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Experiments were carried out to study the sedimentation of a two-dimensional particle cloud. When a large number of particles (glass beads) of uniform size are released from a two-dimensional opening into a column of fresh water, the mixture initially descends as a thermal; however, after some time, the particles start settling individually, thus leaving the parent fluid behind. For a given type of particle, the critical depth zc at which this transition occurs, measured from a virtual origin, was found to change as zcws/ν∼(Q/νws)α, with α[bar_over_tilde:_approx._equal_to]0.3, where ws is the terminal velocity of a single particle, ν is the kinematic viscosity, and Q is the total buoyancy of the released particles per unit length. The descending velocity and the spatial growth of the particle cloud were found to depend on its sedimentation characteristics. [ABSTRACT FROM AUTHOR]

There is increasing awareness that even in fully turbulent boundary layers, large-scale structures in the form of hairpin vortices abound. Although their implications are not all that clear at the present time, they seem to play an important role in turbulent flows. Due to the inherent unpredictability of hairpin vortices in their natural state, in the past effort has been made to generate synthetic hairpin vortices in a laminar boundary layer; from their study considerable insight into the processes underlying various features of turbulent flows has been gained. Contrary to those preceding studies where attention has been directed to the flows external to hairpin vortices, interest here is focused solely upon their interiors: the possible existence of cross-flow transport inside the cores of the hairpin legs. In synthetic hairpin vortices, the presence of such a corewise transport away from a wall surface, or the ‘‘tornado effect,’’ is substantiated in a water tunnel with flow visualization techniques. The effect is also verified using heated fluid injected near the wall surface by measuring the temperature at various points along the hairpin vortex core. [ABSTRACT FROM AUTHOR]

Taylor–Dean vortices are considered in channels whose thickness and curvature vary slowly on a scale 1/δ. The effect of divergence of the channel is shown to be destabilizing and of convergence to be stabilizing. Results for neutral curves are presented for a class of particular channels, and a method of computing such curves for more general channels is given. [ABSTRACT FROM AUTHOR]

The two-dimensional unsteady incompressible Navier–Stokes equations, solved by a fractional time-step method, were used to investigate separation due to the application of an adverse pressure gradient to a low-Reynolds number boundary layer flow. The inviscid pressure distribution of Gaster [AGARD CP 4, 813 (1966)] was applied in the present computations to study the development of a laminar separation bubble. In all cases studied, periodic vortex shedding occurred from the primary separation region. The shed vortices initially lifted from the boundary layer and then returned towards the surface downstream. The shedding frequency nondimensionalized by the momentum thickness was found to be independent of Reynolds number. The value of the nondimensional Strouhal number, however, was found to differ from the results of Pauley et al. [J. Fluid Mech. 220, 397 (1990)], indicating that the shedding frequency varies with the nondimensional pressure distribution, Cp. The computational results were time averaged over several shedding cycles and the results were compared with Gaster. The numerical study accurately reproduced the major characteristics of the separation found in Gaster’s study such as the separation point, the pressure plateau within the upstream portion of the separation bubble, and the reattachment point. The similarity between the experimental results and the time-averaged two-dimensional computational results indicates that the low-frequency velocity fluctuations detected by Gaster are primarily due to the motion of large vortex structures. This suggests that large-scale two-dimensional structures control bubble reattachment and small-scale turbulence contributes a secondary role. [ABSTRACT FROM AUTHOR]

The time evolution of a vortex sheet is calculated by using a simple generalization of Rosenhead’s point vortex approximation. The results confirm that the vortex sheet develops a singularity in curvature at a finite time. Numerical evidence of the rolling up of the vortex sheet is presented. [ABSTRACT FROM AUTHOR]

A weakly nonlinear analysis of the Görtler vortex problem is performed. It is demonstrated that the system of streamwise vortices enhances the heat transfer rate at the wall. The inherently nonlinear physical mechanism responsible for this enhancement is discussed both mathematically, as well as heuristically; the latter using kinematic arguments. Remarks are made on the relation of the weakly nonlinear results to their fully nonlinear counterparts, as well as on the inadequacy of linear analyses. [ABSTRACT FROM AUTHOR]

Consider an airfoil which is impulsively started from rest to a constant speed relative to an otherwise quiescent fluid at an angle of attack. The paper attempts to propose a precise definition for the ‘‘starting vortex’’ in viscous flow and investigate how an airfoil gains its lift through the starting vortex. It is found adequate to view the vortex itself as a source of the lift through the vorticity contained within it. Actually, the total lift on the airfoil is contributed by all the regions of nonvanishing vorticity in the flow. For an impulsive flow, the initial lift is due to the vortex sheet distributed along the airfoil; the lift is then rapidly dominated by the starting vortex near the trailing edge. In the next stage, the regions of vorticity next to the airfoil on both sides gradually become the major contributor to the lift. Relative importance of the starting vortex is assessed based on the angle of attack and the Reynolds number. [ABSTRACT FROM AUTHOR]

