Volume 17, Issue 1, January 2005
 LETTERS


Continuous or catastrophic solid–liquid transition in jammed systems
View Description Hide DescriptionPasty materials encountered in industry and in earth science are intermediate between solids and liquids either in terms of their internal structure (disordered but jammed) or from a mechanical point of view. Our results indicate that the apparent behavior of a particulate system (soils,suspensions, clays, etc.) can range from liquidlike to soil or solidlike depending on the relative importance of the energy supplied to it and its “state of jamming” which evolves in time, and the transition from one state to another may appear either continuous or catastrophic.

Direct numerical simulation of polymerinduced drag reduction in turbulent boundary layer flow
View Description Hide DescriptionWe describe a method for direct numerical simulation of polymerinduced frictiondrag reduction in turbulent boundary layers. The effect of the polymer additives that induce spatial variations of skinfriction drag is included in the momentum equation through a continuum constitutive model for the viscoelastic stress, which is based on the evolution of a parameter describing the fluid microstructure. We demonstrate that the turbulence structure and polymer microstructure evolve asynchronously as one moves in the streamwise direction. We observe an initial development length, which is followed by a quasisteady region where variations in drag reduction are weak. High drag reduction behavior can be present at short downstream distances from the inflow plane.

A friction factor bound for transitional pipe flow
View Description Hide DescriptionAn upper bound on the friction factor is found for transitional pipe flow up to Reynolds numbers of . This bound corresponds to the laminar Hagen–Poiseuille value until the energy stability point of (where ) after which it decreases monotonically to approach a viscosityindependent asymptote of as . Comparison is made with the friction factors associated with recently discovered, finiteamplitude traveling waves in rotating and nonrotating pipe flow as well as experimental data.
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 ARTICLES

 Interfacial Flows

Mean field kinetic theory description of evaporation of a fluid into vacuum
View Description Hide DescriptionThe evaporation of a liquid slab into vacuum is studied by numerical solutions of the Enskog–Vlasov equation for a fluid of spherical molecules interacting by Sutherland potential. The equation provides a simplified description of the microscopic behavior of the fluid but it has the capability of handling both the liquid and vapor phase, thus eliminating the necessity of postulating ad hoc models for boundary conditions at the vaporliquid interface. This work focuses on obtaining the structure of the vaporliquid interface in nonequilibrium conditions as well as the distribution function of evaporating molecules. The results show that the molecules crossing a properly defined vaporliquid boundary have an almost Maxwelliandistribution function and that the vapor phase is reasonably well described by the Boltzmann equation with diffusive boundary condition.

Effect of surfactant on the longwave instability of a shearimposed liquid flow down an inclined plane
View Description Hide DescriptionThe effect of an insoluble surfactant on the linear stability of a shearimposed flow down an inclined plane is examined in the longwavelength limit. It has been known that a free falling film flow with surfactant is stable to longwavelength disturbances at sufficiently small Reynolds numbers. Imposing an additional interfacial shear, however, could cause instability due to the shearinduced Marangoni effect. Two modes of the stability are identified and the corresponding growth rates are derived. The underlying mechanisms of the stability are also elucidated in detail.
 Viscous and NonNewtonian Flows

Radial mixing of granular materials in a rotating cylinder: Experimental determination of particle selfdiffusivity
View Description Hide DescriptionParticle selfdiffusion has a significant effect on mixing and thus on performance of rotating cylinder systems such as rotary kilns and drum mixers. We study experimentally the radial mixing of monodisperse beads of different colors in a quasitwodimensional cylinder rotated in the continuous flow regime. In this regime a shallow surface layer of particles flows steadily while the rest of the material rotates as a solid body. The initial distribution of tracer particles is taken to be radially symmetric and cylinder is taken to be half full. Both facilitate estimation of the particle selfdiffusivity since the evolving concentration distribution during mixing in this case is radial for most part and the mixing in these conditions is shown to be dominated by diffusion of particles. A qualitative study of the mixing is carried out using digital photography. Radial number fraction profiles of the tracer particles are obtained by bulk sampling. Since mixing occurs only in the flowing layer, mixing is considered in terms of “passes” defined as the number of times the material in the bed entirely flows through the layer. Experimental results indicate that the mixing per pass decreases with increasing rotational speed, increases with increasing particle size, and is nearly independent of cylinder size. The mixed state captured by digital photography and the measured radial concentration profiles are well described by a convective diffusion model, using diffusivity as a fitting parameter. The diffusivity obtained from the model follows the scaling proposed by Savage [“Disorder, diffusion, and structure formation in granular flow,” Disorder and Granular Media, edited by A. Hansen and D. Bideau (Elsevier, Amsterdam, 1993), pp. 255–285] and a simple expression for the diffusivity is obtained in terms of the particle diameter and the static and dynamic angles of repose.

