Volume 15, Issue 3, March 2003
 LETTERS


Experimental visualization of Lagrangian coherent structures in aperiodic flows
View Description Hide DescriptionA technique is introduced for extracting the coherence time scale of Lagrangian coherent structures (LCS) in aperiodic flows from experimental, light intensity time series. The technique employs digital photography to record the transport of passive tracers in a chaotic instantaneous flow. Coherent eddies are detected by timeaveraging the instantaneous light intensity field on finitesize temporal windows. The optimal size of the timeaverage window (the coherence time scale of the LCS) is extracted from the light intensity field using statistical scaling arguments based on the central limit theorem. The technique is applied to visualizeLCS in the vicinity of a surfacepiercing rectangular block mounted at one corner of a rectangular open channel.

Inapplicability of the dynamic Clark model to the large eddy simulation of incompressible turbulent channel flows
View Description Hide DescriptionThe inapplicability of the dynamic Clark model to the large eddy simulation of incompressible turbulent channel flows is proved both analytically and numerically. The reason is neither a negative subgridscale eddyviscosity nor an incorrect nearwall scaling, but a negative effective viscosity in the viscous sublayer for the tensor diffusivity term that models the sum of the Leonard and the cross terms.
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 ARTICLES


Statistical theory of compressible turbulence based on massweighted averaging, with an emphasis on a cause of countergradient diffusion
View Description Hide DescriptionStatistical theory of inhomogeneous compressible turbulence is formulated on the basis of massweighted averaging. The velocity and the concentration of matters are resolved into the massweighted means and the fluctuations around them, whereas the density and the pressure are resolved into the ensemble means and the fluctuations around them. The former fluctuations multiplied by the density are normalized by the mean density, leading to new variables characterizing velocity and concentration fluctuations. In the use of those variables, turbulent fluxes may be examined in the presence of spatially varying mean velocity and scalar, as in incompressible flow. With the aid of the theoretical results about the fluxes, a cause of countergradient diffusion is discussed in the context of a premixed turbulentflame.

Chemical fronts in HeleShaw cells: Linear stability analysis based on the threedimensional Stokes equations
View Description Hide DescriptionWe present linear stability results based on the threedimensional Stokes equations for chemically reacting, propagating fronts giving rise to an unstable density stratification in a HeleShaw cell. The results are compared with the experiments in M. Böckmann and S. C. Müller [Phys. Rev. Lett. 85, 2506 (2000)], as well as with a corresponding linear stability analysis based on the Darcy equations that was performed in A. De Wit [Phys. Rev. Lett. 87, 054502 (2001)]. The reason for the good agreement between these earlier Darcy data and the experimentally observed growth rates is found in the relatively low experimental value of the Rayleigh number, for which the flow is approximately of Poiseuille type. Already for Ra values as low as 300, we observe a discrepancy between the stability results based on the Darcy and Stokes equations, respectively, with the Darcy results overpredicting both the most amplified wavenumber, as well as the corresponding growth rate, by about a factor of two. This indicates that threedimensional effects quickly gain importance as Ra increases, so that the stability analysis needs to be based on the full, threedimensional Stokes equations. The stability results based on the Stokes equations furthermore demonstrate the stabilizing influences of both an increasing interfacial thickness, as well as increasing frontal propagation velocities, confirming the earlier Darcybased findings by De Wit. An argument in terms of vorticity is forwarded to explain the latter effect. A more rapidly advancing front deposits vorticity over a wider layer of fluid particles, so that the concentrated regions of vorticity needed for rapid instability growth cannot form. Somewhat surprisingly, however, slowly propagating fronts are seen to be more unstable than nonreacting fronts of equivalent thickness, as the chemical reaction leads to the formation of more compact perturbations in the interfacial region.