Lundgren’s [Phys. Fluids 25, 2193 (1982)] model for turbulent fine structure comprises coherent vortices which wind up vorticity variations into spiral structures; simultaneously the vortices are stretched axially by a background strain field. The model predicts a k-5/3 energy spectrum and is remarkably robust to the form of the coherent vortices and the form of the vorticity variations. To understand this the present article introduces a simple cascade argument which illuminates how the dynamical processes of vortex stretching and reduction of scale conspire to give this Kolmogorov spectrum. Some generalizations are considered. [ABSTRACT FROM AUTHOR]

The linear stability of unbounded strained vortices in a stably stratified rotating fluid is investigated theoretically. The problem is reduced to a Matrix–Floquet problem, which is solved numerically to determine the stability characteristics. The Coriolis force and the buoyancy force suppress the subharmonic elliptical instability of cyclonic and weak anticyclonic vortices, whereas enhances that of strong anticyclonic vortices. The fundamental and superharmonic instability modes occur, in addition. They are due to higher-order resonance. The growth rate of each instability shows complicated dependence on the parameters N (the normalized Brunt–Väisälä frequency) and R0 (the Rossby number: defined inversely as usual), if their values are small. It decreases as the background rotation rate becomes larger and as the stratification becomes stronger. The instability mode whose order of resonance is less than Min(N,2|1+R0|) is inhibited. [ABSTRACT FROM AUTHOR]

The Hamiltonian flow of a set of point vortices of like sign and strength has a low-temperature phase consisting of a rotating triangular lattice of vortices, and a normal temperature turbulent phase consisting of random clusters of vorticity that orbit about a common center along random tracks. The mean-field flow in the normal temperature phase has similarities with turbulent quasi-two-dimensional rotating laboratory and geophysical flows, whereas the low-temperature phase displays effects associated with quantum fluids. In the normal temperature phase the vortices follow power-law clustering distributions, while in the time domain random interval modulation of the vortex orbit radii fluctuations produces singular fractional exponent power-law low-frequency spectra corresponding to time autocorrelation functions with fractional exponent power-law tails. Enhanced diffusion is present in the turbulent state, whereas in the solid-body rotation state vortices thermally diffuse across the lattice. Over the entire temperature range the interaction energy of a single vortex in the field of the rest of the vortices follows positive temperature Fermi–Dirac statistics, with the zero temperature limit corresponding to the rotating crystal phase, and the infinite temperature limit corresponding to a Maxwellian distribution. Analyses of weather records dependent on the large-scale quasi-two-dimensional atmospheric circulation suggest the presence of singular fractional exponent power-law spectra and fractional exponent power-law autocorrelation tails, consistent with the theory. [ABSTRACT FROM AUTHOR]

The scattering dynamics of two vortex pairs with equal circulations ±κ have hitherto been thought to be regular, in contrast to the case of nonidentical pairs where a hierarchy of resonant states gives rise to chaotic behavior. However, no rigorous explanation could be found for such regularity occurring in a nonintegrable Hamiltonian system. This was recently posed as an open problem [H. Aref et al., Fluid Dyn. Res. 3, 63 (1988)], and in this paper the problem is resolved by presenting a counter-example mechanism which yields chaotic scattering dynamics when the initial pair spacings differ markedly. Alternative modes of scattering are characterized by symbolic sequences. These predictions are confirmed by numerical experiments which also show that the chaos persists even when the initial spacings are nearly equal, although the physical origin of the irregular scattering is less clear. Regular behavior is seen only in the integrable case of equal initial pair spacings. [ABSTRACT FROM AUTHOR]

The motion of small, spherical noninteracting bubbles in two-dimensional vortical flows by means of numerical simulations is investigated. After a discussion concerning the various bubble equations, bubble trajectories are calculated in a solid-body vortex, where it is found that the bubble motion can be described in terms of the location where the bubbles accumulate, or equilibrium points, and the rate of entrapment into these equilibrium points. Of importance here is that the rate of entrapment into the vortex has an optimum value for some value of the inertia parameter, or inverse Stokes number. The bubble motion in a temporally evolving shear layer is investigated, where it is found that the solid-body vortex model predicts the trends in the growth in concentration about the vortex center for the case without gravity. For the case with gravity, not all bubbles are captured by the vortex, and the percentage of bubbles captured increases with decreasing inertia parameter. Also discussed is how these factors affect the generation of the interface between regions seeded and not seeded with bubbles. [ABSTRACT FROM AUTHOR]