Exact solutions for twodimensional steady flows of a powerlaw liquid on an incline
View Description Hide DescriptionUnder assumptions that are not too restrictive it is possible to reduce the equations that describe steady viscous gravity flows of a powerlaw liquid on an inclined plane to an equivalent problem consisting of an unsteady onedimensional nonlinear diffusion process. In a paper dealing with the steady spreading flow of a Herschel–Buckley liquid, Wilson and Burgess [“The steady, spreading flow of a rivulet of mud,” J. NonNewtonian Fluid Mech.79, 77 (1998)] noticed a formal analogy between the steady, twodimensional viscous gravity flows of a powerlaw liquid on an incline and a onedimensional timedependent nonlinear diffusion phenomena; however, they did not pursue the matter further. Here we develop the analogy and show how it can be used to find a large number of exact solutions representing steady twodimensional flows of powerlaw liquids, based on the available knowledge concerning nonlinear diffusion. We describe flows whose widths stay constant until a certain distance from the source, which are analogous to the wellknown waitingtime solutions of nonlinear diffusion. We then introduce a phaseplane formalism that allows us to find selfsimilar solutions and we give as examples three different currents limited laterally by a wall that ends abruptly and currents on an inclined stripe. Finally we describe the twodimensional currents that are analogous to the traveling wave solutions of the nonlinear diffusion equation. The approximations involved in the analogy are essentially equivalent to those of the lubrication theory, so that they do not impose restrictions more severe than those usually present in problems of this type. The present theory does not include surface tension effects, which implies that the appropriate Bond number must be large.
 Laminar Flows

Cavitation in flow through a microorifice inside a silicon microchannel
View Description Hide DescriptionHydrodynamiccavitation in flows through a microorifice entrenched in a microchannel has been detected and experimentally investigated. Microfabrication techniques have been employed to design and develop a microfluidic device containing an wide microorifice inside a wide and deep microchannel. The flow of deionized water through the microorifice reveals the presence of multifarious cavitating flow regimes. This investigation divulges both similarities and differences between cavitation in microorifices and cavitation in their macroscale counterparts. The low incipient cavitation number obtained from the current experiments suggests a dominant size scale effect. Choking cavitation is observed to be independent of any pressure or velocity scale effects. However, choking is significantly influenced by the small stream nuclei residence time at such scales. Flow rate choking leads to the establishment of a stationary cavity. Large flow and cavitation hysteresis have been detected at the microscale leading to very high desinent cavitation numbers. The rapid transition from incipient bubbles to choking cavitation and subsequent supercavitation suggests the presence of radically different flow patterns at the microscale. Supercavitation results in a thick cavity, which extends throughout the microchannel, and is encompassed by the liquid. Cavitation at the microscale is expected to considerably influence the design of innovative highspeed microfluidic systems.
 Instability and Transition

