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The Neumann-Michell linear potential flow theory of the short farfield waves created by a ship that advances at a constant speed in calm water is coupled with nonlinear analytical relations for inviscid flow along the wave profile at the ship hull surface, i.e., the contact line between the ship hull surface and the free surface. This ad hoc coupling of linear farfield ship waves and a nonlinear nearfield flow along a ship waterline determines short farfield ship waves in terms of the free-surface elevation along the ship hull surface, and provides insight into the influence of nearfield nonlinearities (most significant at a ship waterline) on short farfield ship waves. For the Wigley parabolic ship model, nearfield nonlinearities are found to be relatively weak and to have a limited, although appreciable, influence on short farfield waves. The steepness of divergent ship waves is also analyzed. This analysis shows that, for a full-scale Wigley hull, divergent waves are too steep to exist inside a broad inner Kelvin wake with angle roughly equal to 13°, i.e., a third of Kelvin's 39° ship wake angle. [ABSTRACT FROM AUTHOR]

This work presents an experimental study of the effects of finite water depth on the waves generated by a ship in a towing tank. The wakes of two hull forms representative of maritime and river ships are measured for both deep water and shallow water configurations and for several Froude numbers. The free surface deformations are measured with an optical stereo-correlation measurement method to access a full and detailed reconstruction of the wave fields. The spatial resolution of the reconstructed wakes allows us to perform a spectral analysis of the waves generated by the ships and to decompose them into a near-field hydrodynamic response and a far-field undulatory component. First, the spectral analysis method is presented and the effects of finite water depth on a theoretical point of view are studied. The analysis of subcritical, trans-critical, and supercritical ship wakes in both real space and spectral space highlights the effects of the finite water depth, of the ship speed, and of the hull shape on the energy distribution in the ship wakes through these different regimes. [ABSTRACT FROM AUTHOR]

In this experimental work, we carry out detailed two-dimensional particle image velocimetry investigations for the near field wakes behind a conventional and two multi-scale planar grids, using stitched camera fields of view. Statistical independent measurements are conducted focusing on the first few mesh distances downstream of the grid. It is found that the multiple integral length scales originated from the grids loose their importance on the turbulence development after about three mesh distances downstream, much earlier than the distance where the turbulence becomes homogeneous. The largest eddy size, represented by the integral length scales, does not show clear differences in its growth rate among the three grids after an initial development of three times the largest grid size downstream. Nevertheless, when examining individual vortex behaviours using conditional averaging and filtering processes, clear differences are found. The grids are found to have different decay rates of peak vorticity and projected vortex strengths. Despite these differences, the in-plane vorticity correlation function reveals that the mean vortex shape of all the grids shows a universal near-Gaussian pattern which does not change much as the turbulence decays. [ABSTRACT FROM AUTHOR]

The wakes resulting from micro-ramps immersed in a supersonic turbulent boundary layer at Ma=2.0 are investigated by means of particle image velocimetry. Twomicroramps are investigated with height of 60% and 80% of the undisturbed boundary layer, respectively. The measurement domain is placed at the symmetry plane of the ramp and encompasses the range from 10 to 32 ramp heights downstream of the ramp. The decay of the flow field properties is evaluated in terms of time-averaged and rootmean- square (RMS) statistics. In the time-averaged flow field, the recovery from the imparted momentum deficit and the decay of upwash motion are analyzed. The RMS fluctuations of the velocity components exhibit strong anisotropy at the most upstream location and develop into a more isotropic regime downstream. The selfsimilarity properties of velocity components and fluctuation components along wallnormal direction are followed. The investigation of the unsteady large scale motion is carried out by means of snapshot analysis and by a statistical approach based on the spatial auto-correlation function. The Kelvin-Helmholtz (K-H) instability at the upper shear layer is observed to develop further with the onset of vortex pairing. The average distance between vortices is statistically estimated using the spatial autocorrelation. A marked transition with the wavelength increase is observed across the pairing regime. The K-H instability, initially observed only at the upper shear layer also begins to appear in the lower shear layer as soon as the wake is elevated sufficiently off the wall. The auto-correlation statistics confirm the coherence of counter-rotating vortices from the upper and lower sides, indicating the formation of vortex rings downstream of the pairing region. [ABSTRACT FROM AUTHOR]

We compute the spatial optimal energy amplification of steady inflow perturbations in a non-parallel wake and analyse their stabilizing action on the global mode instability. The optimal inflow perturbations, which are assumed spanwise periodic and varicose, consist in streamwise vortices that induce the downstream spatial transient growth of streamwise streaks. The maximum energy amplification of the streaks increases with the spanwise wavelength of the perturbations, in accordance with previous results obtained for the temporal energy growth supported by parallel wakes. A family of increasingly streaky wakes is obtained by forcing optimal inflow perturbations of increasing amplitude and then solving the nonlinear Navier-Stokes equations. We show that the linear global instability of the wake can be completely suppressed by forcing optimal perturbations of sufficiently large amplitude. The attenuation and suppression of self-sustained oscillations in the wake by optimal 3D perturbations is confirmed by fully nonlinear numerical simulations. We also show that the amplitude of optimal spanwise periodic (3D) perturbations of the basic flow required to stabilize the global instability is much smaller than the one required by spanwise uniform (2D) perturbations despite the fact that the first order sensitivity of the global eigenvalue to basic flow modifications is zero for 3D spanwise periodic modifications and non-zero for 2D modifications. We therefore conclude that first-order sensitivity analyses can be misleading if used far from the instability threshold, where higher order terms are the most relevant. [ABSTRACT FROM AUTHOR]

