Index of content:
Volume 7, Issue 1, January 1995

Effect of the vessel size on the hydrodynamic diffusion of sedimenting spheres
View Description Hide DescriptionExperiments are described which demonstrate that particle velocityfluctuations and hydrodynamic self‐diffusivities of sedimenting non‐Brownian spheres do not vary as the inner width of the vessel varies by a factor of 4.

Application of optical flow techniques to flow velocimetry
View Description Hide DescriptionOptical flow refers to an image processing technique originally developed for computer and robotvision applications. In this Letter, optical flow algorithms are utilized to obtain two‐dimensional velocity fields corresponding to fluid flows. The performance of the algorithms with regard to three flows is discussed: computer‐simulated suspensionflow, bubble detachment from a submerged needle, and in vivoblood flow in a microvascular network. For small changes in successive images, the algorithms yield good quantitative and qualitative information about the flows.

Instantaneous flow field in an unstable vortex ring measured by holographic particle velocimetry
View Description Hide DescriptionInstantaneous velocity field in the three‐dimensional flow of an unstable vortex ring (Re=1360) in water has been measured by employing a newly developed holographic particle velocimeter, IROV. The vorticity distribution and circulation as a function of radius from the vortex core center are also presented.

Particle velocity fluctuations and hydrodynamic self‐diffusion of sedimenting non‐Brownian spheres
View Description Hide DescriptionThe motion of non‐Brownian spheres settling in the midst of a suspension of like spheres has been experimentally studied under creeping flow conditions. A few glass spheres, marked with a thin coating of silver, were tracked in a suspension of unmarked glass spheres, made optically transparent by matching the index of refraction of the suspending fluid to that of the glass spheres. Particles were tracked with a real time digital imaging processing system. Particle trajectories were examined in the bulk region of the suspension for particle volume fractions ranging from 0% to 40% in 5% steps. Statistical analyses of local particle velocities yield the mean settling velocity, the RMS of the fluctuations of the vertical and horizontal particle velocity and the particle velocity autocorrelation functions. The long time fluctuating particle motion is demonstrated to be diffusive in nature. Vertical and horizontal correlation times and self‐diffusivities are found as a function of particle volume fraction, and a strongly anisotropic diffusion noted.

The role of dynamic surface tension in air assist atomization
View Description Hide DescriptionAqueous surfactant solutions were atomized using an air assist atomizer, and the effects of dynamic surface tension on atomization were studied. The solutions differ from one another in their dynamic behavior, but all have the same equilibrium surface tension. The constant equilibrium surface tension was achieved by choosing surfactant concentrations above the critical micelle concentration (CMC). The dynamic change of surface tension in aqueous Tergitol NP‐10 solutions of 1.5, 3, 6, 12, and 60 mM was measured using the oscillating jet technique. While atomizing the liquid jet, it was found that frequencies and amplitudes of the flapping motion of the liquid jet increased with surfactant concentration showing that surface tension decreases in the region between the nozzle exit and breakup. The length of the intact liquid jet was found to be insensitive to surfactant concentration, suggesting that, due to sudden increase of surface area, surface tension is near its initial value in the breakup region. Measurements in the spray region show a strong influence of the dynamic change of surface tension on drop size. Finally, using an analysis based on a critical Weber number, the actual time average of surface tension was estimated at an axial location of 1.5× the intact length downstream from the nozzle exit, and an overall profile of surface tension as a function of axial location was proposed.

Competition between subharmonic and sideband secondary instabilities on a falling film
View Description Hide DescriptionThe secondary instabilities on a falling film which cause a monochromatic wave to evolve into solitary waves are examined with a weakly nonlinear theory. The unique phase speed dispersion relation dictated by inertia and capillarity is found to favor a nonlinear, two‐wave subharmonic resonance that causes neighboring crests to coalesce. This occurs when the fundamental wave frequency is below a critical value ω_{ c } which can be approximated by a nonlinear resonant frequency. An entire band of secondary waves are excited by this static subharmonic mechanism such that the coalescence occurs nonuniformly. The lower half of this band of secondary waves travels faster than the fundamental and induces the coalesced waves to move faster than the slower fundamental. For monochromatic waves with frequencies above ω_{ c }, a three‐wave oscillatory sideband instability is triggered which generates two secondary waves that are slower than the fundamental. This sideband instability involves a long‐wave modulation that causes several crests to coalesce simultaneously. Both secondary transitions are important intermediate stages of the route to spatiotemporal chaos involving solitary waves.