Vortex pairs interacting with a circular cylinder have been simulated by the numerical simulation of the two-dimensional Navier–Stokes equation in the vorticity streamfunction formulation. The interaction with a cylinder with a diameter equal to the diameter of the dipole has been simulated in the inviscid case with free-slip boundaries. This case has been considered as a way to perturb the initial dipole, which splits into two vortices that rejoin at a different location on the cylinder depending on the initial displacement of the cylinder from the centerline of the primary vortex pair. By the scatter plots it was shown that the Lamb dipole after the perturbation relaxes to its initial k2ψ functional relationship. The case of no-slip interaction has been considered when the cylinder is two orders of magnitude smaller than the dipole. The same features observed in the experiment of Homa et al. [J. Fluid Mech. 197, 571 (1988)] are obtained by the numerical simulations, that is a thin vorticity layer is generated at the cylinder, it rolls up and forms dipolar and tripolar structures, depending on the initial displacement of the cylinder from the centerline of the incoming dipole. Scatter plots of the vortex pair formed by the primary and secondary vorticity show a linear distribution similar to that of the Lamb dipole. The dependence on the Reynolds number has been investigated. [ABSTRACT FROM AUTHOR]

Measurements of the spanwise vorticity fluctuation ωz were made in a low Reynolds number turbulent boundary layer with a four-hot-wire probe. Measurements of the longitudinal velocity fluctuation up were also made with a single hot wire located at a fixed position near the edge of the viscous sublayer. The simultaneously sampled data are used to gain some insight into the vortical structure of the flow in the wall region. The large negative correlation coefficient between up and ωz near the wall may be due partly to a sweeplike motion associated with negative ωz and partly to the association between low-speed fluid and positive ωz. Spanwise vorticity fluctuations near the wall are, in general, negatively correlated with those in the outer part of the buffer region. This result is consistent with the effect of the wall on the velocity field induced by relatively strong vortices of the same sign as the mean shear. It is also consistent with the arrival in the wall region of eddies which rotate in the opposite direction to the mean shear. Conditional averages of the velocity field associated with both positive and negative ωz detections are compared with those obtained from detections of various different features of the organized motion in the wall region. These averages support the conclusions inferred from the correlation between up and ωz. [ABSTRACT FROM AUTHOR]

A theoretical study is carried out for investigating spatial instabilities of a supersonic vortex sheet inside a circular duct. The sheet is cylindrical in shape, separating the flow into an inner region and an outer one of uniform properties. It is found that there is one family of subsonic (Kelvin–Helmholtz) instability waves which are accompanied by two families of neutral modes. Two families of supersonic instability waves can be identified to be associated with two other families of neutral modes. A mathematical analogy indicates that instability modes at high frequencies bear resemblance to those obtained by Tam and Hu [J. Fluid. Mech. 203, 51 (1989).] for plane mixing layers inside a rectangular channel. Geometric effects of both the vortex sheet and the outer confinement are significant only at relatively low frequencies of disturbances. In addition, extensive parametric study reveals interesting features of the dependence of the instability waves on the density ratio, velocity ratio, radius ratio of the inner and outer regions, and three-dimensional disturbances. [ABSTRACT FROM AUTHOR]

It is shown that vortex core dynamics results from the interaction of two slowly deforming, but overlapping, helical vortex structures. These are the left- and right-handed components of the vortex, and are obtained by a generalized Helmholtz decomposition (the complex helical wave decomposition) of the vorticity field. This decomposition is based on a Fourier expansion in eigenfunctions of the curl operator, which has only real eigenvalues λ. The sum of eigenmodes with λ>=0 (λ<0) constitutes the right (left) polarized component, and the vector lines of the field (e.g., vortex lines) are locally right (left) handed helixes. It is found that for a localized vortex the polarized structures are also localized, a crucial result for physical space applications. The polarized vortex structures deform slowly (compared to unpolarized structures) and behave almost like solitary waves when isolated. It is shown that this is because the nonlinearity in the Navier–Stokes equations is largely suppressed between eigenmodes of the same polarity. Moreover, the helicity of polarized structures is very high. The interaction between overlapping polarized structures however gives each structure a different propagation velocity and also results in some additional deformation. The latter is shown to occur mainly in two places: at the front of the structure where a low enstrophy bubble forms (which is a permanent feature in each of the polarized packets), and at the back where a tail develops. Otherwise, the deformation occurs on a much slower time scale compared to that for unpolarized vortices. Thus the rapid changes in the total vorticity field result from the superposition of two slowly deforming structures moving in opposite directions, as is the case for the one-dimensional (1-D) wave equation. The decomposition can also be applied to turbulent flows. In fact, it offers new insight into the structure of turbulent shear flows. The organization of... [ABSTRACT FROM AUTHOR]