The flow past a circular cylinder looses stability at Re ∼ 47, via the primary wake (PW) mode. Linear stability analysis of the steady base flow, in two dimensions, is conducted using a stabilized finite element formulation. A new mode, referred to as the secondary wake (SW) mode, is discovered which is found to be unstable for Re ≥ 110.8. The relative roles of the PW and SW mode in the development of Karman vortex shedding are also investigated. [ABSTRACT FROM AUTHOR]

We study experimentally the impulse response of a cylinder wake below the critical Reynolds number of the Bénard-von Kármán instability. In this subcritical regime, a localized inhomogeneous region of convective instability exists which causes initial perturbations to be transiently amplified. The aim of this work is to quantify the evolution resulting from this convective instability using two-dimensional particle image velocimetry in a hydrodynamic tunnel experiment. The velocity fields allow us to describe the evolution of wave packets in terms of two control parameters: the Reynolds number and the magnitude of the imposed perturbation. The temporal evolution of energy exhibits a transient algebraic growth at short times followed by an exponential decay. [ABSTRACT FROM AUTHOR]

Many wake flows are susceptible to self-sustained oscillations, such as the well-known von Kármán vortex street behind a cylinder that makes a rope beat against a flagpole at a distinct frequency on a windy day. One appropriate method to study these global instabilities numerically is to look at the growth rates of the linear temporal global modes. If all growth rates for all modes are negative for a certain flow field then a self-sustained oscillation should not occur. On the other hand, if one growth rate for one mode is slightly positive, the oscillation will approximately obtain the frequency and shape of this global mode. In our study, we first introduce surface tension between two fluids to the wake-flow problem. Then we investigate its effects on the global linear instability of a spatially developing wake with two co-flowing immiscible fluids. The inlet profile consists of two uniform layers, which makes the problem easily parametrizable. The fluids are assumed to have the same density and viscosity, with the result that the interface position becomes dynamically important solely through the action of surface tension. Two wakes with different parameter values and surface tension are studied in detail. The results show that surface tension has a strong influence on the oscillation frequency, growth rate, and shape of the global mode(s). Finally, we make an attempt to confirm and explain the surface-tension effect based on a local stability analysis of the same flow field in the streamwise position of maximum reverse flow. [ABSTRACT FROM AUTHOR]

The effect of a thin control wire on the wake properties of the flow around a circular cylinder has been investigated numerically. The governing equations are solved using a spectral element method for a Reynolds number of ReD=100. The diameter ratio of the main cylinder and the wire equals D/d=50 so no vortex shedding is expected to occur for the wire. However, the vorticity introduced by the wire in the vicinity of the upper shear layer of the cylinder still affects the vortex dynamics in the wake of the main cylinder. The primary effect of the wire is the reduction of the velocity fluctuations in the vortex formation region of the main cylinder. The maximum decrement occurs at a wire position of yw/D=0.875. The secondary effect of the wire is observed in the kinematics of the vortices, leading to a modified vortex arrangement and strength difference between the upper and lower vortices. Due to these effects, for yw/D≤0.875, a downward wake deflection is observed, while for larger values of yw/D>0.875, an upward deflection is found. The maximum downward deflection occurs at wire position yw/D=0.75 where the maximum positive mean lift coefficient, minimum drag coefficient, and minimum fluctuating lift coefficient are seen. Based on the observations, it is concluded that the deflection of the wake is primarily caused by a modification of the vortex arrangement in the wake. This modified vortex arrangement is caused by different formation times of the upper and lower vortices, by different vortex strengths, or by both. [ABSTRACT FROM AUTHOR]

In the present work, a simple proportional feedback control is designed to suppress the vortex-shedding instability in the wake of a prototype bluff-body flow, i.e., the flow around a square cylinder confined in a channel with an incoming Poiseuille flow. Actuation is provided by two jets localized on the cylinder surface and velocity sensors are used for feedback control. This particular configuration is a pretext to propose a more general strategy for designing a controller, which is independent of the type of actuation and sensors. The method is based on the linear stability analysis of the flow, carried out on the unstable steady solution of the equations, which is also the target flow of the control. The idea is to use sensitivity analysis to predict the displacement in the complex plane of some selected eigenvalues, found by the linear stability analysis of the flow, as a function of the control design parameters. In this paper, it is shown that the information provided by only sensitivity analysis carried out on the uncontrolled system is not sufficient to design a controller which stabilizes the flow. Therefore, the control is designed iteratively by successive linearizations. Apart from possible constraints, the position of the sensors, the direction along which velocity is measured, and the feedback coefficients are outputs of the design procedure. The proposed strategy leads to a successful control up to a Reynolds number which is at least twice as large as the critical one for the primary instability, using only one velocity sensor. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the effect of viscosity on the vorticity distribution and its rate of decay in the Kármán vortex street behind a circular cylinder. We used direct numerical simulation data, which we compare to well-known experimental measurements. By decomposing the incompressible velocity field in a frame of reference attached to the cylinder into its solenoidal and harmonic components, we identify the eddy structures associated with the formation, shedding, and rearrangement of the vortices into the Kármán street, and study their subsequent decay. This allows us to extend the conclusions of the partially viscous model by Hooker ['On the action of viscosity in increasing the spacing ratio of a vortex street,' Proc. R. Soc. London, Ser. A 154, 67 (1936)], who made several simplifying hypotheses: initial infinite-length filament-vortex wake, circular Lamb vortices of equal age at subsequent times, and no overlapping of the vortex cores. We show that the vortices have elliptical cores with an elliptical ratio that evolves downstream according to a systematic law. We also find that the vortex cores exhibit a Gaussian vorticity profile and a vorticity versus stream-function scatter plot clearly consistent with the Lamb-vortex model. The peak vorticity in the core decays downstream with a hyperbolic decay rate determined by the amount of circulation contained in the core at the early stages of the street, which is also consistent with Lamb's solution. [ABSTRACT FROM AUTHOR]

