Volume 16, Issue 4, April 2004
 LETTERS


Instability versus collapse in a flow driven by the radial electric current
View Description Hide DescriptionA flow of an electrically conducting fluid induced by a spherically symmetric current (discharging from a point source located on the fluid free surface) has a striking feature. As increasing total currentJ reaches a threshold, a jet propagating from the source along the axis of symmetry collapses, i.e., velocity becomes unbounded on the axis. It is shown here that the flow becomes unstable at J smaller than the threshold. For a flow in a conical region, (θ is the polar angle from the axis of symmetry), the instability leads to either a timeoscillating or steadyswirling flow depending on In a halfspace, the instability is oscillatory. The steady swirl first develops as J increases in a cone with

Large scale inhomogeneity of inertial particles in turbulent flows
View Description Hide DescriptionPreferential concentration of inertial particles in turbulent flow is studied by high resolution direct numerical simulations of twodimensional turbulence. The formation of networklike regions of high particle density, characterized by a length scale which depends on the Stokes number of inertial particles, is observed. At smaller scales, the size of empty regions appears to be distributed according to a universal scaling law.

Inertiainduced electrophoretic interactions
View Description Hide DescriptionElectrophoretic interactions occurring between two colloidal particles of identical zeta potential are investigated using a perturbation expansion in the small Reynolds number. Particle interactions appear in the form of buoyancytype forces, similar to the pressure forces encountered in bubbly flows. The dynamical system governing the evolution of the pair configuration is derived for the case of spherical particles, and closedform solutions describing remote particle trajectories are obtained therefrom.

Delay of vortex ring pinchoff by an imposed bulk counterflow
View Description Hide DescriptionThe Kelvin–Benjamin variational principle has been previously used to predict that vortex ring pinchoff can be delayed if the energy of the leading vortex ring is decreased during formation and/or the energy delivered by the vortex generator is increased. We present experimental results in which the former and latter energy effects were simultaneously accomplished by imposing a bulk axisymmetric counterflow during vortex ring formation. Measurements indicate that the formation number is retarded sufficiently to allow increased ingestion of fluid circulation by the leading vortex ring. This serves as a first demonstration of artificial manipulation of vortex ring formation for potential propulsive benefits in starting jets.
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 ARTICLES


Craik–Criminale solutions and elliptic instability in nonlinearreactive closure models for turbulence
View Description Hide DescriptionThe Craik–Criminale class of exact solutions is examined for a nonlinearreactive fluids theory that includes a family of turbulence closure models. These may be formally regarded as either large eddy simulation or Reynoldsaveraged Navier–Stokes models of turbulence. All of the turbulence closure models in the class under investigation preserve the existence of elliptic instability, although they shift its angle of critical stability as a function of the rotation rate Ω of the coordinate system, the wave number β of the Kelvin wave, and the model parameter α, the turbulencecorrelation length. Elliptic instability allows a comparison among the properties of these models. It is emphasized that the physical mechanism for this instability is not wave–wave interaction, but rather wave, meanflow interaction as governed by the choice of a model’s nonlinearity.

Optimal mixing in recirculation zones
View Description Hide DescriptionCoarsescale mixing in a recirculation zone is described with a simple vortex model. Timedependent forcing is employed to change the vortex motion and mixing properties. An optimal mixing problem is defined in which the flux across the recirculation region shall be maximized under the sideconstraints of bounded vortex motion and bounded actuation. Concepts of control theory and chaotic advection are used to achieve this goal. In particular, controllability is proven with a transformation into flat coordinates. Thus, a feedforward law for the optimal trajectory and a feedback law for its stabilization are derived. Observability of the vortex motion is indicated by a dynamic observer. Mixing in the optimized flow is studied using Poincaré maps. The lowfrequency modulations to vortex motion are shown to substantially increase mixing in the average. Generalizations of the mathematical framework for mixing optimization are suggested for a larger class of models and flows.

Viscous heating effect on the drag reduction of a bubble towards a nearcontact wall
View Description Hide DescriptionThis work theoretically investigates the thermal effect of viscous dissipation on the drag force of a fast moving spherical bubble in a Newtonian liquid towards a nearcontact planar wall. The bubble is small and is close enough to the wall so that creeping flow conditions are achieved in the thin gap. A lubrication analysis is employed to simplify the momentum and energy equations. For low wall thermal conductivity, simple governing equations can be derived and then solved numerically. At sufficiently high constant velocity, the drag force can be substantially reduced due to the viscosity decrease caused by viscous heating in the thin film. Under the action of a prescribed external force, the bubble velocity can be considerably increased at sufficient closeness to the wall, as compared with that if the viscosity were temperature independent.