Previous measurements in a two-stream plane mixing layer have shown that the mean streamwise vorticity decays monotonically with downstream distance such that it is absent in the far-field (self-similar) region [J. H. Bell and R. D. Mehta, J. Fluid Mech. 239, 213 (1992); AIAA J. 28, 2034 (1990)]. It was not clear at that time if this measured decay reflected the diffusion of the instantaneous streamwise vorticity or was a result of increasing vortex meander within the mixing layer. The present experimental study was conducted in order to determine the existence of streamwise vortex meander in a mixing layer, and if present, its significance on the measured properties. The dependence of the velocity cross-correlation on the fixed probe location was shown to be a good indicator of the stationarity of the streamwise vortex location. The cross-correlation measurements obtained here indicate that spanwise meander is negligible, although transverse apparent meander (normal to the plane of the mixing layer) was indicated. The transverse meander, exemplified by the elliptical shape of the mean streamwise vorticity contours, was expected, since the streamwise vorticity in the braid region is essentially inclined, with respect to the streamwise direction. These conclusions were supported by results of estimated spanwise profiles of the transverse velocity component. The balance of evidence suggests that the measured mean streamwise vorticity decay is representative of the decay of the vorticity rather than an artifact of meander. [ABSTRACT FROM AUTHOR]

Detailed velocity measurements have been made to investigate the structure of the low-frequency vortex dislocations that appear in the indigenous wake of a circular cylinder. It is shown that one mechanism for the production of vortex dislocations is the superposition of two waves with slightly different frequencies, where the higher frequency wave is parallel to the cylinder axis and the lower frequency is an oblique wave. In contrast to the discrete vortex concept that implies discontinuous shedding frequencies, the measured amplitude and phase distribution of the interacting waves are shown to be continuous along the span of the cylinder. Both waves (parent modes) exist simultaneously and overlap in the wake. The difference mode associated with the vortex dislocations is produced by the nonlinear interaction of the parent modes, and its maximum amplitude is at the location where the parent modes have comparable magnitude. The spanwise phase and amplitude distributions of the difference mode are ‘‘predicted’’ by taking the product of the complex wave amplitudes of the parent modes. [ABSTRACT FROM AUTHOR]

Two-dimensional calculations are performed for a Reynolds number of 1000 and an effective Prandtl number of unity to study the dynamics of large-scale spanwise vortices with a passive scalar field in a separation and reattaching flow over a blunt plate. A triple decomposition technique is used to isolate the quasiperiodic fluctuations related to the large-scale vortices shed from the separated shear layer. Three vortex shedding modes are identified in the reattachment zone, two of which involve partial pairings. The coherent vortices shed from the reattachment zone have a dominating effect on scalar transport, and act as ‘‘large-scale mixers’’ by entraining wall scalar around their upstream periphery and free-stream scalar on their lower downstream edge. There is a definite relationship between the phase-averaged perturbations (due to the presence of coherent vortices) in the wall friction factor and wall scalar transport with their respective time mean maximums. On the other hand, although there does exist an explicit spatial relationship between the instantaneous stagnation point and instantaneous location of maximum wall scalar transport, there is no such relationship in the mean between the two locations, except that both are dependent on the vorticity dynamics in the reattachment region. [ABSTRACT FROM AUTHOR]

A new feature of the long-time evolution of a strong vortex with initially monotonic potential vorticity is found by direct numerical solution of the quasigeostrophic equivalent barotropic equation. Two satellites, which emerge after splitting of an annulus, appear at the vortex periphery. Rotation and oscillation of the tripolar structure may lead to increased mixing near the boundary of the vortex core. The translation of strong monopoles is found to be well described, even for times longer than the linear Rossby wave period, by a recent approximate theory for the evolution of an azimuthal perturbation with mode number l=1. [ABSTRACT FROM AUTHOR]

The equation of motion of small, heavy, rigid spherical particles in a periodic Stuart vortex flow is studied as a four-dimensional nonlinear dynamical system with a parametric space of five dimensions. The five parameters are a scaled Reynolds number, the Stokes number, the fluid-to-particle density ratio, the vorticity distribution in the flow, and a gravitational parameter. Depending on the values of these parameters, heavy particles may either settle or remain indefinitely suspended against gravity. When suspension occurs, suspended particles asymptotically collect along periodic, quasiperiodic, or chaotic open trajectories located above or below the vortices. The nature of these asymptotic paths is investigated using the standard tools of power spectrum and bifurcation diagram (Poincaré sections). Furthermore, the basins of attraction in the physical and parametric spaces are also computed for both types of suspensions (above and below the vortices). In addition to the two types of upper and lower asymptotic orbits, the dynamical system of this study also exhibits the phenomenon of intermittency, whereby a particle remains suspended alternately above and below the vortices. Apart from open trajectories, closed orbits encircling one or several vortices are also observed in this work. [ABSTRACT FROM AUTHOR]

Three-dimensional, incompressible Euler calculations of the interaction of perturbed antiparallel vortex tubes using smooth initial profiles in a bounded domain with bounded initial vorticity are discussed. A numerical method that uses symmetries and additional resolution in the direction and location of maximum compression is used to simulate periodic boundary conditions in all directions. For an initial condition that yields singular behavior, the growth of the peak vorticity, the peak axial strain, and the enstrophy production obey (tc-t)-1, and the enstrophy grows logarithmically. The enstrophy growth is associated with the energy spectrum approaching k-3. Self-similar development and equal rates of collapse in all three directions are shown. [ABSTRACT FROM AUTHOR]