Direct numerical simulation is employed to study the effect of the Prandtl number, Pr=ν/α with ν the molecular viscosity and α the molecular diffusivity, on a turbulent wake in a stratified fluid. Simulations were conducted at a Reynolds number of 10 000, Re=UD/ν with U the velocity of the body and D the diameter of the body, for a range of Prandtl numbers: 0.2, 1, and 7. The simulations were run from x/D=6 to x/D=1200, a range that encompasses the near, intermediate, and far wake. Mean quantities such as wake dimensions and defect velocity were found to be weakly affected by Prandtl number, the same result was observed for vorticity as well. The Prandtl number has a strong effect on the density perturbation field and this results in a number of differences in quantities such as the total energy of the wake, wave flux, scalar and turbulent dissipation, mixing efficiency, spectral distribution of energy in the density and velocity fields, and the transfer of energy between kinetic and potential modes. The approximation Pr=1 for the ocean is often used in practice. As the qualitative behavior of the large-scale features was the same for the three cases, we conclude that Pr=1 is a reasonable approximation for the Pr=7 case in stratified wake simulations, given the significantly higher computational cost required at large Prandtl number. [ABSTRACT FROM AUTHOR]

Using a phase-averaged technique, the dependence of the wake vortical structures on cylinder yaw angle α (=0°–45°) was investigated by measuring all three-velocity and vorticity components simultaneously using an eight-hot wire vorticity probe in the intermediate region (x/d=10) of a yawed stationary circular cylinder wake. For all yaw angles, the phase-averaged velocity and vorticity contours display apparent Kármán vortices. It is found that when α≤15°, the maximum coherent concentrations of the three vorticity components do not change with α. However, when α is increased to 45°, the maximum concentrations of the coherent transverse and spanwise vorticity components decrease by about 33% and 50%, respectively, while that of the streamwise vorticity increases by about 70%, suggesting that the strength of the Kármán vortex shed from the yawed cylinder decreases and the three dimensionality of the flow is enhanced. The maximum coherent concentrations of u and v contours decrease by more than 20% while that of w increases by 100%. Correspondingly, the coherent contributions to the velocity variances 〈u2〉 and 〈v2〉 decrease, while that of increases. These results may indicate the generation of the secondary axial vortices in yawed cylinder wakes when α is larger than 15°. The incoherent vorticity contours <ωxr2> are stretched along an axis inclining to the x-axis at an angle β in the range of 60°–25° for α=0°–45°. The magnitudes of <ωxr2>* and <ωyr2>* through the saddle points are comparable to the maximum concentration of the coherent spanwise vorticity ωz* at all cylinder yaw angles, supporting the previous speculation that the strength of the riblike structures in the cylinder wake is about the same as that of the spanwise structures, even in the yawed cylinder wakes. [ABSTRACT FROM AUTHOR]

The flow around a slender body with a blunt trailing edge is unstable in most situations of interest. Usually the flow instabilities are generated within the wake behind the bluff body, inducing fluctuating forces and introducing the possibility of resonance mechanisms with modes of the structure. Base bleed is a simple and well-known means of stabilizing the wake. In the present research, we investigate the global instability properties of the laminar-incompressible flow that develops behind a cylinder with sharp edges and axis aligned with the free stream using a spectral domain decomposition method. In particular, we describe the flow instability characteristics as a function of the Reynolds number, Re=ρW∞D/μ, and the bleed coefficient, defined as the bleed-to-free-stream velocity ratio, Cb=Wb/W∞, where D is the diameter of the body and ρ and μ the density and viscosity of the free stream, respectively. For a truncated cylinder of aspect ratio L/D=5, where L is the length of the body, our calculations reveal the presence of a first steady bifurcation in the wake at Re≃391, as well as a second oscillatory one at Re≃715 with an associated Strouhal number St≃0.0905 for the most unstable azimuthal mode |m|=1. In addition, we report the existence of two critical values of the bleed coefficient Cb1*(Re,|m|) and Cb2*(Re,|m|)

Imposing axial flow in the annulus and/or radial flow through the cylindrical walls in a Taylor–Couette system alters the stability of the flow. Theoretical methods and numerical simulations were used to determine the impact of imposed axial and radial flows, homogeneous in the axial direction, on the first transition of Taylor–Couette flow in the framework of convective and absolute instabilities. At low axial Reynolds numbers the convective instability is axisymmetric, but convective helical modes with an increasing number of helices having a helicity opposite that of the base flow dominate as the axial flow increases. The number of helices and the critical Taylor number are affected only slightly by the radial flow. The flow becomes absolutely unstable at higher Taylor numbers. Absolutely unstable axisymmetric modes occur for inward radial flows, while helical absolute instability modes having a helicity identical to that of the base flow occur at high enough axial Reynolds numbers for outward radial flow. [ABSTRACT FROM AUTHOR]

