Volume 16, Issue 5, May 2004
 LETTERS


A predictive model for the detachment of bubbles injected in a viscous shear flow with small inertial effects
View Description Hide DescriptionAir bubble injection at the wall of a viscousshear flow is filmed using a highspeed video camera. The temporal evolution of the bubble radius and position of its center of gravity throughout its growth is determined from image processing. The experimental results are then used to validate a balance of the forces acting on the bubbles during their growth and after their detachment within the limit of small bubble Reynolds numbers. The contact angles calculated from the force balance agree well with those obtained by image processing. Finally, the force balance is used to predict the bubble radius at detachment versus the gas flow rate injected through the wall and the shear rate of the liquid flow.

Leadingedge tubercles delay stall on humpback whale (Megaptera novaeangliae) flippers
View Description Hide DescriptionThe humpback whale (Megaptera novaeangliae) is exceptional among the baleen whales in its ability to undertake acrobatic underwater maneuvers to catch prey. In order to execute these banking and turning maneuvers, humpback whales utilize extremely mobile flippers. The humpback whale flipper is unique because of the presence of large protuberances or tubercles located on the leading edge which gives this surface a scalloped appearance. We show, through wind tunnel measurements, that the addition of leadingedge tubercles to a scale model of an idealized humpback whale flipper delays the stall angle by approximately 40%, while increasing lift and decreasing drag.

Turbulent drag reduction by Lorentz force oscillation
View Description Hide DescriptionAn experimental investigation into an electromagnetic technique to reduce skinfriction drag of turbulent boundary layers was conducted with an electroconductive solution in water, with potential applications to ships and underwater vehicles. We used an array of actuators made of permanent magnets interleaved with copperelectrodes, which are set flush with the wall surface across the flow. This setup created the Lorentz force in the crossflow direction within a thin region near the wall. More than 40% of turbulent skinfriction reductions were observed when the electromagnetic force is oscillated across the flow.

Intermittency effect on energy spectrum in highReynolds number turbulence
View Description Hide DescriptionThe energy spectrum in fully developed turbulence shows the powerlaw relation, The deviation from −5/3 is due to the effect of intermittency.Analyzing data in highReynolds number turbulence it was found that there are two different powerlaw regions in One locates close to the spectral bump and the other is in the lower wave number range. Intermittency corrections are and respectively. This result is compared with recent direct numerical simulations [Phys. Fluids 15, L21 (2003)] in which μ is not negligible, but is evaluated to be 0.1. We also comment on the Kolmogorov constant and the scaling exponent of velocity structure function.
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 ARTICLES


Dynamics of ring vortices impinging on planar shock waves
View Description Hide DescriptionIn the present paper the encounter of vortex rings with planar shock waves is studied in a threedimensional environment, with the objective to assess the influence of shock and vortex strength and vortex orientation on the dynamics of the process. The study relies on numerical simulations performed by means of a stateoftheart hybrid compact/WENO (weighted essentially nonoscillatory) shockcapturing algorithm to solve the Euler equations of gas dynamics. The study focuses on the characterization of the interaction in terms of the evolution of the geometrical parameters of the vortex and the mean flow properties such as kinetic energy and enstrophy. The vortex is compressed as it passes through the shock, and its characteristic dimensions decrease; at the same time its axis is deflected and the ring follows a complex dynamic evolution, even though a nearly steady state is reached for the global quantities. In particular, it has been found that the total vortex kinetic energy is generally nonincreasing after the interaction, while the enstrophy always increases. A simple theory is developed here to shed some light onto the physical phenomena involved, which is found to compare reasonably well with the results of the computations. Some final comments are made regarding the extension of the results reported in the present study to the analysis of shockcompressed turbulence.

A variational analysis of flowreversal condition in a turbulent swirling pipe flow using the bulkhelicity concept
View Description Hide DescriptionThe magnitude of axialflow retardation near the center of a turbulent swirling flow is estimated from the results of the variational analysis with the aid of the helicity concept. It is analytically shown that the axialflow reversal in a swirl occurs if the bulk helicity imparted to the mean flow exceeds the critical value, which is proportional to the square of the flux. It is suggested that the bulk helicity in the center region plays an important role in determining the flowreversal condition. Through the comparison with the experimental observations in a turbulent swirling pipe flow, the reliability of the theoreticallyderived reversal condition is confirmed.