The structure and behavior of a streamwise rib vortex in a direct numerical simulation of a time-developing three-dimensional incompressible plane mixing layer is examined. Where the rib vortex is being stretched, the vorticity vector is primarily directed in the vortex axial direction and the radial and azimuthal velocity distribution is similar to that of a Burgers vortex. In the region where the vortex stretching is negative, there is a change in the local topology of the vortex. The axial flow is decelerated and a negative azimuthal component of vorticity is induced. These features are characteristic of vortex breakdown. The temporal evolution of the rib vortex is similar to the evolution of an axisymmetric vortex in the early stages of vortex breakdown. The effect of vortex breakdown on other parts of the flow is, however, not as significant as the interaction between the rib vortex and other vortical structures. [ABSTRACT FROM AUTHOR]

The disturbance field induced by a small isolated vortex in a compressible shear layer is studied using direct simulation in a convected frame. The convective Mach number, Mc, is varied from 0.1 to 1.25. The vorticity perturbation is rapidly sheared by the mean velocity gradient. The resulting disturbance pressure field is observed to decrease both in magnitude and extent with increasing Mc, becoming a narrow transverse zone for Mc>=0.8. A similar trend is seen for the perturbation velocity magnitude and for the Reynolds shear stress. By varying the vortex size, it was verified that the decrease in perturbation levels is due to the mean-flow Mach number and not the Mach number across the vortex. At high Mc, the vortex still communicates with the edges of the shear layer, although communication in the mean-flow direction is strongly inhibited. The growth rate of perturbation kinetic energy declines with Mc primarily due to the reduction in shear stress. For Mc≥0.6, the pressure dilatation also contributes to the decrease of growth rates. Calculation of the perturbation field induced by a vortex doublet revealed the same trends as in the single-vortex case, illustrating the insensitivity of the Mach-number effect to the specific form of initial conditions. [ABSTRACT FROM AUTHOR]

The equations which describe a boundary layer on a curved wall in a rotating system are derived and a linear stability analysis of a basic Blasius velocity profile is performed. Rotation can be either stabilizing or destabilizing corresponding to whether a rotation number is negative or positive, respectively. The stability boundaries at different rotation numbers and curves of constant positive growth rates are presented. It is shown that the flow is completely stabilized when the rotation number is ≤-1 in agreement with an inviscid Rayleigh-type analysis. For the cases examined growth rates increase linearly, in the initial phase, with streamwise distance. [ABSTRACT FROM AUTHOR]

Novel physical-space vortex properties of nearly inviscid, unforced two-dimensional (2-D) turbulence are presented. They are obtained from the analysis of a large ensemble of calculations all beginning with a random distribution of vortex patches of equal vorticity magnitude on a spherical surface. The numerical method (MACS) is a combination of contour dynamics/surgery (CD/CS) and a moment expansion for calculating separated vortex interactions. This method calculates approximately 100 times faster than CD/CS thereby permitting the formation of a large database for obtaining meaningful statistics. The numerical method can resolve a much wider range of spatial scales than conventional (pseudospectral) methods, and it is found that the statistical vortex properties produced differ in significant respects from those obtained previously. This conclusion is drawn from not just one set of calculations, but three at different spatial resolutions. While algebraic decay of basic flow statistics (e.g., enstrophy, vortex population) is observed at late times, the decay exponents are smaller than previously obtained and furthermore do not come in the ratios suggested by the recently proposed ‘‘universal scaling theory.’’ In addition, the vortex number density distribution is not found to be self-similar but steepens continuously and appreciably with decreasing vortex size. This forces a reevaluation of the nature of 2-D turbulence in the inviscid limit. A proper description of this limit needs (more) quantitative information concerning the most probable vortex interactions. Such interactions will not be between just two vortices, as is commonly supposed. [ABSTRACT FROM AUTHOR]

The effect of axial pressure gradient in producing gradual changes in amplitude and wavelength of both axisymmetrical and helical waves on a vortex core is studied analytically using an idealized model of a vortex with uniform axial vorticity across the core in an unbounded space. Possible implications of the findings on the vortex breakdown phenomenon are also considered. In agreement with previous literature on the subject, the steady solution for a supercritical vortex flow in an adverse pressure gradient is found to become complex (and hence break down) at a certain critical point. The axisymmetric waves on the core obey a hyperbolic system of equations. An explicit solution of these equations for small-amplitude axisymmetric waves indicates that the wave amplitude becomes unbounded at the critical point in the linear theory. An implicit nonlinear solution of these equations shows the formation of ‘‘shocks’’ along the core considerably upstream of the critical point, which seem to correspond to formation of bubble-type vortex breakdowns. A solution is also obtained for evolution of long helical waves on a vortex core in the presence of an axial pressure gradient, and this solution is used to suggest an explanation for why the vortex breakdown at times adopts a bubble form while at other times it adopts a spiral form. [ABSTRACT FROM AUTHOR]