The three-dimensional axisymmetry-breaking instability of axisymmetric flow between a rotating lid and a stationary cylinder is analyzed both numerically and experimentally for the case of tall cylinders with the height/radius aspect ratio between 3.3 and 5.5. A complete stability diagram for the primary three-dimensional instability is obtained experimentally and computed numerically. The instability sets in due to different three-dimensional disturbance modes that are characterized by different azimuthal wavenumbers. The critical Reynolds numbers and associated frequencies are identified for each mode. The onset of three-dimensional flow behavior is measured by combining the high spatial resolution of particle image velocimetry and the temporal accuracy of laser Doppler anemometry. The results are compared to the numerical stability analysis. The measured onset of three dimensionality is in a good agreement with the numerical results. Disagreements observed in supercritical regimes can be explained by secondary bifurcations that are not accounted for by linear stability analysis of the primary base flow. [ABSTRACT FROM AUTHOR]

The prediction of the rise speed of large buoyant bubbles is a fundamental fluid mechanics problem relevant to a number of applications ranging from carbon sequestration technology to chemical engineering or astrophysics. Single large bubbles typically have a spherical cap shape with bubbles of larger volume rising faster than the ones of smaller volume. However, except in well-controlled experiments, the released gas splits into a leading cap bubble, followed by a crown of satellite bubbles that can contain up to 50% of the total volume of gas. We find that in this case the satellite bubbles rearrange in a characteristic toroidal crown and the leading bubble takes a lenticular shape. The rise speeds of these multipart bubble systems and the ratios of the torus radii to the leading cap curvature radii are quite constant and predictable in the mean and are furthermore independent of the gas partitioning between the leading lenticular bubble and the crown of satellite bubbles. We also find that this multipart bubble system rises slightly faster than a single cap bubble with the same total injected volume of gas. [ABSTRACT FROM AUTHOR]

Previous studies of the interaction between boundary layer streaks and Tollmien–Schlichting (TS) waves have shown puzzling effects. Streaks were shown to reduce the growth rate of primary TS waves and, thereby, to delay transition; however, they can also promote transition by inducing a secondary instability. The outcome of the interaction depends on the spanwise wavelength and intensity of the streaks as well as on the amplitude of the TS waves. A Floquet analysis of secondary instability is able to explain many of these features. The base state is periodic in two directions: it is an Ansatz composed of a saturated TS wave (periodic in x) and steady streaks (periodic in z). Secondary instability analysis is extended to account for the doubly periodic base flow. Growth rate computations show that, indeed, the streak can either enhance or diminish the overall stability of the boundary layer. The stabilizing effect is a reduction in the growth rate of the primary two-dimensional TS wave; the destabilizing effect is a secondary instability. Secondary instability falls into two categories, depending on the spanwise spacing of the streaks. The response of one category to perturbations is dominated by fundamental and subharmonic instability; the response of the other is a detuned instability. [ABSTRACT FROM AUTHOR]

The drag coefficient for freely falling cones with a vertex angle of 60° was determined experimentally in the Reynolds number range from 90 to 8×103 and described by empirical equations. The drag was determined by measurement of the terminal velocity of the cones falling through water. Flow-visualization experiments showed the different regimes of the wake structure for a wide range of the Reynolds numbers covering the successive destabilizations of the wake on the way to turbulence. Especially, a very regular staggered array of two rows of ring-shaped hairpin vortices appeared behind the cones in the Reynolds number range from 170 to 235. The Strouhal number was determined in the Reynolds number range from 170 to 1.2×103. The arrangement of the double row of vortex rings and the oscillatory motion of the cones were given in some detail. [ABSTRACT FROM AUTHOR]

The flow normal to a cylinder with hemispherical ends is computed using a spectral-element/Fourier method. With variation in the ratio of cylinder length to diameter, this body varies smoothly from a sphere to a straight circular cylinder, providing insight into the relationship between body topology and wake dynamics. This letter displays the wake structure for a range of cylinder lengths up to a Reynolds number of 300 and considers the wake alignment and symmetry at length ratios approaching a spherical body. A time-invariant wake consistent with that behind a sphere is found to preferentially align with a symmetry plane bisecting the major axis of short cylinders, whereas the periodic “hairpin” wake aligns with the minor axis; thus the hairpin vortices shed from alternate sides of the cylinder, just as with Kármán vortex shedding from a circular cylinder. The plane of symmetry is found to break via a supercritical transition at a Reynolds number of 350±2. [ABSTRACT FROM AUTHOR]

Experiments were conducted to understand the effect of an axial jet on the merging process of a simulated flap-edge and wing-tip corotating vortex pair in the near wake. Cross-flow velocity measurements and flow visualization were performed for the three realistic jet positions on both equal and unequal strength like-signed vortices for a range of momentum coefficients. The main finding was that the initial jet position has a vastly contrasting effect on the merging process. If the jet turbulence rapidly interacts with only one of the vortices, severe diffusion of that vortex occurs which ultimately wraps around and becomes consumed by the unaffected vortex structure. The jet causes a reduction in the vortex spacing and an increase in the rotation angle; hence, merging is promoted. If the jet turbulence does not directly interact with either vortex but instead interferes with the mechanism in the outer-recirculation region that advects vorticity to a larger radius, then merging can be retarded. In this case, an increase in vortex spacing and reduction in rotation angle were observed. Increasing the momentum coefficient, hence, introducing more turbulence into the flow, has a greater effect on the merging process. [ABSTRACT FROM AUTHOR]