Actuation and control of a turbulent channel flow using Lorentz forces
View Description Hide DescriptionResults concerning the design and fabrication of electromagnetic actuators, and their application to affect the wall shear stress in a fully turbulent channel flow are discussed. The actuators utilize a Lorentz force to induce fluid motion due to the interaction between a magnetic field and a current density. The actuators are comprised of spanwisealigned rows of permanent magnets interlaced with surfacemounted electrodes, segmented to allow the Lorentz force to be propagated in the spanwise direction. Problems commonly associated with electromagnetic flowcontrol—electrolysis, bubble formation, and electrode corrosion are substantially reduced, and in most cases eliminated by the use of a conductive polymer coating. The actuators generate velocity profiles with a penetration depth into the flow of approximately 1 mm (set by the electrode/magnet pitch) and maximum velocities of approximately 4 cm/s. The actuation velocities are found to scale linearly with forcing voltage and frequency. The electrical to mechanical efficiency is found to be very low primarily due to the limitations on the magnetic field strength and the low conductivity of the working fluid (saltwater). The actuators are used in a fully turbulent low Reynolds number channel flow and their effect on the turbulent skin friction is measured using a direct measurement of drag. Maximum drag reductions of approximately 10% are measured when the flow is forced using a spanwise oscillating Lorentz force. A scaling argument for the optimal amplitude of the current density is developed. The efficiency of this method for drag reduction, and its application at higher Reynolds numbers is also discussed.

Low viscosity contrast fingering in a rotating HeleShaw cell
View Description Hide DescriptionWe study the fingering instability of a circular interface between two immiscible liquids in a radial HeleShaw cell. The cell rotates around its vertical symmetry axis, and the instability is driven by the density difference between the two fluids. This kind of driving allows studying the interfacial dynamics in the particularly interesting case of an interface separating two liquids of comparable viscosity. An accurate experimental study of the number of fingers emerging from the instability reveals a slight but systematic dependence of the linear dispersion relation on the gap spacing. We show that this result is related to a modification of the interface boundary condition which incorporates stresses originated from normal velocity gradients. The early nonlinear regime shows nearly no competition between the outgrowing fingers, characteristic of low viscosity contrast flows. We perform experiments in a wide range of experimental parameters, under conditions of mass conservation (no injection), and characterize the resulting patterns by data collapses of two characteristic lengths: the radius of gyration of the pattern and the interface stretching. Deep in the nonlinear regime, the fingers which grow radially outwards stretch and become gradually thinner, to a point that the fingers pinch and emit drops. We show that the amount of liquid emitted in the first generation of drops is a constant independent of the experimental parameters. Further on there is a sharp reduction of the amount of liquid centrifugated, punctuated by periods of no observable centrifugation.

Chaininduced effects in the Faraday instability on ferrofluids in a horizontal magnetic field
View Description Hide DescriptionThe linear stability analysis of the Faraday instability on a viscousferrofluid in a horizontal magnetic field is performed. Strong dipole–dipole interactions lead to the formation of chains elongated in the field direction. The formation of chains results in a qualitative new behavior of the ferrofluid. This new behavior is characterized by a neutral stability curve similar to that observed earlier for Maxwellviscoelastic liquids and causes a significant weakening of the energy dissipation at high frequencies. In the case of a ferrofluid with chains in a horizontal magnetic field, the effective viscosity is anisotropic and depends on the field strength as well as on the wave frequency.