The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(ε-1), where ε<1 is the cross-flow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by a breakdown in the numerical procedure. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the terminal location. [ABSTRACT FROM AUTHOR]

A steady, inviscid, incompressible, two-dimensional flow in a channel containing a vortex patch bounded by a vortex sheet is calculated numerically. The results cover a wide range of the channel width and the value of the jump in Bernoulli’s constant across the vortex sheet. An asymptotic theory is used to check the results for very narrow channels. A comparison with the solutions of the Navier–Stokes equations around an infinite array of circular cylinders [Fornberg, J. Fluid Mech. 225, 655 (1991)] is performed to check if the present flow can be used as a model for the wake. [ABSTRACT FROM AUTHOR]

The propagation of three-dimensional small-amplitude long waves on a vortex filament running down the center of a circular tube is investigated analytically. The vortex flow is idealized by an infinite concentrated potential vortex filament immersed in an axial uniform flow that is displaced from the axis of the tube by a small three-dimensional perturbation. The rigid walls of the tube are represented by a potential surface source distribution that also has the nature of a small perturbation. A linearization of the flow-field equations, with respect to the basic state of a straight filament along the tube axis, results in an eigenvalue problem. The analytical solution shows that the vortex in the center of the tube is stable and the disturbances propagate as constant amplitude displacement waves along the vortex line and as source-intensity fluctuations along the inner surface of the tube wall. Two different basic modes of either a helical or rotating sinusoidal wave can propagate along the vortex filament. A ‘‘supercritical’’ state is defined by the characteristics of the flow in which waves can propagate only downstream. It is shown from available experimental data that vortex flows in tubes that experienced vortex breakdown farther downstream, were ‘‘supercritical’’ at the tube inlet. [ABSTRACT FROM AUTHOR]

This paper addresses a specific reactive-flow configuration, namely, the interaction of a detonation wave with convected homogeneous isotropic weak turbulence (which can be constructed by a Fourier synthesis of small-amplitude vorticity waves). The effect of chemical heat release on the rms fluctuations downstream of the detonation is presented as a function of Mach number. In addition, for the particular case of the von Kármán spectrum, the one-dimensional power spectra of these flow quantities are given. [ABSTRACT FROM AUTHOR]

The dynamics of tilted dipole vortices in the equivalent barotropic vorticity (or Hasegawa–Mima) equation is studied. A recent theory is compared with numerical simulations and found to describe the short time behavior of dipole vortices well. In the long time limit the dipoles are found to either disintegrate or relax toward a steady eastward propagating dipole vortex. This relaxation is a consequence of nonviscous enstrophy loss by the dipole vortex. [ABSTRACT FROM AUTHOR]

Laminar vortex rings approaching a solid planar surface and a free surface have been investigated experimentally over the range of Reynolds numbers based on the circulation, ReΓ, from 900 to 2350. The emphasis is on the process of vortex stretching, induction of boundary layer on the surface, formation of secondary vortices, and rebounding of the primary vortex ring. Detailed measurements were made using laser-induced photochemical anemometry (LIPA), a nonintrusive visualization technique which enables multipoint simultaneous measurement of the unsteady velocity field. Results show that enstrophy, rather than circulation, clearly signifies three stages of the behavior of the primary vortex ring—free-traveling stage, vortex stretching stage, and vortex rebounding stage. Although the flow phenomena are very similar when a vortex ring approaches a solid surface or a slightly contaminated free surface, the difference between the induced boundary layers under two surface conditions is obvious in terms of the circulation and the enstrophy. In addition, the surface deformation and subsequent surface waves resulting from the impacting vortex ring on the contaminated free surface are also discussed. The present study provides a basis for validation and comparison with numerical simulations. [ABSTRACT FROM AUTHOR]

Decaying two-dimensional turbulence is characterized by the emergence of coherent vortices, which subsequently dominate the evolution. The temporal scaling behavior of the flow is analyzed using a scaling theory, a long-time integration of the fluid equations, and a dissipative, modified point-vortex model that represents the turbulence as a system of interacting coherent structures. Good agreement is found in the behavior of average vortex properties, low-order moments of the flow fields, and the form of self-similar evolution. [ABSTRACT FROM AUTHOR]

The instability of a two-dimensional triangular array of vortices with respect to inviscid perturbations is investigated. A numerical treatment in the framework of Floquet theory provides critical parameters for instability onset and the spatial structure of unstable oscillatory modes which are in agreement with experiments of Sommeria et al. [Mechanics of Fluids and Transport Processes (Kluwer Academic, Dordrecht, The Netherlands, 1989), Vol. 10] in electromagnetically driven flows of a liquid metal layer. A point vortex model allows one to relate the dynamics of infinitesimal displacements of vortices to the concept of waves in a lattice of linearly coupled oscillators. [ABSTRACT FROM AUTHOR]