Recent laboratory experiments [G. Perret, A. Stegner, M. Farge, and T. Pichon, Phys. Fluids 18, 036603 (2006)] have shown that the vortex-street formed in the wake of a towed cylinder in a rotating shallow-water layer could present a strong cyclone-anticyclone asymmetry. In extreme cases, only large-scale anticyclones were observed in the far wake. This asymmetry occurs in the so-called frontal regime when the Rossby number is small and the surface deviation is large. This asymmetry may have various origins and in particular may be attributed to the asymmetry of the flow around the cylinder, to the linear stability property of the wake, or to its nonlinear evolution. To discriminate between these mechanisms, we study the stability of two idealized parallel flows in the quasigeostrophic and in the frontal regimes. These parallel flows correspond to two velocity profiles measured just behind the cylinder in a region where the perturbations are negligible. According to our linear stability analysis, the most unstable mode, in the frontal regime, is localized in the anticyclonic shear region whether the base flow profile is symmetric or not. On a linear basis, it is thus more the instability that imposes the asymmetry than the base flow. Direct numerical simulations of the synthetic parallel wake flows show that nonlinearity exacerbates the dominance of the anticyclonic mode linearly selected. By numerically studying the spatio-temporal evolution of a small perturbation localized in space, we show that, unlike incompressible two–dimensional wake flows and the symmetric wake in the quasigeostrophic regime, the parallel asymmetric wake is strongly convectively unstable in the frontal regime, and not absolutely unstable. When the surface deformation becomes large, the wake instability changes from the absolute instability in the quasi-geostrophic regime to the strongly convective instability of the frontal regime. This explains well the changes. [ABSTRACT FROM AUTHOR]

The wake flow structures and the drag force for a cylinder rolling along a wall without slipping were calculated for the Reynolds number range 20

In this paper we construct two-dimensional steady potential flows past a circular cylinder as generalizations of the point-vortex Föppl system. For a given classical Föppl system, these higher-order systems form a two-parameter family depending on the truncation order N and the area A of the vortex region desingularizing the original Föppl solution. We characterize the higher-order equilibria analytically and numerically, and show that their modified linear stability properties make the higher-order systems useful models for a class of flow control problems. [ABSTRACT FROM AUTHOR]

We have studied the flow induced by a macroscopic spherical particle settling in a Laponite suspension that exhibits a yield stress, thixotropy, and shear thinning. We show that the fluid thixotropy (or aging) induces an increase with time of both the apparent yield stress and shear-thinning properties but also a breaking of the flow fore-aft symmetry predicted in Hershel-Bulkley fluids (yield-stress, shear-thinning fluids with no thixotropy). We have also varied the stress exerted by the particles on the fluid by using particles of different densities. Although the stresses exerted by the particles are of the same order of magnitude, the velocity field presents utterly different features: whereas the flow around the lighter particle shows a confinement similar to the one observed in shear-thinning fluids, the wake of the heavier particle is characterized by an upward motion of the fluid (“negative wake”), whatever the fluid’s age. We compare the features of this negative wake to the one observed in viscoelastic shear-thinning fluids (polymeric or micelle solutions). Although the flows around the two particles strongly differ, their settling behaviors display no apparent difference which constitutes an intriguing result and evidences the complexity of the dependence of the drag factor on flow field. [ABSTRACT FROM AUTHOR]

A general model is described for drag wakes in a linearly stratified fluid, based on the self-preservation of the flow. It is assumed that the buoyancy-controlled self-similar wake expands in the horizontal direction due to turbulent diffusion and in the vertical direction due to viscous diffusion. The mean characteristics of the wake (height, width and velocity defect) are analytically derived and show good agreement with existing data from experimental and numerical results. Moreover, the three regimes previously found in the literature that characterize different dynamical phases of the wake evolution are recovered, and two new regimes are found. The model allows for prediction of characteristic length and velocity scales at the high Reynolds numbers of large-scale applications of geophysical and naval origin. [ABSTRACT FROM AUTHOR]

Base blowing is a simple and well-known means of stabilizing both two-dimensional and axisymmetric bluff-body wakes at supercritical Reynolds numbers. In the present Brief Communication we consider a generalization of previous works by studying the effect of the bleed-to-freestream density ratio, S=ρb/ρ∞, on the stability properties of the wake behind an axisymmetric, slender body with a blunt trailing edge. Since a lower density in the slow stream is known to inhibit absolute instability, here we restrict our attention to the case of light bleed fluid, S<1. This mechanism is shown to inhibit the wake for values of the bleed coefficient, defined as the bleed-to-freestream velocity ratio Cb=ub/u∞, smaller than those obtained in the homogeneous case of S=1. Our approach consists of obtaining the basic, axisymmetric flow by integration of the full set of Navier-Stokes and species conservation equations in cylindrical coordinates, and calculating its linear, local, spatio-temporal stability downstream of the body base. The analysis predicts a critical bleed coefficient Cb*, which decreases with the density ratio according to the linear law Cb*≃0.01+0.05S for 0.1≼S≼1. [ABSTRACT FROM AUTHOR]

The analysis of the near-wake flow downstream of a flat plate is reported in this paper for the case of a non-Newtonian (power-law) constitutive model. To our knowledge, the present paper is the first to address this problem, as previous work on near-wakes has been limited to the use of a Newtonian model. The motivation for this work comes from the biomedical engineering problem of blood flow around the bileaflet of a mechanical heart valve. In the present paper, the series method has been used to calculate the flow near the centerline of the wake, while an asymptotic method has been used for larger distances from the centerline. The effects of power-law inlet conditions on the wake flow are reported for various values of the power-law index n, within the range 0.7≤n≤1.3. The present analysis has been successfully validated by comparing the results for n=1 to the near-wake results by Goldstein [Proc. Cambridge Philos. Soc. 26, 1 (1930)]. We generalized the equations for arbitrary values of n, without any special considerations for n=1. Therefore, the accurate results observed for n=1 validate our procedure as a whole. The first major finding is that a fluid with smaller n develops faster downstream, such that decreasing n leads to monotonically increasing velocities compared to fluids with large n values. Another finding is that the non-Newtonian effects become more significant as the downstream distance increases. Finally, these effects tend to be more pronounced in the vicinity of the wake centerline compared to larger y locations. [ABSTRACT FROM AUTHOR]