Equilibrium similarity, effects of initial conditions and local Reynolds number on the axisymmetric wake
View Description Hide DescriptionEquilibrium similarity considerations are applied to the axisymmetric turbulent wake, without the arbitrary assumptions of earlier theoretical studies. Two solutions for the turbulent flow are found: one for infinite localReynolds number which grows spatially as and another for small localReynolds number which grows as Both solutions can be dependent on the upstream conditions. Also, the localReynolds number diminishes with increasing downstream distance, so that even when the initial Reynolds number is large, the flow evolves downstream from one state to the other. Most of the available experimental data are at too low an initial Reynolds number and/or are measured too near the wake generator to provide evidence for the solution. New results, however, from a laboratory experiment on a disk wake and direct numerical simulations (DNS) are in excellent agreement with this solution, once the flow has had large enough downstream distance to evolve. Beyond this the ratio of turbulence intensity to centerline velocity deficit is constant, until the flow unlocks itself from this behavior when the localReynolds number goes below about 500 and the viscous terms become important. When this happens the turbulence intensity ratio falls slowly until the region is reached. No experimental data are available far enough downstream to provide unambiguous evidence for the solution. The prediction that the flow should evolve into such a state, however, is confirmed by recent DNS results which reach the solution at about 200 000 momentum thicknesses downstream. After this the turbulence intensity ratio is again constant, until boxsize affects the calculation and the energy decays exponentially.

Vortex streets generated by a moving momentum source in a stratified fluid
View Description Hide DescriptionThe aim of this paper is to present the results of experiments conducted in a stratified fluid with a momentum source modeled by a moving jet in the asymptotic case when the size of the source is negligibly small but the resulting force (momentum flux), which acts on the fluid, remains finite. In this case the forcing may be considered as a “point” force moving in the fluid and the problem has no obvious characteristic length scale, compared to the case of a bluff body. The latter, towed horizontally in the stratified fluid, frequently leaves behind a highly organized vortex street, the characteristics of which strongly depend on the body diameter. It is shown that a similar type of the vortex streets may be generated by a “point” momentum source and conditions when this occurs are found. Experimental data on the characteristics of the vortex streets are presented and compared with the towed body case.

The statistics of power injected in a closed turbulent flow: Constant torque forcing versus constant velocity forcing
View Description Hide DescriptionA confined turbulent flow forced by two counterrotating stirrers is investigated. Two processes of energy injection are studied. In the first one, called the Ω mode, the forcing devices are driven at constant angular velocity. In the second, called the Γ mode, the forcing devices are driven with a constant torque. For each forcing mode, the power injected and the wall pressure fluctuations are simultaneously measured in the range of Reynolds numbers from 20 000 to 500 000. For each mode, the probability density functions of the injected power are approximately Gaussian with slight reversed skewness between both modes. These asymmetries are due to an excess of low dissipation events compared to high dissipation events. For each mode, the skewness varies as the logarithm of the Reynolds number. On the other hand, the fluctuation rate of the injected power does not depend on the Reynolds number whatever the forcing modes, however, their magnitudes are drastically different. A value of only 5.9% is obtained for the Γ mode against 10.9% for the Ω mode. The local properties of the turbulence at smaller scales, deduced from either hot film anemometry or wall pressure measurements, are identical for both forcing modes. The mean dissipated power remains unchanged as well. It is then deduced that the injected power fluctuations are caused by the turbulence feedback rather than the turbulence production. The difference in the fluctuation rates is a consequence of the natural control of the turbulence feedback that occurs for the Γ mode.

The effect of electric fields on the rupture of thin viscous films by van der Waals forces
View Description Hide DescriptionWe examine the stability of a thin twodimensional incompressible liquid film when an electric field is applied in a direction parallel to the initially flat bounding fluid interfaces, and study the competition between surface tension, van der Waals, viscous, and electrically induced forces. The film is assumed to be sufficiently thin, and the surface tension and electrically induced forces are large enough that gravity can be ignored to the leading order. We analyze the nonlinear stability of the flow by deriving and numerically solving a set of nonlinear evolution equations for the local film thickness and the horizontal velocity. We find that the electric field forces enhance the stability of the flow and can remove rupture. If rupture occurs then the form of the singularity, to leading order, is that found in the absence of an electric field.

