at smaller Stokes numbers, St≪φ−3/2, fluid‐dynamic interactions play a more important role in determining the particle velocity distribution and the distribution is not Maxwellian. The amount of energy contained in the particle velocity fluctuations is...

Journal ArticleDOI
TL;DR: In this article, a database obtained by direct numerical simulation of turbulent channel flow was used to compute the three-dimensional frequency/wave-number spectrum of wall pressure fluctuations and to evaluate the similarity form for the power spectrum.
Abstract: A database obtained by direct numerical simulation of turbulent channel flow was used to compute the three‐dimensional frequency/wave‐number spectrum of wall‐pressure fluctuations. The spectrum was used to deduce scaling laws for pressure fluctuations and to evaluate the similarity form for the power spectrum. The convection velocity as a function of frequency, wave number, and spatial and temporal separations was calculated and compared with the experimental data. The problem of artificial ‘‘acoustics’’ in numerical simulation of incompressible flows is discussed.

Journal ArticleDOI
TL;DR: In this paper, the renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients.
Abstract: The renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients. The model results from a perturbation expansion that is truncated systematically at second order with subsequent terms contributing no further information. The resulting turbulence model applied to both low and high Reynolds number flows without requiring wall functions or ad hoc modifications of the equations. All constants are derived from the renormalization group procedure; no adjustable constants arise. The model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in noncircular ducts.

Journal ArticleDOI
TL;DR: In this article, the planarization of 1-4 μm thick liquid epoxy films over 25-200 μm wide isolated trenches on a silicon substrate during spin coating is determined by photochemically hardening the film and measuring the film profiles over the trenches with a profilometer.
Abstract: The planarization, that is leveling, of 1–4 μm thick liquid epoxy films over 25–200 μm wide isolated trenches on a silicon substrate during spin coating is determined by photochemically hardening the film and measuring the film profiles over the trenches with a profilometer. The profiles are quantitatively described by a simple lubrication theory that takes advantage of the thinness of the film compared to the feature width, the narrowness of the feature width compared with the distance of the feature from the substrate center, and the rapidity of change in the film profile compared to the overall rate of centrifugally driven film thinning. For a fixed ratio of film thickness to trench depth hf/d, the experimental data fall on a single curve when planarization is plotted against a dimensionless parameter Ω2≡ρω2w3r0/γhf, where ρ is the density of the liquid film, ω is the substrate angular velocity, w is the trench width, r0 is the radial position of the trench, and γ is the film surface tension. For a fix...

Journal ArticleDOI
TL;DR: In this article, a model for the joint pdf of velocity and dissipation following a fluid particle is developed by constructing stochastic models for the velocity and dissolution following a particle.
Abstract: In probability density function (pdf) methods, statistics of inhomogeneous turbulent flow fields are calculated by solving a modeled transport equation for a one‐point joint probability density function. The method based on the joint pdf of velocity and fluid compositions is particularly successful since the most important processes—convection and reaction—do not have to be modeled. However, this joint pdf contains no length‐scale or time‐scale information that can be used in the modeling of other processes. This deficiency can be remedied by considering the joint pdf of velocity, dissipation, and composition. In this paper, by reference to the known properties of homogeneous turbulence, a modeled equation for the joint pdf of velocity and dissipation is developed. This is achieved by constructing stochastic models for the velocity and dissipation following a fluid particle.

Journal ArticleDOI
TL;DR: In this paper, the results of numerical simulations of the lattice Boltzmann equation in three-dimensional porous geometries constructed by the random positioning of penetrable spheres of equal radii are presented.
Abstract: The results of numerical simulations of the lattice‐Boltzmann equation in three‐dimensional porous geometries constructed by the random positioning of penetrable spheres of equal radii are presented. Numerical calculations of the permeability are compared with previously established rigorous variational upper bounds. The numerical calculations approach the variational bounds from below at low solid fractions and are always within one order of magnitude of the best upper bound at high solid fractions ranging up to 0.98. At solid fractions less than 0.2 the calculated permeabilities compare well with the predictions of Brinkman’s effective‐medium theory, whereas at higher solid fractions a good fit is obtained with a Kozeny–Carman equation.