We report experiments on liquid curtains falling between two vertical wires. The flow is mainly driven by gravity, so that the Weber number (We) (ratio of momentum flux to twice the surface tension) is close to zero at the top of the curtain and increases downstream, with the possible existence of a location where We equals 1 (which turns out to be a singular point in the sheet, in terms of waves propagation). In the present paper, we focus on the curtain response to localized perturbations, i.e., formation of either surface waves or free edges behind a thin needle touching the curtain, with a special emphasis to what happens near the break-up limit. We extract and compare the shapes of two kind of “wakes” left behind the obstacle: classical triangular wake of standing sinuous waves and stationary hole involving two free edges pinned on the needle. It is found that these two wakes are very similar for high enough We, but behave very differently when We reaches 1 from above; the sinuous wake disappears, while the “hole wake” still exists, and its shape becomes rounded. Below We=1, the hole can either stay stable, oscillate or expand and break the curtain. We provide exact analytical expressions for stationary free-edges that compare very well with experiments. [ABSTRACT FROM AUTHOR]

The effects of initial conditions on interaction between a boundary layer over a flat plate and flow around a wall-mounted finite-length cylinder were experimentally investigated. A square cylinder with a characteristic width (d) of 20 mm and a length of H=5d was vertically mounted on a horizontal flat plate. Three different boundary layers were investigated, their momentum thickness being 0.07d, 0.13d, and 0.245d, respectively, measured at the cylinder axis in the absence of the cylinder. All the experiments were carried out in a closed-loop water tunnel at a Reynolds numbers of 11 500 based on d and the free-stream velocity U∞. It is found that initial boundary layer conditions have a profound effect on the near wake, including the flow near the cylinder free end that is well beyond the boundary layer. With increasing boundary layer thickness, the base vortex is enhanced, inducing a stronger upwash flow from the cylinder base, which acts to weaken the downwash free-end shear layer and the tip vortex. Consequently, spanwise vortices gain strength near the free end but impair near the wall, causing the ratio of symmetrically to antisymmetrically arranged vortices to vary and subsequently the Reynolds stresses to increase significantly in magnitude near the free end but to decrease near the wall. [ABSTRACT FROM AUTHOR]

Large gas bubbles rising under the effect of buoyancy are known to adopt either a spherical cap shape or to undergo a topological transition after which they become toroidal. We carry out an axisymmetric numerical investigation of the evolution of such large bubbles in the presence of both capillary and viscous effects. The numerical approach is of the volume of fluid type (it solves the Navier-Stokes equations on a fixed grid and transports the local volume fraction of one of the fluids), but does not involve any explicit reconstruction of the interface. The transition from spherical cap to toroidal bubbles is studied in the parameter space built on the Bond (Bo) and Archimedes (Ar) numbers, which compare the strength of inertial effects to that of capillary and viscous effects, respectively. Preliminary tests show that the position of this transition is very sensitive to the grid resolution; these tests are used to select grid characteristics that yield grid-independent results. Two markedly different transition scenarios, corresponding to the limit of large Ar and large Bo, respectively, are then identified. In the first case, the front of the bubble is pierced by an upward jet coming from the rear of the bubble. In contrast, in the limit of large Bo, a downward jet develops at the front part and pierces the rear of the bubble, unless viscous effects are sufficient to stabilize the front. We also determine the position of the transition for intermediate values of Bo and Ar and discuss the connection between present axisymmetric results and experimental situations in which the bubble is followed by a turbulent wake. We finally examine a puzzling feature of these large bubbles which is that, given an initial gas volume, the final bubble topology appears to depend dramatically on the initial conditions. Indeed, we find that initially oblate bubbles may result in stable spherical cap bubbles for values of Bo and Ar well beyond those for which initially spherical bubbles of similar volume undergo the topological transition. This remarkable influence of the initial shape is shown to be due to the influence of the oblateness on both the bubble acceleration and the hydrostatic pressure difference between the two bubble poles. [ABSTRACT FROM AUTHOR]

The paper presents a nonparallel stability analysis of the intermediate region of the two-dimensional wake behind a bluff body. In particular, it analyzes the convective instabilities using a Wentzel-Kramers-Brillouin-Jeffreys method on a basic flow previously derived from intermediate asymptotics [D. Tordella and M. Belan, Phys. Fluids 15, 1897 (2003)]. The multiscaling is carried out to explicitly account for the effects associated to the lateral momentum dynamics at a given Reynolds number. These effects are an important feature of the base flow and are included in the perturbative equation as well as in the associated modulation equation. At the first order in the multiscaling, the disturbance is locally tuned to the property of the instability, as can be seen in the zero-order theory (near-parallel parametric Orr-Sommerfeld treatment). This leads to a synthetic analysis of the nonparallel correction of the instability characteristics. The system is, in fact, considered to be locally perturbed by waves with a wave number that varies along the intermediate wake and which is equal to the wave number of the dominant saddle point of the zero order dispersion relation, taken at different Reynolds numbers. In this study, the Reynolds number is thus the only parameter. It is shown that the corrections to the frequency, and to the temporal and spatial growth rates are remarkable in the first part of the intermediate wake and lead to absolute instability in regions that extend to about ten body scales. The correction increases with the Reynolds number and agrees with data from laboratory and numerical experiments in literature. An eigenfunction and eigenvalue asymptotic analysis for the far wake is included, which is in excellent agreement with the complete problem. [ABSTRACT FROM AUTHOR]