Three‐dimensional instabilities of film flows
View Description Hide DescriptionTwo‐dimensional (2‐D) interfacial waves on flowing films are unstable with respect to both two‐ and three‐dimensional instabilities. In this paper, several distinct three‐dimensional instabilities that occur in different regions of the parameter space defined by the Reynolds numberR and the frequency f of forced two‐dimensional waves are discussed in detail. (a) A synchronous 3‐D instability, in which spanwise deformations of adjacent wave fronts have the same transverse phase, appears over a wide range of frequency. These transverse modulations occur mainly along the troughs of the primary waves and eventually develop into sharp and nearly isolated depressions. The instability involves many higher harmonics of the fundamental 2‐D waves. (b) A 3‐D surbharmonic instability occurs for frequencies close to the neutral curve f _{ c }(R). In this case, the transverse modulations are out of phase for successive wave fronts, and herringbone patterns result. It is shown that this weakly nonlinear instability is due to the resonant excitation of a triad of waves consisting of the fundamental two‐dimensional wave and two oblique waves. The evolution of wavy films after the onset of either of these 3‐D instabilities is complex. However, sufficiently far downstream, large‐amplitude solitary waves absorb the smaller waves and become dominant.

Interaction between longitudinal convection rolls and transverse waves in unstably stratified plane Poiseuille flow
View Description Hide DescriptionNonlinear interaction between a Tollmien–Schlichting wave and longitudinal rolls resulting from Rayleigh–Bénard instability has been investigated in an unstably stratified plane Poiseuille flow of infinite extent. Cubic order amplitude equations for the interacting modes are derived on a weakly nonlinear basis in the neighborhood of a crossover point at which both modes become unstable on a linear basis simultaneously. A bifurcationanalysis based on use of the actual numerical coefficients obtained from the governing equations and evaluated for various values of the Prandtl number is performed, and the results, such as the effect of longitudinal rolls on the subcritical instability characteristic of a Tollmien–Schlichting wave, are discussed.

Asymmetry and Hopf bifurcation in spherical Couette flow
View Description Hide DescriptionSpherical Couette flow is studied with a view to elucidating the transitions between various axisymmetric steady‐state flow configurations. A stable, equatorially asymmetric state discovered by Bühler [Acta Mech. 81, 3 (1990)] consists of two Taylor vortices, one slightly larger than the other and straddling the equator. By adapting a pseudospectral time‐stepping formulation to enable stable and unstable steady states to be computed (by Newton’s method) and linear stability analysis to be conducted (by Arnoldi’s method), the bifurcation‐theoretic genesis of the asymmetric state is analyzed. It is found that the asymmetric branch originates from a pitchfork bifurcation; its stabilization, however, occurs via a subsequent subcritical Hopf bifurcation.

Convection rolls and their instabilities in the presence of a nearly insulating upper boundary
View Description Hide DescriptionThe problem of steady convection rolls and their instabilities in a fluid layer heated from below is studied numerically in the case of a highly conducting, rigid lower and a nearly insulating, stress‐free upper boundary. A Galerkin method is used to obtain two‐dimensional solutions in dependence on the Rayleigh number R and the wave number α for different values of the Prandtl number P. Their stability is analyzed through the superposition of general three‐dimensional infinitesimal disturbances. Most instabilities correspond qualitatively to those found in the case of symmetric highly conducting, rigid boundaries. A new instability, the subharmonic varicose instability, is found, however, which restricts the region of stable rolls toward a higher Rayleigh number in the case of moderate Prandtl numbers.