Journal ArticleDOI
TL;DR: In this paper, a simple experiment to study the mixing of two different density fluids by the Rayleigh-Taylor instability has been performed and the results show a contraction in the width of the mixing interface that is a result of the stretching action of the large-scale motion.
Abstract: A simple experiment to study the mixing of two different density fluids by the Rayleigh–Taylor instability has been performed. Several experiments are reported for nominally one‐dimensional homogeneous mixing and for experiments characterized by a large two‐dimensional motion superimposed on the mixing process. The one‐dimensional experiments show a plane mixing region that expands by Rayleigh–Taylor instabilities. The two‐dimensional experiments show a contraction in the width of the mixing interface that is a result of the stretching action of the large‐scale motion. Image analysis techniques have been developed to provide quantitative measurements for use in a ‘‘two‐fluid’’ model of the mixing phenomena.

Journal ArticleDOI
TL;DR: In this article, a three-dimensional adaptive mesh code is used to search for singularities in the incompressible Euler equations, and the maximum vorticity eventually grows only exponentially.
Abstract: A three‐dimensional adaptive mesh code is used to search for singularities in the incompressible Euler equations. For the initial conditions examined, the maximum vorticity eventually grows only exponentially. The small scales are quasi‐two‐dimensional and the vorticity has a pronounced tendency to develop sharp jumps in magnitude. The vorticity is very nearly parallel to the eigenvector of the rate‐of‐strain matrix whose eigenvalue is the smallest in magnitude. This eigenvalue is positive and much smaller than the others.

Journal ArticleDOI
TL;DR: In this paper, the structure of the subgrid scale fields in plane channel flow has been studied at various stages of the transition process to turbulence, and the results of a large eddy simulation of transition on a flat-plate boundary layer compare quite well with those of a direct simulation, and require only a small fraction of the computational effort.
Abstract: The structure of the subgrid scale fields in plane channel flow has been studied at various stages of the transition process to turbulence. The residual stress and subgrid scale dissipation calculated using velocity fields generated by direct numerical simulations of the Navier-Stokes equations are significantly different from their counterparts in turbulent flows. The subgrid scale dissipation changes sign over extended areas of the channel, indicating energy flow from the small scales to the large scales. This reversed energy cascade becomes less pronounced at the later stages of transition. Standard residual stress models of the Smagorinsky type are excessively dissipative. Rescaling the model constant improves the prediction of the total (integrated) subgrid scale dissipation, but not that of the local one. Despite the somewhat excessive dissipation of the rescaled Smagorinsky model, the results of a large eddy simulation of transition on a flat-plate boundary layer compare quite well with those of a direct simulation, and require only a small fraction of the computational effort. The inclusion of non-dissipative models, which could lead to further improvements, is proposed.

Journal ArticleDOI
TL;DR: In this paper, a boundary integral method was used to compute the wave growth on a cylindrical jet and the initial wave growth is in agreement with Rayleigh's linear theory, when followed to completion these waves pinch off large drops separated by smaller satellite drops that decrease in size with decreasing wavelength.
Abstract: Computations of finite‐amplitude, spatially periodic wave growth on a cylindrical jet have been carried out using a boundary integral method. The initial wave growth is in agreement with Rayleigh’s linear theory. When followed to completion these waves pinch off large drops separated by smaller satellite drops (spherules) that decrease in size with decreasing wavelength. The computed sizes of both drops and satellites agree with experiment. It is found that satellites will form for all unstable wave numbers. The small satellites that are computed at wave numbers near the critical wave number were not predicted by near‐linear analysis but are observed in experimental photographs of jet breakup. Computation of the collapse of elongated satellites shows short waves propagating on their surfaces.

Journal ArticleDOI
TL;DR: The existence of a minimum in the cylindrical Poiseuille flow of a rarefied gas has been known since the experiments of Knudsen [Ann. Phys. 4, 75 (1909)] as discussed by the authors.
Abstract: The existence of a minimum in the cylindrical Poiseuille flow of a rarefied gas has been known since the experiments of Knudsen [Ann. Phys. 4, 75 (1909)]. Previously, the phenomenon has been studied with models of the Boltzmann equation, but results for the Boltzmann equation itself have not been reported. In the present paper, proceeding from recent studies, first the SN numerical algorithm for solving the linearized Boltzmann equation for the cylindircal geometry is outlined. Then, explicit numerical results for a rigid sphere gas and the boundary condition of diffuse specular reflection are obtained. The results show a minimum of the flow rate, and generally, provide a good description of the experimental data.