Shock gaseous cylinder interactions: Dynamically validated initial conditions provide excellent agreement between experiments and numerical simulations to late–intermediate time
View Description Hide DescriptionWe present numerical simulations of a planar shock interacting with a twodimensional sulfur hexafluoride cylinder. We have excellent agreement with experiments at two Mach numbers [Jacobs, Phys. Fluids A 5, 2239 (1993)] and [Zoldi, Ph.D. thesis, SUNY Stony Brook, 2002]. This includes intermediate scale features and quantities such as bounding box dimensions of coherent structures and velocity magnitude distribution function. Our simulations use a validated viscous FLASH [ASCI FLASH Center, “FLASH User’s Guide,” University of Chicago, 2002] environment initialized with a cylinder bounded by a finitethickness interfacial transition layer of specific shape. The shape parameters are determined through iteration, beginning with the uncertain experimental images and optimizing to obtain maximal agreement with early to intermediate time evolving structures. The visiometric approach and the vortex paradigm [Hawley and Zabusky, Phys. Rev. Lett. 63, 1241 (1989)] are essential to obtain insight into this Richtmyer–Meshkov environment. We verify our recent discovery [Zabusky and Zhang, Phys. Fluids 14, 419 (2002)] that after the primary shockdeposition of vorticity by the incident shock, a vortex bilayer of large circulation magnitude grows significantly through intermediate times. The inclusion of physical viscosity allows us to examine some aspects of preturbulence at late–intermediate times.

The dielectrophoresis of cylindrical and spherical particles submerged in shells and in semiinfinite media
View Description Hide DescriptionThe dielectrophoretic forces acting on and the resulting velocities of cylindrical and spherical particles embedded in perfectly dielectricviscous fluids are calculated analytically. The fluids are confined in cylindrical/spherical shells and in semiinfinite media with prescribed potential distributions along the surfaces of the media. The forces are calculated by evaluating the Maxwell stress tensor. The velocities of the particles are obtained by solving the Stokes equation for creeping flow. The range of validity of force calculations based on the dipolemoment approximation is estimated.

A directnumericalsimulationbased secondmoment closure for turbulent magnetohydrodynamic flows
View Description Hide DescriptionA magnetic field, imposed on turbulent flow of an electrically conductive fluid, is known to cause preferential damping of the velocity and its fluctuations in the direction of Lorentz force, thus leading to an increase in stress anisotropy. Based on direct numerical simulations (DNS), we have developed a model of magnetohydrodynamic(MHD) interactions within the framework of the secondmoment turbulence closure. The MHDeffects are accounted for in the transport equations for the turbulent stress tensor and energy dissipation rate—both incorporating also viscous and wallvicinity nonviscous modifications. The validation of the model in plane channel flows with different orientation of the imposed magnetic field against the available DNS large eddy simulation and experimental data and show good agreement for all considered situations.

Anisotropic evolution of small isolated vortices within the core of the Earth
View Description Hide DescriptionIn this paper we examine the evolution of a freely evolving vortex in a rotating conducting fluid. The work is motivated by the study of smallscale motion in the fluid core of the Earth where magnetic and Coriolis forces dominate over nonlinear and viscous forces. The flow is incompressible and the magnetic Reynolds number is small. Two configurations are considered: (i) the rotation axis is perpendicular to a homogeneous imposed magnetic field; (ii) the two are parallel. Large time asymptotic expressions suggest that, in the context of configuration (i), the global kinetic energy of the vortex decays algebraically on a time scale of the Joule damping time. Configuration (ii) exhibits a strong channelling of energy along the axis which leads to a slowdown of the Joule dissipation. Several initial conditions are studied by varying the initial orientation of the vortex. The characteristic shapes of the resulting flows are examined in detail and it is shown that, for Earthlike parameters, the flow evolves and decays on a time scale of days. The second part of this paper examines flows subject to continuous forcing. In particular, we discuss radiation patterns in forced rotating conducting flows. It is observed that Taylor columns are developed while magnetic effects (such as pseudodiffusion and the fracturing of vortices) shape the flow to form a series of platelike cells orientated parallel to the magnetic and rotation axes.

Largeeddy simulation of conductive flows at low magnetic Reynolds number
View Description Hide DescriptionUsing the method of largeeddy simulation, we study decaying homogeneous turbulence of a conductive flow under the influence of an applied external magnetic field at low magnetic Reynolds number. In order to assess the performance of largeeddy simulation, comparison with high resolution direct numerical simulation is performed. Results show that the modeling of subgrid scales using the dynamic Smagorinsky model is very effective in the present context.