The distortion of a passive scalar by two‐dimensional objects
View Description Hide DescriptionThe response of a heated, nearly homogeneous and isotropic turbulent field to a nonuniform rapid distortion upstream of two‐dimensional objects placed in a homogeneous grid generated flow is investigated experimentally. In particular, the effect of the nonuniform distortion on the single‐point statistical properties of the velocity and a passive scalar (temperature), the axial heat flux and higher‐order cross moments are presented. The nearly homogeneous, turbulent flow is produced by a biplane grid of rods and a square mesh grid of electrically heated wire that is placed downstream of the turbulence producing grid. Spatially and temporally resolved, simultaneous measurements of the streamwise turbulent velocity and temperature are obtained upstream of several two‐dimensional objects along the mean stagnation streamline. The effects of the blocking and vortex stretching mechanisms on the root‐mean‐square (RMS) velocity for various ratios of the integral length scale to the characteristic length of the object, L _{0}/D, are in agreement with previous results, i.e., for L _{0}/D≪1, the velocity intensity is increased and for, L _{0}/D≫1, it is decreased. In contrast, to within a distance equal to about one integral scale from the object, the distorted RMS temperature remains nearly a constant. When L _{0}/D≪1, where vortex stretching is important, the axial heat flux and the diffusion of temperature variance increase as the object is approached. In contrast, when L _{0}/D≫1, where the blockage effect is dominant, they decrease as the object is approached.

Resonance phenomena in viscous fluids inside partially filled spinning and nutating cylinders
View Description Hide DescriptionSpin‐stabilized projectiles with liquid payloads may experience different types of flight instabilities caused by the fluid motion in the payload cylinder. The first type is known to occur in low‐viscosity fluids, i.e., at high Reynolds numbers, owing to resonance with inertial waves at critical frequencies. The second type originates from a forced secondary flow at arbitrary frequency, and is most pronounced for fluids of high viscosity, i.e., relatively low Reynolds numbers. For cylinders completely filled with a single fluid, these instabilities were analyzed by eigenfunction expansion developed by Selmi, Li, and Herbert [Phys. Fluids A 4, 1998 (1992)]. The method permits unified analysis of both types of instability, since it can be used for flows at moderate as well as high Reynolds numbers. Often in practice, cylinders are made to include a central rod to alter resonance properties or are partially filled during production, to ensure safety as the liquid payload may expand under different conditions. In this paper, the eigenfunction approach is extended to analyze the moments caused by the flow in a spinning and nutating cylinder, containing a partial fill or a central rod. The analysis shows that the fill ratio (defined as the ratio of the volume of the fluid to the volume of the cylinder) affects resonance with inertial waves. The inviscid flowequations are solved analytically to provide criteria for the onset of resonance in the two configurations.

Large‐scale flows and resonances in 2‐D thermal convection
View Description Hide DescriptionRecent experiments of thermal convection in finite containers of intermediate and large aspect ratios have shown the presence of flows spanning the largest dimension of the container [R. Krishnamurti and L. N. Howard, Proc. Natl. Acad. Sci. 78, 1985 (1981); J. Fluid Mech. 170, 385 (1986)]. Large‐scale flows of this kind computed from two‐dimensional (2‐D) numerical simulations are presented. The marginal stability curves for the bifurcations are computed in the range of aspect ratios L=1,...,6 and for Prandtl number σ =10. The nonlinear dynamics of the bifurcated solution is explored for containers with aspect ratios L=1,2,4. By increasing the Rayleigh number from criticality the system produces different sequences of symmetry breaking, Hopf‐type bifurcations, which finally result in large scale flows, oscillatory net mass flux and chaos. The bifurcation involves different mode resonances with vertical and horizontal couplings, which are modeled using formal group theoretical techniques.

The persistence of trailing vortices: A modeling study
View Description Hide DescriptionThe principal subject of this paper is analysis and modeling of turbulent wing tip vortexflows in a far‐field region of the vortex evolution. The choice of a Reynolds stress closure (RSC) to model the vortexturbulence is shown to be indispensable for representation of the flow rotation effects on turbulence. The principal result reported is the model–experiment comparison of the vortex growth rates for different vortexReynolds numbers. The mean vortical flow generated by the wing tip very effectively suppresses the Reynolds shear stress, which mediates the extraction of energy from the mean flow by turbulence. In consequence, the vortex‐core growth rate is controlled only by molecular viscosity and the vortexturbulence decays since the turbulence production rate is very nearly zero. This rather unexpected result is shown to be supported by experiments. Finally, it is shown that the computed turbulence structure is consistent with experimental data at the NASA Ames Research Center.