Experimental friction factor of a liquid flow in microtubes
View Description Hide DescriptionThe friction factor of a water laminar flow through fused silica microtubes with diameters ranging from 50 to 530 μm is investigated experimentally. The existing works in the literature are analyzed. They show a range of experimental results which agree or not with the conventional theory. Pressure drops and flowing masses are measured to determine the flow characteristics using a transient method. Several experiments are developed for two fluids (distilled and tap water) and tube compositions. The experimental results are discussed. The disparity from the classical theory is found to be due to the fluid’s ionic composition. The experimental results for tap water and classical fused silica surfaces indicate a disparity from the conventional theory. A friction factor increase with small uncertainties is observed for decreasing diameters.

The velocity distribution function in direct simulation Monte Carlo method with an application to extended thermodynamics
View Description Hide DescriptionA numerical experiment is carried out to prove the difference between the value of the kinetic temperature and that of the thermodynamic temperature in a gas in the presence of molecular transport. As a reference situation the velocity distribution function is evaluated between two concentric cylinders at different wall temperatures. A direct simulation Monte Carlo method (DSMC) is adopted for various Knudsen numbers Kn and comparisons are made with existing data. The results prove quantitatively that the difference between the two differently defined temperatures increases with Kn and with the temperature gradient, as predicted by the theory for systems which are almost in thermodynamical equilibrium. The present article does not aim to validate DSMC, but rather to illustrate how the method can be used to address fundamental issues in gas dynamics.

Threedimensional linear stability analysis of the flow in a liquid spherical droplet driven by an alternating magnetic field
View Description Hide DescriptionThe paper presents a numerical stability analysis of the flow driven by an alternating (ac)magnetic field in an electromagnetically levitated liquid metaldroplet. The basic axisymmetric flow is found to become unstable at Reynolds numbers in the order of 100. The critical Reynolds number and the corresponding most unstable azimuthal wave number m are found for several configurations of the magnetic field depending on the skindepth For a uniform external acmagnetic field the azimuthal wave number of the most unstable mode is An additional steady (dc) magnetic field imposed along the axis of symmetry increases the stability of the flow.

Thin front propagation in steady and unsteady cellular flows
View Description Hide DescriptionFront propagation in twodimensional steady and unsteady cellular flows is investigated in the limit of very fast reaction and sharp front, i.e., in the geometrical optics limit. For the steady flow, a simplified model allows for an analytical prediction of the front speed dependence on the stirring intensity which is in good agreement with numerical estimates. In particular, at large the behavior is predicted. By adding small scales to the velocity field we found that their main effect is to renormalize the flow intensity. In the unsteady (timeperiodic) flow, we found that the front speed locks to the flow frequency and that, despite the chaotic nature of the Lagrangiandynamics, the front evolution is chaotic only for a transient. Asymptotically the front evolves periodically and chaos manifests only in its spatially wrinkled structure.

Vapor flows condensing at incidence onto a plane condensed phase in the presence of a noncondensable gas. I. Subsonic condensation
View Description Hide DescriptionA steady flow of a vapor in a half space condensing onto a plane condensed phase of the vapor at incidence is considered in the case where another gas that neither evaporates nor condenses (the noncondensable gas) is present near the condensed phase. The behavior of the vapor and noncondensable gas is investigated on the basis of kinetic theory under the assumption that the molecules of the noncondensable gas are mechanically identical with those of the vapor. In particular, the relation, among the parameters of the vapor at infinity (the pressure, temperature, and flow velocity of the vapor), those related to the condensed phase (the temperature of the condensed phase and the corresponding saturation pressure of the vapor), and the amount of the noncondensable gas, that admits a steady solution is obtained numerically by the use of a modelBoltzmann equation proposed by Garzó et al. [Phys. Fluids A 1, 380 (1989)]. The present analysis is the continuation of an earlier work by Sone et al. [Transp. Theory Stat. Phys. 21, 297 (1992)], where the case in which the vapor flow is condensing perpendicularly onto the condensed phase is investigated exclusively. The case with subsonic condensation is discussed in the present paper (the case with supersonic condensation is left to the subsequent paper).