Nonlinear evolution of Mack modes in a hypersonic boundary layer
View Description Hide DescriptionIn hypersonic boundary layerflows the nonlinear disturbance evolution occurs relatively slowly over a very long length scale and has a profound effect on boundary layertransition. In the case of lowlevel freestream disturbances and negligible surface roughness, the transition is due to the modal growth of exponentially growing Mack modes that are destabilized by wall cooling. Crossbicoherence measurements, derived from hotwire data acquired in a quiet hypersonic tunnel, are used to identify and quantify phaselocked, quadratic sum and difference interactions involving the Mack modes. In the early stages of the nonlinear disturbance evolution, crossbicoherence measurements indicate that the energy exchange between the Mack mode and the mean flow first occurs to broaden the sidebands; this is immediately followed by a sum interaction of the Mack mode to generate the first harmonic. In the next stages of the nonlinear disturbance evolution, there is a difference interaction of the first harmonic, which is also thought to contribute to the mean flow distortion. This difference interaction, in the latter stages, is also accompanied by a difference interaction between Mack mode and first harmonic, and a sum interaction, which forces the second harmonic. Analysis using the digital complex demodulation technique, shows that the lowfrequency, phaselocked interaction that is identified in the cross bicoherence when the Mack mode and first harmonic have large amplitudes, arises due to the amplitude modulation of Mack mode and first harmonic.

Amplification of boundary layer instability by hot wall thermal oscillation in a side heated cavity
View Description Hide DescriptionA numerical study has been conducted to investigate the amplification of boundary layer instability in a sideheated enclosure with a thermal oscillation of vertical hot wall. The impetus of the present study is to elucidate the influence of wall thermal oscillation, in which the imposing frequency is one order of magnitude higher than that of the internal gravity wave on the fluctuationcharacteristics of boundary layer flow and internal flow in an enclosure. The numerical results show that the intensity of fluctuation of boundary layer flow is augmented and the internal flow in the cavity core is substantially influenced when the wall thermal oscillation is in tune with the characteristic frequency of boundary layer instability. For the wall thermal oscillation with a specific frequency, the modulated frequency fluctuation appears in the corner region due to the flow interaction between the vertical boundary layer flow and the wall jet along the horizontal walls. The amplified fluctuation of boundary layer flow affects the timeaveraged heat transfer. The maximum enhancement of Nusselt number is obtained for the wall thermal oscillation in tune with the boundary layer instability frequency. The effect of wall thermal oscillation on heat transfer is more pronounced when the forcing amplitude is the average value of nondimensional temperature difference between the hot and cold walls.

Nonlinear waves in the pressure driven flow in a finite rotating pipe
View Description Hide DescriptionTo investigate the nature of nonlinear waves appearing in an axially rotating pipe, we have performed a series of timedepending, threedimensional numerical simulations of the incompressible Navier–Stokes equations in a rotating long pipe. As a difference with some previous works on the subject, which look for several given types of traveling wave solutions in pipes of infinite length, we leave the flow to evolve freely after a pressure difference is set between two points, one on each end of the finite rotating pipe. We use a recently developed numerical method that allows us to simulate numerically the threedimensional flow produced in a pipe when Dirichlet boundary condition for the pressure is given on part of the inlet and outlet sections of the pipe. This technique is further improved here so that the pressure is only fixed at just one point on each one of the open boundaries of the pipe. Thus, no restrictions on the flow properties are given in these sections, allowing the free entrance and exit of possible waves through the pipe. We find that packets of traveling spiral waves are formed for values of the Reynolds numbers based on both the axial and the azimuthal velocities just above the critical ones given by the linear stability theory. These traveling waves have the same characteristics predicted by the linear stability theory and produce no significant mean flux defect. As the values of these parameters are increased above their critical values, the spiral waves become more involved and their amplitude increase, giving rise to a significant axial mean flow defect. For sufficiently high Reynolds numbers, we detect the apparition of spiral waves traveling also upstream, in agreement with the stability analysis for absolute instabilities. At the end, these traveling waves appearing above the onset for absolute instabilities transform into a standing spiral wave superimposed to the rotating Hagen–Poiseuille flow.

Nonmodal growth of threedimensional disturbances on plane Couette–Poiseuille flows
View Description Hide DescriptionThe time development of threedimensional disturbances superimposed on a variety of mean flow profiles representing plane Couette–Poiseuille flow is investigated numerically. Specifically, with representing the wall normal coordinate, the mean flow profiles are represented by , where when and when . For streamwise independent disturbances, which are the most amplified ones, there is an increase of the disturbance peak amplification when the parameter increases in the interval . In the interval , and especially for , the disturbance peak amplification decreases rapidly when is increased. For close to 1, a slight reduction of will therefore cause a strong increase of the disturbance amplification.