The influence of the aspect ratio on the three-dimensionalization and subsequent saturation of freely decaying two-dimensional turbulence is studied numerically. We show that the aspect ratio strongly affects the saturation level of the perturbation and its feedback on the base flow. The saturation level scales linearly with the aspect ratio, as does the total damping exerted by the perturbation. In spectral space the feedback yields a positive eddy viscosity at large scales and a small eddy viscosity at small scales. A surprising result is the persistence of coherent vortices even after the saturation of the perturbation. [ABSTRACT FROM AUTHOR]

The effect of the initial conditions on scalar mixing in the turbulent wake of a circular cylinder is studied. The scalar under consideration is temperature and it is injected by means of an array of parallel, heated, fine wires (a mandoline). The initial length scale of the velocity field is varied (relative to that of the scalar field) by changing the downstream location of the mandoline. The initial length scale of the scalar field is modified by changing the number of mandoline wires and their spacing. In accordance with previous results in homogeneous, isotropic, grid turbulence, increasing the initial length scale of the velocity field was found to (i) increase the decay rate of scalar variance (m), (ii) decrease the integral scale of the scalar field (lθ), and (iii) increase the mechanical to thermal time scale ratio r. Varying the mandoline wire spacing had little effect on m, lθ, or r. Increasing the width of the mandoline decreased the scalar variance decay rate. Doing so, however, had negligible effect on the structure of the scalar field (i.e., lθ or r). The independence of the scalar variance decay rate and the structure of the scalar field—the opposite of what is observed in grid turbulence—is attributed to the inhomogeneous nature of the flow. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An experimental investigation was carried out in the very near wake of a circular cylinder over the Reynolds number range of 260

Solutions for the (steady or unsteady) wake flows induced by a localized single force or a force doublet in a uniform stream are obtained in Oseen approximation for two-dimensional (planar) as well as for three-dimensional (axisymmetric) flows. These solutions are compared with the steady solutions obtained previously by other authors in boundary layer approximation. The straightforward approach to the general problem of the flow induced by any distribution of localized forces which was developed here, can be used to obtain the vorticity and stream function distributions for the flows generated by forcing of more complicated spatial symmetry in both two and three dimensions. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Coarse-scale mixing in a recirculation zone is described with a simple vortex model. Time-dependent 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 side-constraints 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 low-frequency 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. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The 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. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Similarity solutions for laminar two-fluid jets and wakes are derived in the boundary-layer 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 χ=ρ[sub 1]μ[sub 1]/ρ[sub 2]μ[sub 2], where ρ[sub i] and μ[sub i] are, respectively, the density and absolute viscosity of the fluid in the upper (i=1) and lower (i=2) fluid domains, while the momentumless wake profile depends on the parameter Ω=ρ[sub 1]μ[sub 2][sup 3]/ρ[sub 2]μ[sub 1][sup 3]. Generally, all interfaces deflect from horizontal except the fan jet. However, while the interface for the classical planar two-fluid wake is never flat, the interfaces for the planar jet and the momentumless wake become flat in the particular case μ[sub 1]=μ[sub 2]. Velocity profiles illustrating the strongly asymmetrical jet and wake profiles that arise in air-over-water, oil-over-water, and air-over-oil flows are presented. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper we compare the wakes of various bluff bodies in a stratified fluid at moderately high Froude numbers (F≡2U[sub B]/ND>8) and Reynolds numbers (Re≈5000). The size and amplitude of the long-lasting wakes clearly depend on the shape of the bluff body, the wake width being small for a streamlined object and large for an object with sharp edges. However, the wake width can be collapsed when it is normalized by an effective diameter based on the drag force, often called the momentum thickness. General laws for the wake width, the velocity defect, and the Strouhal number are thus deduced and fit the data well. Finally, the cross-fluctuations of the velocity and the turbulent kinetic energy are analyzed. Their amplitudes and widths are proportional to those of the mean profile. Thus, the wake remembers only the momentum flux given by the bluff body to the fluid and not any other aspects of its geometry. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

An analytical solution was obtained for the virtual mass coefficient of a spherical-cap bubble. The flow field around the bubble was divided into two regions: the frontal and the wake region. The solution is valid by its asymptotic approach to the two geometric limits of the circular disk and the complete sphere. [ABSTRACT FROM AUTHOR]

A known bifurcation scenario describing the development and interaction of Mode A and Mode B vortex shedding modes of a circular cylinder wake is extended to predict the Strouhal-Reynolds number profile over the three-dimensional transitions. The mode amplitudes are described by coupled Landau equations and, with frequency information being included by the addition of complex coefficients, the model predicts the discontinuous nature of the Strouhal-Reynolds number shedding profile of the circular cylinder wake throughout the laminar three-dimensional transition regime. The model coefficients are determined from computations of the three-dimensional modes of a circular cylinder wake. [ABSTRACT FROM AUTHOR]