Wallpressurearray measurements beneath a separating/reattaching flow region
View Description Hide DescriptionA database of wallpressurearray measurements was compiled for studying the space–time character of the surfacepressure field within a separating/reattaching flow region. The experimental setup consisted of a long splitter plate located within the wake of a fence and instrumented with an array of flushmounted microphones. Data were acquired for a Reynolds number of 7900, based on the fence height above the splitter plate. Two distinctive regions, defined based on their location relative to the position of the mean reattachment point of the shear layer, emerged from this investigation. Upstream, from the fence to the surfacepressure signature was dominated by large time scale disturbances and an upstream convection velocity of Beyond turbulent structures with smaller time scales and a downstream convection velocity of generated most of the pressure fluctuations. Interestingly, the lowfrequency wallpressure signature typically associated with the flapping of the separated shear layer was found to be composed of standing and downstream/upstream propagating wave components. The latter seemed to originate from a point near the middle of the reattachment zone, suggesting the existence of an absolute instability of the recirculation bubble, which may be the cause of the flapping of the shear layer.

Shortwave, localized disturbances in jets, with applications to flows on a beta plane with topography
View Description Hide DescriptionWe examine the stability of jets over topography on the socalled barotropic beta plane (which models oceanic currents in midlatitudes). Attention is focused on disturbances with a large wave number, for which an asymptotic solution of the normalmode eigenvalue problem is presented. It is demonstrated that shortwave modes, if they exist, are localized in narrow strips “centered” at local extrema of the velocity profile (y is the transverse variable). It is further shown that an extremum, say can support a shortwave mode only if the vorticity gradient and potential vorticity (PV) gradient at are of opposite signs. If they are, the leadingorder solution of the eigenvalue problem describes a mode with a phase speed slightly larger than if is a maximum; or slightly smaller than if is a minimum. In other words, the mode does not have critical levels in the vicinity of although it may have them elsewhere, at a distant point. If that indeed happens, an additional condition is required to guarantee the existence of the mode: namely, the PV gradient at and that at the critical level must have opposite signs. If they do, the mode exists and is weakly unstable (the phase speed has a small imaginary part). Thus, a change of sign of the PV gradient does not necessarily destabilize the flow; and in order to guarantee instability, the PV gradient should have opposite signs at the “important” points, i.e., the localization point and critical level. The asymptotic results are tested against the numerical solution of the exact normalmode eigenvalue problem. The former and the latter are in good agreement, and not only for large wave numbers, but also for moderate ones. It is also demonstrated that our approach can be applied to other cases of jets in fluids and plasmas.

The undular hydraulic jump in turbulent open channel flow at large Reynolds numbers
View Description Hide DescriptionPlane flow over a bottom of constant slope is considered in the double limit of very large Reynolds numbers, i.e., and Froude numbers approaching the critical value, i.e., with Fully developed turbulent flow far upstream is assumed. Owing to the large Reynolds number the inclination angle of the bottom, α, is small. The undular jump is analyzed for a parameter regime that is characterized by values of α that are of the same order of magnitude as i.e., The firstorder perturbation equations contain unknown functions that are determined from a solvability condition of the secondorder equations. Without making use of a turbulencemodel or empirical parameters, the following equation is obtained for the shape of the free surface: with as denotes the firstorder perturbation of the surface elevation as a function of the nondimensional longitudinal coordinate and the parameter characterizes the slow changes of amplitudes and wavelengths, respectively. Numerical solutions of this ordinary differential equation are compared with experimental data.