Flow-visualization methods were used to explore the structure of streamwise vortices and their interactions with the von Kármán vortices in the immediate wakes of cylinders. The experiments were conducted in a water tunnel at Reynolds numbers from 330–21 000 based on cylinder diameter. Over this entire range of Reynolds number, pairs of counter-rotating streamwise vortices were observed immediately behind the cylinders, with a mean spanwise spacing of approximately one pair per diameter. The streamwise vortices significantly distorted the von Kármán vortices, but only on their upstream-facing sides. The cylinder near-surface-flow topology was found to include a secondary separation line containing ‘‘dominant-foci structures’’ whose spanwise locations correlated with those of the streamwise vortices. [ABSTRACT FROM AUTHOR]

Simplified asymptotic equations describing the nonlinear dynamics of perturbed pairs of parallel vortex filaments are derived and analyzed here. The derivations are general enough to allow for vortices of unequal strength, but emphasis here is on the antiparallel vortex pair. The simplified asymptotic equations account for both the internal effects of self-induction and self-stretching for each filament and also the external effects of mutual induction that lead to a nontrivial coupling of the perturbations of the two filaments. When these nonlinear equations are linearized at the unperturbed filament pair, the linearized stability theory of Crow [AIAA J. 8, 2172 (1970)] is recovered in a systematic fashion. The asymptotic equations are derived in a novel singular limit at high Reynolds numbers through assumptions similar to the authors’ recent theories [Physica D 49, 323 (1991); ibid. 53, 267 (1991); Phys. Fluids A 4, 2271 (1992)] for the dynamics of a single perturbed vortex filament. Through the Hasimoto transform [J. Fluid Mech. 51, 477 (1972)], these equations become two coupled perturbed nonlinear Schrödinger equations for a pair of filament functions. A series of numerical solutions of the asymptotic equations exhibits several new phenomena in the nonlinear instability of pairs of antiparallel vortex filaments. [ABSTRACT FROM AUTHOR]

A new computational method extending the contour dynamics/surgery (CS) algorithm is announced which gives typical speed-up factors of two orders of magnitude in calculations of flows involving many interacting vortices. The method makes use of an alternative expression for the velocity field in the exterior of a vortex that takes the form of a rapidly convergent series. Each term in this series can be expressed as a complex coefficient divided by the complex distance x+iy from the vortex center. The complex coefficient, or moment, is a real number pair that describes shape characteristics of the vortex (e.g., circulation, eccentricity, etc.). In numerical calculations, where accuracy is necessarily limited, it is frequently sufficient to retain only the leading-order terms in this series, particularly for a gas of well-separated vortices. The real computational gain is made, however, by reexpanding the series of all vortices that are sufficiently separated from a given vortex as a single, truncated series in positive powers of the complex distance from this vortex’s center. The coefficients of this series involve only the moments of the other vortices and their centroid separation from the given vortex. The leading-order truncation, for instance, simply gives point vortex dynamics, except that self- or close-range interactions are computed using the full contour integral expression of contour dynamics (hence, all vortices retain nontrivial spatial structure, vital to a proper dynamical description of close-range interactions). In general, the optimal truncation depends on a dynamic balance between the cost of all moment computations and the cost of all contour integrations. This method, called ‘‘moment-accelerated contour surgery,’’ which is briefly outlined above for the planar case, has a direct analog in spherical geometry. There are also extensions to generalized two-dimensional (2-D) flows having more general linear... [ABSTRACT FROM AUTHOR]

The dynamics of hollow, cylindrically shaped pure electron plasmas are studied. Since these plasmas behave like two-dimensional (2-D) fluids with low viscosity, their evolution parallels the evolution of 2-D fluid vorticity annuli inside frictionless circular containers. Growth of the Kelvin–Helmholtz instability in circular geometry is observed. The formation and subsequent interaction of vortices are studied as a function of ring thickness. Small initial perturbations can dramatically increase the symmetry and repeatability of the dynamics. [ABSTRACT FROM AUTHOR]

Pitot pressure measurements and flow visualizations were used to investigate streamwise vortices previously observed in underexpanded jets. A simple model was developed, which gives reasonable agreement with the pressure measurements. A converging nozzle and converging–diverging nozzle of design Mach number 1.5 were used to generate jet flows of equivalent Mach numbers up to 2.5 (stagnation to ambient pressure ratios up to 17.1). By operating the nozzles fully expanded, overexpanded, and underexpanded, insight was gained into both the occurrence and cause for formation of the vortices. Spatially stationary streamwise vortices were found to exist in the near-field region around the circumference of underexpanded jets in the vicinity of the jet boundary. Short exposure visualizations show the vortices persist much farther downstream with a loss of spatial organization. Visualizations suggest adjacent vortices have streamwise vorticity of opposite sign, so the action of adjacent vortices is to either pump jet fluid radially outward or entrain ambient fluid radially inward toward the jet. The downstream extent, strength, and number of vortices around the jet circumference increase with degree of underexpansion. A large number of vortices is found near the nozzle exit. Fewer vortices of larger scale are found farther downstream, indicative of a merging process. The absence of the vortices in fully expanded and overexpanded jets suggests the vortices are a consequence of a Taylor–Goertler-type instability. [ABSTRACT FROM AUTHOR]