Multiscalar mapping closure for mixing in homogeneous turbulence
View Description Hide DescriptionA new methodology to use mapping closures for the mixing of several scalars in homogeneous turbulence is explained. The main idea is the unidimensional mapping for each scalar, with the cross‐dissipation handled by a joint reference field. A restricted and a general closure are described. A Monte Carlo code based on a fractional step technique has been developed. As an example, the segregated double‐delta two‐scalar mixing is analytically and numerically solved and predictions are shown.

Horseshoe vortex systems resulting from the interaction between a laminar boundary layer and a transverse jet
View Description Hide DescriptionThe horseshoe vortex system resulting from the interaction between a laminar boundary layer and a round transverse jet was studied over a range of Reynolds numbers and velocity ratios using hydrogen bubble wire visualization in a water channel. The study shows that the horseshoe vortex system can be steady, oscillating, or coalescing, depending on the flow conditions. Topological concepts are used to interpret the observed flow patterns and compare these patterns with those observed and computed upstream of wall‐mounted circular cylinders. The Strouhal numbers of the observed oscillating and coalescing systems agree reasonably well with those appearing in the literature for wall‐mounted circular cylinders. The relationship between the unsteady horseshoe vortexmotions and the unsteady vortexmotions in the wake is studied for a velocity ratio of 4. Here it is shown that the oscillating regime occurs at the same frequency as the wake and the coalescing regime occurs at approximately double the frequency of the wake. The results indicate that the wake intermittently becomes coupled to the horseshoe vortexmotions and that this occurs either at the horseshoe vortex frequency in the case of the oscillating system or a subharmonic in the case of the coalescing system.

Effect of a rapid expansion on the development of compressible free shear layers
View Description Hide DescriptionDetailed mean velocity and turbulence data have been obtained with a laser Doppler velocimeter for two axisymmetric shear layers downstream of rapid expansions of different strengths. A comparison of the data in the near field (immediately downstream of separation) and far field (shear layer approaching self‐similarity) is presented, and the fluid dynamiceffects of the rapid expansion are ascertained for each regime. In general, the rapid expansion was found to distort the initial mean velocity and turbulence fields in the shear layer, in a manner similar to that in rapidly expanded, attached supersonic boundary layers; namely, two distinct regions were found in the initial shear layer: an outer region, where the turbulent fluctuations are quenched primarily due to mean compressibility effects (bulk dilatation), and an inner region, where turbulence activity is magnified due to the interaction of organized large‐scale structures in the shear layer with low‐speed fluid at the inner edge. With increasing strength of the rapid expansion, the effects in both regions become more pronounced, especially in the inner region, where turbulent fluctuations and mass entrainment rates are greatly magnified. Farther downstream, the turbulence activity of the large‐scale eddies remains elevated, due to the rapid expansion, even though the relative distribution of the turbulence energy between the Reynolds stress components (structure of the turbulence) is independent of expansion strength.

The interaction of a shock with a vortex: Shock distortion and the production of acoustic waves
View Description Hide DescriptionNumerical simulations of a shock interacting with a compressible vortex are presented for shocks and vortices of various relative strengths. The simulations show the effects of the vortex on the shock structure and the structure of the acoustic field generated by the shock–vortex interaction. A relatively weak vortex perturbs the transmitted shock only slightly, whereas a strong vortex leaves the transmitted shock with a structure corresponding to either a regular or Mach reflection. The acoustic wave generated by the interaction consists of two components: a ‘‘quadrupolar’’ component produced by the initial shock–vortex interaction and the complex reflected shock system. When these waves merge, they form the asymmetric structure seen in experiments.

The spatial stability of compressible elliptic jets
View Description Hide DescriptionThis paper describes the spatial stability characteristics of compressible elliptic jets. Solutions are obtained to the compressible, inviscid, linearized equations of motion; the compressible Rayleigh equation. Separable forms of solution are obtained in the jet potential core and outside the jet in terms of series of Mathieu and modified Mathieu functions. These solutions are matched using a shooting method that integrates the Rayleigh equation through the region of nonuniform velocity and density. Four classes of instability modes are studied; modes that are odd or even about the jet’s major and minor axes. Their stability characteristics are documented for a range of jet aspect ratios, jet Mach numbers and temperatures, and azimuthal distributions of jet shear layer thickness. The growth rates of the modes are found to depend on their class and the jet thickness on the major and minor axes. The mode that ‘‘flaps’’ about the jet major axis is found to be the most unstable as the jet Mach number or aspect ratio increases.