Force on a spinning sphere moving in a rarefied gas
View Description Hide DescriptionThe force acting on a spinning sphere moving in a rarefied gas is calculated. It is found to have three contributions with different directions. The transversal contribution is of opposite direction compared to the socalled Magnus force normally exerted on a sphere by a dense gas. It is given by where is the accommodation coefficient of tangential momentum, R is the radius of the sphere, m is the mass of a gas molecule, n is the number density of the surrounding gas, is the angular velocity, and is the velocity of the center of the sphere relative to the gas. The dimensionless factor ξ is close to unity, but depends on ω and κ, the heat conductivity of the body.

Freesurface evolution due to an impulsive bottom sink at uniform depth
View Description Hide DescriptionThe freesurface evolution due to an impulsively started point sink at the bottom of a uniform horizontal layer of inviscid and incompressible fluid is investigated analytically. A thirdorder smalltime expansion of the full nonlinear problem is performed. The dip formation above the sink depends on the Froude number of the sink. An initially critical Froude number 0.1376 is found for the sign change of the thirdorder elevation above the point sink. A physically critical Froude number 0.109 is identified for the threshold for the dip to be swallowed into the point sink. The same problem is solved in two dimensions, where a uniform line sink is turned on impulsively at the bottom.

Vorticity production and turbulent cooling of “hot channels” in gases: Three dimensions versus two dimensions
View Description Hide DescriptionHot channels (HCs), created in a gas by a rapid energy release in the quasicylindric geometry, cool anomalously fast by turbulent flow. Picone and Boris [Phys. Fluids 26, 365 (1983)] suggested that turbulent mixing results from the vorticity generation by the baroclinic mechanism during the early, shockwave dominated stage of the dynamics. This scenario was confirmed, with important modifications, in a recent series of twodimensional (2D) hydrodynamic simulations. This work reports threedimensional (3D) hydrodynamic simulations of the HC evolution, and compares the results with those of 2D simulations. Assuming a small perturbation of the cylindric shape of the energy release region, we followed a typical HC up to acoustic times. The simulations capture well the phenomenology of the HC cooling. The details of vorticity production, that results in a fast mixing of the cold ambient gas into the HC, are clearly identified. The cooling process can be interpreted as turbulent diffusion. The empiric diffusion coefficient and cooling time agree with experiment. The latetime morphology of the HC and the empiric turbulent diffusion coefficient are dimensiondependent, the 3D cooling being faster than 2D cooling.

Mechanisms of particle deposition in a fully developed turbulent open channel flow
View Description Hide DescriptionParticle dispersion and deposition in the region near the wall of a turbulent open channel is studied using direct numerical simulation of the flow, combined with Lagrangian particle tracking under conditions of oneway coupling. Particles with response times of 5 and 15, normalized using the wall frictionvelocity and the fluid kinematicviscosity, are considered. The simulations were performed until the particle phase reached a statistically stationary state before calculating relevant statistics. For both response times, particles are seen to accumulate strongly very close to the wall in the form of streamwise oriented streaks. Deposited particles were divided into two distinct populations; those with large wallnormal deposition velocities and small nearwall residence times referred to as the freeflight population, and particles depositing with negligible wallnormal velocities and large nearwall residence times (more than 1000 wall time units), referred to as the diffusional deposition population. Diffusional deposition (deposition induced by the small residual turbulent fluctuations near the wall) is found to be the dominant mechanism of deposition for both particle response times. The freeflight mechanism is shown to gain in importance only for particles. For particles only 10% deposit because of free flight, whereas the fraction is around 40% for particles. This result runs counter to the widely held opinion that free flight is the dominant mechanism of deposition in wallbounded flows and clearly quantifies the relative importance of the two mechanisms. A simple relationship between the particle wallnormal velocity on deposition and the residence time for freeflight particles is presented. Particle deposition locations over the period of the entire simulation reveal that, while diffusional deposition occurs mostly along streamwise oriented lines below the nearwall particle accumulation patterns, freeflight particles deposit more evenly over the wall.