Journal ArticleDOI
TL;DR: In this paper, the boundary between absolute and convective instability of two-dimensional inertial jets and wakes is determined as a function of the ratio of jet/wake to ambient density.
Abstract: The boundary between absolute and convective (linear) instability of two‐dimensional inertial jets and wakes is determined as a function of the ratio of jet/wake to ambient density, as well as the ratio of mixing layer thickness to jet/wake width, the velocity ratio, and the Reynolds number. For this, a viscous, heat‐conducting ideal gas is taken as the fluid, a zero Mach number, no buoyancy and a parallel basic flow are assumed, and the density variation is achieved by specifying a mean temperature profile similar to the velocity profile. Considering both ‘‘varicose’’ and ‘‘sinuous’’ disturbances, results are obtained for the inviscid top‐hat jet/wake bounded by two vortex sheets, the inviscid jet with continuous velocity and density profiles, and the viscous wake. For the latter, both constant and temperature‐dependent viscosity are investigated. In all the cases it is found that low density of the high‐speed fluid promotes absolute instability, while low density of the low‐speed fluid has the opposite ...

Journal ArticleDOI
TL;DR: In this article, a stochastic model for velocity gradients following fluid particles in incompressible, homogeneous, and isotropic turbulence is presented and demonstrated, and the model is constructed so that the velocity gradient satisfies the incompressibility and isotropy requirements exactly.
Abstract: In this paper a stochastic model for velocity gradients following fluid particles in incompressible, homogeneous, and isotropic turbulence is presented and demonstrated. The model is constructed so that the velocity gradients satisfy the incompressibility and isotropy requirements exactly. It is further constrained to yield the first few moments of the velocity gradient distribution similar to those computed from full turbulence simulations (FTS) data. The performance of the model is then compared with other computations from FTS data. The model gives good agreement of one‐time statistics. While the two‐time statistics of strain rate are well replicated, the two‐time vorticity statistics are not as good, reflecting perhaps a certain lack of embodiment of physics in the model. The performance of the model when used to compute material element deformation is qualitatively good, with the material line‐element growth rate being correct to within 5% and that of surface element correct to within 20% for the lowest Reynolds number considered. The performance of the model is uniformly good for all the Reynolds numbers considered. So it is conjectured that the model can be used even in inhomogeneous, high‐Reynolds‐number flows, for the study of evolution of surfaces, a problem that is of interest particularly to combustion researchers.

Journal ArticleDOI
TL;DR: In this article, the development, stability, and disintegration of liquid sheets issuing from a two-dimensional air-assisted nozzle have been studied using a phase Doppler particle analyzer.
Abstract: The development, stability, and disintegration of liquid sheets issuing from a two‐dimensional air‐assisted nozzle have been studied. Detailed measurements of mean drop size (SMD) and velocity have been made using a phase Doppler particle analyzer. Without air flow the liquid sheet converges toward the axis as a result of surface tension forces. There is a linear increase in convergence length with increases in liquid flow rate. With air flow a quasi‐two‐dimensional expanding spray is formed. It is shown that the air flow is responsible for the formation of large, ordered, and small, chaotic ‘‘cell’’ structures. These structures are bounded by large diameter ligaments containing thin membranes inside. The ligaments are the origin of the large droplets in the spray and the membranes contribute to the formation of the smaller droplets. The air flow causes small variations in sheet thickness to develop into major disturbances with the result that disruption starts before the formation of the main breakup region. The phase Doppler measurements show that the spray two‐dimensionality breaks down at a short distance from the nozzle in the downstream region. Boundary layer growth and turbulent mixing result in the redistribution of droplets according to their size class. The droplets detached from the central part of the sheet are subject to further breakup because of high local relative velocities. Droplets detached from the rims are outside the main air flow field and have diameters close to that of the rims. The spray acquires a Gaussian velocity profile in both the Y and Z directions.

Journal ArticleDOI
TL;DR: The influence of intermittency on turbulent diffusion is expressed in terms of the statistics of the dissipation field by using the concept of scale similarity of the breakdown coefficients (bdc) as mentioned in this paper.
Abstract: The influence of intermittency on turbulent diffusion is expressed in terms of the statistics of the dissipation field The high‐order moments of relative diffusion are obtained by using the concept of scale similarity of the breakdown coefficients (bdc) The method of bdc is useful for obtaining new models and general results, which then can be expressed in terms of multifractals In particular, the concavity and other properties of spectral codimension are proved Special attention is paid to the logarithmically periodic modulations The parametrization of small‐scale intermittent turbulence, which can be used for large‐eddy simulation, is presented The effect of molecular viscosity is taken into account in the spirit of the renorm group, but without spectral series, e expansion, and fictitious random forces