Principal instabilities of large amplitude inertiogravity waves
View Description Hide DescriptionWe analyze the threedimensional stability properties of monochromatic, largeamplitude, nonhydrostatic inertiogravity waves propagating in a rotating stratified fluid with no mean shear. The ratio of Coriolis parameter f to the BruntVäisälä frequency N is fixed at a value chosen to be representative of the Earth’s atmosphere and upper oceans in extratropical latitudes. By using Floquet theory combined with suitable coordinate transformations, our analysis provides an exact representation of the spatial and temporal periodicity of the basic wave state. Growth rates are computed for several discrete phaseelevation angles spanning the frequency range in which rotational effects become important, and the basic wave state changes from fully overturned to suboverturned. For each basic wave, we identify the growth rate peaks in disturbance wavenumber space—these are the principal modes. At the lowest phaseelevation angle considered, the dominant principal mode is similar to its lowfrequency nonrotating counterpart, with disturbance roll axes aligned in, or nearly in, the direction of the largest component of basic wave shear. As θ increases to values where the effects of rotation are more strongly manifested, the dominant rotating mode shifts to oblique orientation. At still higher values of θ, the fastestgrowing modes have roll axes oriented orthogonal to the main shear component of the basic wave. At the highest values of θ considered in this study, the waves are no longer vertically overturned, but still feature minimum Richardson numbers below . We find that such lowfrequency waves are subject to wavescale instabilities: for the largest amplitude considered, the instability shows no preferred orientation, while at a somewhat lower amplitude, the dominant instability prefers an oblique orientation. Dominant oblique instabilities have not been reported in previous approximate stability analyses of inertiogravity waves, although they have been found in nonlinear simulations. Our analysis resolves this discrepancy.

Ghost effect of infinitesimal curvature in the plane Couette flow of a gas in the continuum limit
View Description Hide DescriptionThe timeindependent plane Couette flow of a gas in the continuum limit is studied on the basis of kinetic theory as the limit of the cylindrical Couette flow of a rarefied gas between two rotating coaxial circular cylinders when the mean free path and the curvature (or the inverse of the radius) of the inner cylinder tend to zero simultaneously, keeping the difference of the radii of the two cylinders fixed. The fluiddynamictype equations and their boundary conditions governing the limiting state are derived for arbitrary circumferential speeds of rotation of the cylinders and for arbitrary temperature difference of the two cylinders. The resulting equations depend on the relative speed of decay of the two parameters and contain a term due to the infinitesimal curvature of the cylinder, as well as nonNavier–Stokes stress terms, when the curvature decays not faster than some function (generally, the square) of the mean free path. The bifurcation analysis of the plane Couette flow of a linear profile is carried out when the speeds of the walls and their temperature difference are small. The bifurcation point and the bifurcated flow fields, where the linear profile is considerably deformed by infinitesimal cross flows induced by the infinitesimal curvature, are obtained.

Flow pattern and heat transfer rate in Rayleigh–Bénard convection
View Description Hide DescriptionThe threedimensional Rayleigh–Bénard convection is simulated numerically using the lattice Boltzmann method. Flow patterns are observed and the heat transfer rate is estimated in terms of the Nusselt number. The dependence of the Nusselt number on the Rayleigh number is shown to agree well with that obtained by the twodimensional calculations of the Navier–Stokes equations. It is shown that several roll patterns with different wave numbers and heat transfer rates are established even though the ratio of the horizontal size to the vertical size is a multiple of 2. Two types of oscillatory roll patterns are shown: one is with oscillatory heat transfer rate and the other is with the constant heat transfer rate. It is found that the square pattern is possible under the same condition for the stable or oscillatory roll pattern. The heat transfer rate decreases with decreasing wave number.

Effects of arbitrary directional system rotation on turbulent channel flow
View Description Hide DescriptionA series of direct numerical simulations is carried out to study the effects of system rotation on a fully developed turbulent channel flow. The rotating axis is in an arbitrary direction to the channel walls. Three cases are considered by combining two of the orthogonal rotating vectors, i.e., streamwise, wallnormal, and spanwise rotations. The spanwise rotation effect is still dominant even when another orthogonal rotation is imposed to the system. However, the streamwise rotation induces the recovery of turbulence on the suction side, the enhancement of the secondary flow rotating in the positive streamwise direction, and the redirection of the nearwall vortical structures if this rotation is much stronger than the spanwise rotation. The wallnormal rotation reduces the slope of the linear region of the streamwise mean velocity distribution and increases the streamwise friction coefficient. In the case of combined streamwise and wallnormal rotation, turbulence is also enhanced on one side and depressed on the other side, while rotationinduced largescale vortices also appear, extending in the absolute mean flow direction, even though no explicit spanwise rotation is imposed to the system.

Differential diffusion in a shocked helium jet
View Description Hide DescriptionWe present direct numerical simulations of a shock tube experiment in which a cylindrical laminar jet of helium doped with biacetyl is injected into air and subjected to a weak shock wave. Computed species distributions in a planar cross section of the jet are compared to planar laserinduced fluorescenceimages produced by the experiment. Given the qualitative nature of the published experimental images, the agreement with spatial flow features is quite good. We find that differential diffusion of species is an important feature of this experiment, leading to a significant decoupling of the helium and the biacetyl tracer.