The relaxation of twodimensional rolls in Rayleigh–Bénard convection
View Description Hide DescriptionLarge aspect ratio, twodimensional, periodic convection layers containing a Boussinesq fluid of finite Prandtl number bounded by rigid or free horizontal surfaces are investigated numerically. The fluid equations are solved using both a standard pseudospectral and a Fourier integral method for the time evolution of finite initial perturbations, both random thermal perturbations and localized roll disturbances, into a final equilibrium state. The suggestion that a Fourier integral solution method is required to yield roll relaxation, the twodimensional process increasing the convection wavelength to values larger than critical, is investigated. Roll relaxation is found for both freeslip and noslip surfaces using either solution method as long as the initial state is chosen to be of the form of a localized roll disturbance. A wide variety of simulations are performed and roll relaxation is found to be independent of the periodic domain length, weakly dependent on the Rayleigh number and dependent upon the magnitude of the initial localized roll disturbances.

A study of laminar flow of polar liquids through circular microtubes
View Description Hide DescriptionRecently, the validity of using classical flowtheory to describe the laminar flow of polar liquids and electrolytic solutions through microtubes has been questioned for tube diameters as large as 500 μm [Brutin and Tadrist, Phys. Fluids 15, 653 (2003)]. This potential increase in flowresistance, which has been attributed to electrokinetic effects and enhanced surface roughness effects, is critical to the understanding of certain biofluid systems. We seek to characterize this phenomenon for a variety of capillary/liquid systems. Using a numerical solution to the Poisson–Boltzmann equation, we have calculated the electroviscous effect for the systems under consideration. We have also measured the pressure drop as a function of flow rate across wellcharacterized stainless steel and polyimide microtubes ranging in diameter from 120 μm to 440 μm. Deionized water, tap water, a saline solution, and a variety of glycerol/water mixtures were used. The calculations and measurements suggest that any deviation from Poiseuille flow for tubes larger than 50 microns in diameter is more likely caused by the enhanced importance of surface roughness in microtubes than by electrokinetic effects.

Numerical simulations of flow and heat transfer past a circular cylinder with a periodic array of fins
View Description Hide DescriptionThreedimensional, timedependent solutions of flow and heat transfer past a circular cylinder with a periodic array of circular fins is obtained using an accurate and efficient spectral multidomain methodology. A Fourier expansion with a corresponding uniform grid is used along the circumferential direction. A spectral multidomain method with Chebyshev collocation is used along the plane to handle the periodic array of circular fins attached to the surface of the cylinder. At a Reynolds number of 300 based on the cylinder diameter, results for the finned cylinder are compared with those of a smooth cylinder in order to see the effects of the presence of the fin array on flow and heat transfer. Detailed structure of fluid flow and temperature fields are obtained as a function of time to investigate how the fin array changes heat transfer mechanism related to the vortical structure in the wake region.

On Boussinesq models of constant depth
View Description Hide DescriptionThe mathematical properties, such as integrability, symmetries and multiple solitary wave solutions of Boussinesq models of constant depth are studied. An integrable modified Boussinesq model has been identified.

A novel application of Curle’s acoustic analogy to aeolian tones in two dimensions
View Description Hide DescriptionA new twodimensional formula to describe aeolian tones radiated from rigid bodies in a uniform flow at low Mach numbers is proposed as an improved approximation of Curle’s dipole solution. This modified Curle’s dipole is composed mainly of two simple terms; one depends on time and the other does not, which represent the acoustic propagation and the hydrodynamic mean effect, respectively. The acoustic term includes the Doppler effect by regarding the sound speed to be directional in the sourcefixed frame. The formula is verified in comparison with the results by direct numerical simulations (DNS) of the twodimensional compressible Navier–Stokes equations for sounds from a circular cylinder in low Mach numberflows. The results show that the modified Curle’s dipole approximates well the DNS results not only for the fluctuation pressure but also for the mean pressure in the far field. The mathematical basis of the formula is also presented in relation to the exact dipole term of the Ffowcs Williams–Hawkings equation.

A numerical investigation of wall effects up to high blockage ratios on twodimensional flow past a confined circular cylinder
View Description Hide DescriptionA finite volume method based on a velocityonly formulation is used to solve the flow field around a confined circular cylinder in a channel in order to investigate lateral wall proximity effects on stability, Strouhal number, hydrodynamic forces and wake structure behind the cylinder for a wide range of blockage ratios and Reynolds numbers For blockage ratios less than approximately 0.85 a first critical Reynolds number is identified at which a supercritical Hopf bifurcation of the symmetric solution occurs. For blockage ratios greater than about 0.687 and at Reynolds numbers exceeding the first critical Reynolds number a second curve of neutral stability is seen, representing a pitchfork bifurcation of the steady symmetric solution to one of two possible steady asymmetric solutions. Either side of the neutral stability curve for the pitchfork bifurcation our linear stability analysis and direct numerical simulations demonstrate that although the flow is linearly stable it is unstable to finite twodimensional perturbations. At blockage ratios larger than about 0.82 the steady asymmetric solutions also become unstable through a Hopf bifurcation. In contrast with the first Hopf bifurcation of the symmetric solution at lower Reynolds numbers numerical calculations of the lift coefficient reveal that the oscillations are no longer symmetric in the rising and falling parts of each cycle. Very strong vortices shed from the cylinder and the wall cause drastic increases in the amplitudes of the lift and drag coefficients. A codimension 2 point where pitchfork and Hopf bifurcations occur simultaneously has been located in parameter space. Altogether, four distinct regions in the parameter space have been identified, each corresponding to a different class of flow: (i) Steady symmetric flow, (ii) symmetric vortex shedding, (iii) steady asymmetric flow, and (iv) asymmetric vortex shedding, where a periodicintime flow is classed as symmetric or asymmetric depending on whether the timeaverage over one cycle of the lift coefficient is zero or not. Numerical solutions are computed on meshes having up to 1.8 million degrees of freedom. Extensive comparisons are made with the results available in the literature.