Vortex dynamics in starting square water jets
View Description Hide DescriptionThis paper presents the results of an experimental study on starting square jets at three Reynolds numbers utilizing planar laser induced fluorescence. Starting circular jets under the same initial were also investigated as a basis for comparison. Observations showed that for both circular and square jets, the rate of penetration is almost constant within the first four diameters from the exit plane. Beyond that, the rate reaches an asymptotic behavior that is inversely proportional to the square root of time . It was also found that the jet front travels slower in square jets. The interaction and deformation between the spanwise and streamwise vortices in square jets lead to an enhanced entrainment. The phenomena of axis switching, vortex pinchoff, vortices leapfrogging and coalescence were all observed in the experiments and their formation mechanisms are discussed in detail. The normalized value for the pinchoff time obtained is found to be about 7 and the expansion rate of the head vortex core is proportional to .

Crystal shapes and crystallization in continuum modeling
View Description Hide DescriptionA crystallization model appropriate for application in continuum modeling of complex processes is presented. As an extension to the previously developed Schneider equations [W. Schneider, A. Köppel, and J. Berger, “Nonisothermal crystallization of polymers,” Int. Polym. Proc.2, 151 (1988)], the model presented here allows one to account for the growth of crystals of various shapes and to distinguish between one, two, and threedimensional growth, e.g., between rodlike, platelike, and spherelike growth. It is explained how a priori knowledge of the shape and growth processes is to be built into the model in a compact form and how experimental data can be used in conjunction with the dynamic model to determine its growth parameters. The model is capable of treating transient processing conditions and permits their straightforward implementation. By using thermodynamic methods, the intimate relation between the crystal shape and the driving forces for phase change is highlighted. All these capabilities and the versatility of the method are made possible by the consistent use of four structural variables to describe the crystal shape and number density, irrespective of the growth dimensionality.
 Turbulent Flows

Statistical analysis of the velocity field in a mechanical precessing jet flow
View Description Hide DescriptionAn experimental investigation of a precessing jet issuing from a mechanically rotating nozzle directed at an angle of relative to the axis of rotation is reported. Both conventional and conditional statistics of the velocity field of the jet were measured using a combined hotwire and coldwire (to identify any reverse flow) probe. Three distinct values (, 0.01, and 0.02) of the precession Strouhal number (≡ rotation frequency × nozzle diameter / jet exit bulk velocity) were used to assess the effect of varying . The measurements reveal that the Strouhal number in general has significant influence on the entire mixing field generated by a precessing jet. The occurrence of precession at all the Strouhal numbers of investigation produces a central recirculation zone at , where is a distance measured from the rotating nozzle exit. A critical Strouhal number, i.e., for the present case, is identified: at the core jet converges to the axis of rotation while at it does not. The characteristics of the turbulent flow in the near and intermediate regions are quite different and depend upon the magnitude of . The nearfield region, , is dominated by a regime of global precession of the entire jet. As a result, the largescale entrainment of the ambient fluid is substantially enhanced while the finescale turbulent mixing is suppressed. Under the supercritical regime (i.e., ), the jet in the far field resembles some features of the nonprecessing counterpart. Nevertheless, significant differences still retain in the statistical properties.