On the translation of a cylinder in a long tube
View Description Hide DescriptionWe study the motion of a cylindrical particle translating slowly in a long tube as a function of the particle’s dimensions and placement both in the presence and the absence of external pressure gradients. The cylinder acts as a “leaky” piston, generating both fluid recirculation and through flow. When the particle is long, analytic expressions are obtained for both the velocity field and the force needed to sustain the particle’s motion as functions of the particle’s position and dimensions. When the particle is short, a superpositionbased algorithm is outlined to facilitate economical numerical calculations. When the particle is placed off center in the tube, torque will act on the particle. When the particle is unguided, this torque will preclude coaxial motion and cause the particle to follow an oscillatory trajectory.

Vortex ring formation at the open end of a shock tube: A particle image velocimetry study
View Description Hide DescriptionThe vortex ring generated subsequent to the diffraction of a shock wave from the open end of a shock tube is studied using particle image velocimetry. We examine the early evolution of the compressible vortex ring for threeexit shock Mach numbers, 1.1, 1.2, and 1.3. For the three cases studied, the ring formation is complete at about where t is time, is fluid velocity behind shock as it exits the tube and D is tube diameter. Unlike in the case of piston generated incompressible vortex rings where the piston velocity variation with time is usually trapezoidal, in the shockgenerated vortex ring case the exit fluid velocity doubles from its initial value before it slowly decays to zero. At the end of the ring formation, its translation speed is observed to be about 0.7 During initial formation and propagation, a jetlike flow exists behind the vortex ring. The vortex ring detachment from the tailing jet, commonly referred to as pinchoff, is briefly discussed.

NonFickian diffusion and tau approximation from numerical turbulence
View Description Hide DescriptionEvidence for nonFickian diffusion of a passive scalar is presented using direct simulations of homogeneous isotropic turbulence. The results compare favorably with an explicitly timedependent closure model based on the tau approximation. In the numerical experiments three different cases are considered: (i) zero mean concentration with finite initial concentration flux, (ii) an initial top hat profile for the concentration, and (iii) an imposed background concentration gradient. All cases agree in the resulting relaxation time in the tau approximation relating the triple correlation to the concentration flux. The firstorder smoothing approximation is shown to be inapplicable.

Aerosol deposition in periodic shock waves
View Description Hide DescriptionThe paper considers deposition of small aerosol particles inside a closed tube filled with a gas at resonance, when the flow is accompanied by periodic shock waves traveling back and forth along the tube. It is found that resonance gas oscillations cause vigorous aerosol deposition leading to a rapid concentration decrease. We study the effect of the Saffman lift and thermophoretic forces on particle trajectory in the boundary layer near the tube wall. The thermophoretic force arises due to gas heating by periodic shock waves, while the lift force is caused by the interaction of the shock with the viscous boundary layer. Both forces move particles toward the wall causing their deposition. The effect of turbulence on aerosol deposition is also considered. It is found that for particles less than 1 μm in diameter, the effect of turbulent fluctuations on their deposition is dominant, while for larger particles, the Saffman lift force prevails. The effect of the thermophoretic force is found to be slight. It is also found that at resonance the Saffman lift force causes instability in motion of large particles resulting in their rapid deposition. Our experiments of aerosol deposition in a resonance tube compare favorably with the results of the numerical study.

Twofluid jets and wakes
View Description Hide DescriptionSimilarity solutions for laminar twofluid jets and wakes are derived in the boundarylayer approximation. Planar and axisymmetric fan jets as well as classical and momentumless planar wakes are considered. The interface between the immiscible fluids is stabilized by the action of gravity, with the heavier fluid, taken to be a liquid, placed beneath the lighter fluid. Velocity profiles for the jets and the classical wake depend intimately, but differently, on the parameter where and are, respectively, the density and absolute viscosity of the fluid in the upper and lower fluid domains, while the momentumless wake profile depends on the parameter Generally, all interfaces deflect from horizontal except the fan jet. However, while the interface for the classical planar twofluid wake is never flat, the interfaces for the planar jet and the momentumless wake become flat in the particular case Velocity profiles illustrating the strongly asymmetrical jet and wake profiles that arise in airoverwater, oiloverwater, and airoveroil flows are presented.