NonBoussinesq simulations of Rayleigh–Bénard convection in a perfect gas
View Description Hide DescriptionWe present direct numerical simulations of Boussinesq and nonBoussinesq Rayleigh–Bénard convection in a rigid box containing a perfect gas. For small stratifications, which includes Boussinesq fluids, the first instability after steady rolls was an oscillatory instability (a Hopf bifurcation). The resulting convection was characterized by two hot and two cold blobs circulating each convective roll. The same sign thermal perturbations (blobs) are at diametrically opposite points on the circular rolls, i.e., they are symmetric about the roll center. The time for a hot (or cold) blob to circulate a roll was between two and three roll turnover times. When the stratification was of sufficient strength, there was a dramatic change in the nature of the bifurcation. The sign of the thermal perturbations became antisymmetric with respect to the roll center, i.e., a hot blob was diametrically opposite a cold blob. In this case, a hot or cold blob circulated around each roll in about one turnover time. In a stratified layer, the Rayleigh number varies with height. We found that at the Hopf bifurcation, the Rayleigh number at the base was closest to the Boussinesq value. The change in instability appeared to be related to an increase in the speed (or Mach number) of the circulating rolls. It did not seem to be affected by the transport property variation with temperature. If the along roll aspect ratio was less than 2 or the walls perpendicular to the roll axis periodic, then only the symmetric instability could be found. We describe how our results might be reproduced in a laboratory experiment of convection in cryogenic helium gas.

Damping and pumping of a vortex Rossby wave in a monotonic cyclone: Critical layer stirring versus inertia–buoyancy wave emission
View Description Hide DescriptionThis paper further examines the rate at which potential vorticity in the core of a monotonic cyclone becomes vertically aligned and horizontally axisymmetric. We consider the case in which symmetrization occurs by the damping of a discrete vortex Rossby (VR) wave. The damping of the VR wave is caused by its stirring of potential vorticity at a critical radius outside the core of the cyclone. The decay rate generally increases with the radial gradient of potential vorticity at Previous theories for the decay rate were based on “balance models” of the vortex dynamics. Such models filter out inertia–buoyancy (IB) oscillations, i.e., gravity waves. However, if the Rossby number is greater than unity, the core VR wave can excite a frequencymatched outward propagating IB wave, which has positive feedback. To accurately account for this radiation, we here develop a theory for the decay rate that is based on the hydrostatic primitive equations. Starting from conservation of wave activity (angular pseudomomentum), an expression for the decay rate is derived. This expression explicitly demonstrates a competition between the destabilizing influence of IB wave emission, and the stabilizing influence of potential vorticity stirring at Moreover, it shows that if the radial gradient of potential vorticity at exceeds a small threshold, the VR wave will decay, and the vortex will symmetrize, even at large Rossby numbers.

On some common features of drop impact on liquid surfaces
View Description Hide DescriptionThe impact of a drop on liquid surfaces is studied experimentally and theoretically in the region of the fully developed splashing. In order to reveal the influence of viscosity and target liquid depth on the resulting flow patterns, the experiments were carried out with water and 70% glycerol–water solution, and for different target liquid depths. Based on the experimental observations, a dynamic model of the central jet formation at the cavity collapse is developed. This model predicts an emergence of a liquid flow up into the central jet and simultaneously a small flow velocity downward and allows us to evaluate the velocities of these two flows. A theoretical model for the cavity submergence is presented. This model gives the constant velocity of the cavity submergence which is half the initial drop impact velocity. Analytical solution for the gravity–capillary cavity collapse has been derived and provides a good fit to the experimental results. Theoretical analysis and experiments have shown that the maximum cavity radius and the cavity collapse time depend on both the Froude number and the dimensionless capillary length.