Toward improved consistency of a priori tests with a posteriori tests in large eddy simulation
View Description Hide DescriptionIt is well known that conventional a priori tests based on the instantaneous true subgrid scale (SGS) stress do not provide a useful diagnostic information on deterministic SGS models due to the stochastic nature of unresolved scales. In this study, the possibility of an alternative diagnostics based on the “best deterministic” model is investigated. The optimal SGS model [J. A. Langford and R. D. Moser, “Optimal LES formulation for isotropic turbulence,”J. Fluid Mech.398, 321 (1999)] is considered as one of nearly best deterministic models. The validity of the optimal model is confirmed by a posteriori test, showing that the field from the optimal large eddy simulation can be regarded as one of the representative fields among all the possible realizations of filtered direct numerical simulation. Then, a priori and a posteriori tests for several SGS models are performed on the forced isotropic turbulence with a sharp cutoff filter. It is shown that a priori tests based on the optimal model are highly consistent with a posteriori tests. Also, dynamic eddyviscositymodels are very close to the optimal model both in a priori and a posteriori senses, which implies that the accurate prediction of backward dissipation is not necessarily required for the deterministic model to predict accurate flow statistics at least for the isotropic turbulence. Therefore, the direct application of scaleinvariance concept to the resolved field is shown to be unsuccessful for the spectral cutoff filter. The present study strongly suggests that this concept should be realized in terms of the dynamic constant(s) of dissipative models.

Vortical structures over rectangular cavities at low speed
View Description Hide DescriptionExperiments have been performed to acquire qualitative and quantitative flowfield data for an open cavityflow using the particle imagevelocimetry technique. The study focuses on the timemean and instantaneous development of the turbulent flow structures in the cavity shear layer. The effects of geometry (lengthtodepth ratio) and flow speed on these structures are investigated. The shear layers are found to be characterized by coherent vortical structures whose size and rate of growth vary with geometry. The smaller scales of the flow are investigated using a largeeddy decomposition method. Results show these stochastic structures to predominate primarily in the shear layer and aft wall regions.

Characterization of nearwall turbulence in terms of equilibrium and “bursting” solutions
View Description Hide DescriptionNearwall turbulence in the buffer region of Couette and Poiseuille flows is characterized in terms of recentlyfound nonlinear threedimensional solutions to the incompressible Navier–Stokes equations for wallbounded shear flows. The data suggest that those solutions can be classified into two families, of which one is dominated by streamwise vortices, and the other one by streaks. They can be associated with the upper and lower branches of the equilibrium solutions for Couette flow found by Nagata [“Threedimensional finiteamplitude solutions in plane Couette flow: Bifurcation from infinity,” J. Fluid Mech.217, 519 (1990)]. The quiescent structures of nearwall turbulence are shown to correspond to the vortexdominated family, but evidence is presented that they burst intermittently both in minimal and in fully turbulent flows. The intensity and period of the bursts are Reynoldsnumber dependent, but they saturate at high enough Reynolds numbers. The timeperiodic exact solution found for Couette flow by Kawahara and Kida [“Periodic motion embedded in plane Couetteturbulence: Regeneration cycle and burst,” J. Fluid Mech.449, 291 (2001)] can be used as a simplified model for the bursting process.

Direct numerical simulation of homogeneous turbulence with hyperviscosity
View Description Hide DescriptionWe perform direct numerical simulations (DNS) of the hyperviscous Navier–Stokes equations in a periodic box. We consider values of the hyperviscosity index , 2, 8, and vary the hyperviscosity to obtain the largest range of lengthscale ratios possible for wellresolved pseudospectral DNS. It is found that the spectral bump, or bottleneck, in the energy spectrum observed at the start of the dissipation range becomes more pronounced as the hyperviscosity index is increased. The calculated energy spectra are used to develop an empirical model for the dissipation range which accurately represents the bottleneck. This model is used to predict the approach of the turbulent kinetic energy to its asymptotic value, , as the hyperviscosity tends to zero.
 Geophysical Flows

Longtime evolution of linearly stratified spinup flows in axisymmetric geometries
View Description Hide DescriptionWe present results of laboratory experiments on the evolution of continuously stratified rotating flows initiated via incremental spinup in either cylindrical or annular geometries. It is found that the flow behavior is governed mainly by the Rossby and Burger numbers. Cyclonic and anticyclonic eddies are formed in a large region of parameter space due to instability of the flow, after the Ekman layer arrest time scale. The extended Eady model of baroclinic instability, in which the sheared wall layers are taken into account, is advanced to explain this mechanism of eddy formation. This model accounts for most of the observed features of the instability, and provides a realistic estimate for the time of onset of eddy formation.