The wake transition regime in square cylinder flow is investigated experimentally. Mode A and B transitions similar to those captured in circular cylinder flows are found to exist in this regime and by using dye- and laser-induced fluorescence visualization, the spanwise and streamwise vortex structures are captured. Upon comparison with their corresponding modes in circular cylinder flows, some differences are noted. Most notably, the critical Reynolds numbers at which Mode A and B occur for square cylinder flows were estimated to be approximately 160 and 200, respectively, and are lower than those found in circular cylinder flows, which are generally agreed to be approximately 188--190 and 230--260, respectively. Also, the spanwise wavelengths for the two modes in square cylinder flows 5.2 D s and 1.2 D s for Modes A and B, respectively! are longer than their counterparts in circular cylinder flows (3 -- 4D o and 0.8--1D o , respectively!. Furthermore, by using a hot wire to measure the shedding frequency, it was found that the Mode A transition here does not exhibit a hysteresis phenomenon, which is unlike the case in circular cylinder flows. The Mode A to B transition here is also not associated with a sudden increase in Strouhal number, which is again unlike the corresponding situation in circular cylinder flows. However, the vortical structures are noted to be similar between the corresponding modes for the two bluff body shapes, and hence the formation mechanism can be deemed to be similar. [ABSTRACT FROM AUTHOR]

The present study contributes to the numerical simulations of weak compressible effects for laminar flows around heated circular cylinders. Our aim in this work is to understand the physics of the flow around a heated cylinder and the reasons for the decrease in the frequency of vortex shedding in the wake behind the cylinder as the ratio of surface temperature to freestream temperature increases for moderate Re numbers. The previous achievements on this subject rely mainly on experimental investigations by using a "representative" or "film temperature" and therefore should be investigated more accurately by the numerical considerations. In that context, numerical experiments are carried out. A technique which was previously tested and validated on a variety of flow problems is utilized in the numerical experiments. The results show that the temperature is not a passive contaminant especially for flows with temperature ratios T[SUB*]=T[SUBw]/T[SUBinfin] greater than 1.1. The temperature boundary layer surrounding the wall introduces weak compressible effects on the velocity and on the pressure field especially for Re numbers below 100. As a consequence of this result, the local Ma number effects are shown on a Re-Nu curve for the laminar unsteady vortex shedding regime. [ABSTRACT FROM AUTHOR]

This study describes large eddy simulations of the interaction between an exhaust jet and a trailing vortex, in the near-field of an aircraft wake. Two cases are analyzed: in the first one, typical of cruise flight, the jet and the vortex axes are sufficiently well separated to study first the jet dynamics before considering its interaction with the vortex. Dynamics and mixing are controlled both by the jet diffusion and its entrainment around the vortex core. In the second case the jet partially blows in the vortex core, making the flow similar to a Batchelor vortex. The strong perturbations injected into the core cause an instability of the system which is continuously fed by the jet elements wrapping around the core. This leads to a strong decay of angular momentum and diffusion of the core. Global mixing properties, such as plume area and global mixedness evolutions, are analyzed and two applications to environmental problems are finally discussed. [ABSTRACT FROM AUTHOR]

An approximated Navier-Stokes steady solution is here presented for the two dimensional bluff body wake region that is intermediate between the field on the body scale L[SUBD], which includes the two symmetric counter-rotating eddies, and the ultimate far wake. The nonparallelism of the streamlines in the intermediate wake cannot yet be considered negligible. The R is of the order of the critical value for the onset of the first instability and the limiting behavior for large R is not considered. The solution is obtained by matching an inner solution -- a Navier -- Stokes expansion in powers of the inverse of the longitudinal coordinate -- and an outer solution, which is a Navier-Stokes asymptotic expansion in powers of the inverse of the distance from the body. The matching is built on the criteria that, where the two solutions meet, the longitunal pressure gradients and the vorticities must be equal and the flow toward the inner layer must be equal to the outflow from the external stream. At high orders in the inner expansion solution, the lateral decay turns out to be algebraic. This approximate solution is here examined in relation to the class of asymptotic solutions that, in the past, were obtained by adopting the rapid decay principle, which implies an irrotational outer flow. The theme running through this paper is the necessity of the addition of this criterion to the equations of motion to build a solution that describes the intermediate wake. The present solution has been obtained by relaxing the imposition of the rapid decay principle. It can be concluded that, at Reynolds numbers as low as the first critical value and where the nonparallelism of the streamlines is not yet negligible, the division of the field into two basic parts -- an inner vortical boundary layer flow and an outer potential flow -- is spontaneously shown up to the second order of accuracy: at higher orders in the expansion solution the vorticity is first convected and then... [ABSTRACT FROM AUTHOR]

A computerized flow analysis of wake phenomena caused by a discontinuity in cylinder diameter is presented. The vortex linkage and half-loop formation observed experimentally by Lewis and Gharib [Phys. Fluids A 4, 104 (1992)] have for the first time been reproduced numerically. The instantaneous vorticity and pressure fields provide a distinct picture of the direct-mode interaction, from which it is concluded that a new half-loop is formed every third shedding cycle. [ABSTRACT FROM AUTHOR]

Studies instability characteristics of curved incompressible free shear layers, with mean velocity profiles having a wake component. Use of linear inviscid stability theory in spatial formulations; Consideration of both two- and three-dimensional disturbances; Amplification rates of the shear layer mode and the wake mode.

Studies fluid flow in the wake of single and two interacting air bubbles freely rising in water. Determination of the path and shape oscillations of the bubble; Coupling of the zigzagging motion to a regular generation and discharge of alternate oppositely oriented hairpin-like vortex structures; Suggestion that bubble interaction is strongly triggered by wake dynamics.

Investigates the linear versus nonlinear convective/absolute instability of a family of plane wake profiles at low Reynolds number. Comparison of the linearized and the fully nonlinear impulse responses; Retrieval of the linear temporal and spatiotemporal instability properties; Selection of the velocity of the fronts.