Journal ArticleDOI
TL;DR: In this article, the authors introduced the concept of apparent permeability to establish a relationship existing between mean velocity and macroscopic pressure gradient characterized by a finite Reynolds number flow, and showed that the apparent permeabilities of both square and hexagonal monodisperse arrays are observed to diminish with increasing Reynolds number.
Abstract: Flow fields within spatially periodic arrays of cylinders arranged in square and hexagonal lattices are calculated, with microscale Reynolds number ranging between zero and 200, employing a finite element numerical scheme. The terminology of an ‘‘apparent permeability’’ is introduced to establish a relationship existing between mean velocity and macroscopic pressure gradient characterized by a finite Reynolds number flow. In contrast with the low Reynolds number ‘‘true ’’ permeability, the apparent permeability is shown here to generally depend upon the direction of the applied pressure gradient, owing to nonlinearities existing within the local fluid motion. The orientation‐dependent permeabilities of both square and hexagonal monodisperse arrays are observed to diminish with increasing Reynolds number. Similar behavior is also observed for a bidisperse square array, though the apparent permeability of the latter is shown less sensitive to Darcy velocity orientation at large Reynolds numbers in comparison to the corresponding monodisperse square array, for all cylinder concentrations examined.

Journal ArticleDOI
TL;DR: In this paper, the Navier-Stokes equations are solved by a finite difference method, and the interface is kept sharp by front tracking, while the difference between the large-amplitude stages of flows initiated by two and three-dimensional perturbations is discussed.
Abstract: The fully three‐dimensional deformation of an interface between two fluids resulting from a Rayleigh–Taylor instability is studied numerically in the limit of weak stratification. The Navier–Stokes equations are solved by a finite difference method, and the interface is kept sharp by front tracking. The difference between the large‐amplitude stages of flows initiated by two‐ and three‐dimensional perturbations is discussed.

Journal ArticleDOI
TL;DR: In this article, the weakly nonlinear stability of two-phase core-annular film flows in the limit of small film thickness and in the presence of both viscosity stratification and interfacial tension is examined.
Abstract: In this paper the weakly nonlinear stability of two‐phase core‐annular film flows in the limit of small film thickness and in the presence of both viscosity stratification and interfacial tension is examined. Rational asymptotic expansions are used to derive some novel nonlinear evolution equations for the interface between the phases. The novel feature of the equations is that they include a coupling between core and film dynamics thus enabling a study of its effect on the nonlinear evolution of the interface. The nonlinear interfacial evolution is governed by modified Kuramoto–Sivashinsky equations in the cases of slow and moderate flow [the former also developed by Frenkel, Sixth Symposium on Energy Engineering Sciences (Argonne Lab. Pub. CONF‐8805106, 1988), p.100, using different asymptotic methods], which include new nonlocal terms that reflect core dynamics. These equations are solved numerically for given initial conditions and a range of parameters. Some interesting behavior results, such as tran...

Journal ArticleDOI
TL;DR: In this paper, a direct simulation of turbulent flow in a channel is analyzed by the method of empirical eigenfunctions (Karhunen-Loeve procedure, proper orthogonal decomposition).
Abstract: A direct simulation of turbulent flow in a channel is analyzed by the method of empirical eigenfunctions (Karhunen-Loeve procedure, proper orthogonal decomposition). This analysis reveals the presence of propagating plane waves in the turbulent flow. The velocity of propagation is determined by the flow velocity at the location of maximal Reynolds stress. The analysis further suggests that the interaction of these waves appears to be essential to the local production of turbulence via bursting or sweeping events in the turbulent boundary layer, with the additional suggestion that the fast acting plane waves act as triggers.

Journal ArticleDOI
TL;DR: In this paper, the effects of transverse strain on an initially two-dimensional turbulent boundary layer are studied in a direct numerical simulation of a planar channel flow with impulsively started transverse pressure gradient.
Abstract: The effects of transverse strain on an initially two‐dimensional turbulent boundary layer are studied in a direct numerical simulation of a planar channel flow with impulsively started transverse pressure gradient. Consistent with experiments in three‐dimensional boundary layers, the simulation shows a decrease in the Reynolds shear stress with increasing transverse strain. Also, the directions of the Reynolds shear stress vector and the mean velocity gradient vector were found to differ. In addition, the simulation shows a drop in the turbulent kinetic energy. Terms in the Reynolds stress transport equations were computed. The balances indicate that the decrease in turbulent kinetic energy is a result of a decrease in turbulence production, along with an increase in turbulent dissipation. Intuitive reasoning and current turbulence models would predict an increase in kinetic energy along with increases in production and dissipation rates as a result of increased mean‐flow strain rate. Later in the evolution of the flow, both turbulence production and dissipation increase.