Natural, or intrinsic, coordinates are examined for an unsteady, compressible, viscous, Newtonian fluid in two-dimensional or axisymmetric flow. The corresponding Navier–Stokes equations are obtained along with Crocco’s equation, an entropy production equation, and an equation for the rate of change of vorticity following a fluid particle. The extension to a three-dimensional flow is discussed. [ABSTRACT FROM AUTHOR]

The strained-spiral vortex model of turbulent fines scales given by Lundgren [Phys. Fluids 25, 2193 (1982)] is used to calculate vorticity and velocity-derivative moments for homogeneous isotropic turbulence. A specific form of the relaxing spiral vortex is proposed modeled by a rolling-up vortex layer embedded in a background containing opposite signed vorticity and with zero total circulation at infinity. The numerical values of two dimensionless groups are fixed in order to give a Kolmogorov constant and skewness which are within the range of experiment. This gives the result that the ratio of the ensemble average hyperskewness S2p+1≡ (∂u/∂x)2p+1/[(∂u/∂x)2](2p+1)/2 to the hyperflatness F2p≡(∂u/∂x)2p/[(∂u/∂x)2] p, p=2,3,..., is constant independent of Taylor–Reynolds number Rλ, as is the ratio of the 2pth moment of one component of the vorticity Ω2p≡ω2px/(ω2x)p to F2p. A cutoff in a relevant time integration is then used to eliminate vortex-sheet-induced divergences in the integrals corresponding to ω2px, p=2,3,..., and an assumption is made that the lateral scale of the spiral vortex in the model is the geometric mean of the Taylor and the Kolmogorov microscales. This gives Ω2p=Ω2pRλp/2-3/4, F2p=F2pRλp/2-3/4 and S2p+1=S2p+1Rλp/2-3/4, p=2,3,..., with explicit calculation of the numbers Ω2p, F2p, and S2p+1. The results of the model are compared with experimental compilation of Van Atta and Antonia [Phys. Fluids 23, 252 (1980)] for F4 and with the isotropic turbulence calculations of Kerr [J. Fluid Mech. 153, 31 (1985)] and of Vincent and Meneguzzi [J. Fluid Mech. 225, 1 (1991)]. [ABSTRACT FROM AUTHOR]

The instability of a columnar vortex under axial compression is studied analytically. Prediction of the change with time of an initial perturbation in the form of a small-amplitude helical wave on the vortex core is reduced to solution of a system of two linear, second-order ordinary differential equations. For small rates of compression, a closed-form asymptotic solution of these equations is obtained using a two-variable expansion in time. The results indicate that a vortex under compression may bend (or ‘‘buckle’’) or it may remain columnar with an increase in core radius. The choice of which of these possible outcomes will occur is found to depend on the value of a single dimensionless parameter given by the product of the wave number k of the helical perturbation and the radius σ of the vortex core. When kσ is greater than a critical value, found to be approximately 1.77, the perturbation amplitude will decrease with axial compression and no ‘‘buckling’’ will occur. When kσ is less than this critical value, the perturbation amplitude will increase as the vortex axis is compressed and ‘‘buckling’’ will be observed. [ABSTRACT FROM AUTHOR]

Two-dimensional inviscid flows governed by a vortex pair in the presence of another point vortex or vortex pair on an unbounded plane are considered analytically and via numerical simulations. For some integrable cases of vortex motion, the stirring process of a fixed closed volume of surrounding fluid (‘‘atmosphere’’) initially trapped by vortex pair is investigated. Using the full classification of vortex movement types, it is shown that for all cases of vortex pair direct and exchange scattering the stirring process is regular. Some internal atmosphere regions conserve their existence and form after vortex interaction, resulting a ‘‘solitonlike’’ behavior. For general cases of vortex pair mutual trapping, the stirring process is chaotic. For limiting cases of vortex motions, the fluid particles reveal a regular behavior. A simple model for the qualitative description of recent experiments on vortex dipoles interaction is discussed. Although clearly an extreme idealization, the model appears to shed some light on what to expect in laboratory experiments. [ABSTRACT FROM AUTHOR]

Recently, two of the authors have derived [Physica D 49, 323 (1991)] and analyzed [Physica D 53, 267 (1991)] a new asymptotic equation for the evolution of small-amplitude short-wavelength perturbations of slender vortex filaments in high Reynolds number flows. This asymptotic equation differs significantly from the familiar local self-induction equation in that it includes some of the nonlocal effects of self-stretching of the filament in a simple fashion. Here, through systematic asymptotic expansions, the authors derive a modification of this asymptotic equation that incorporates the important additional effects of strain and rotation from a general background flow field. The main requirement on the background flow is that it does not displace the unperturbed background filament. The new asymptotic equations exhibit in a simple fashion the direct competition in filament dynamics between internal effects such as self-induction and self-stretching and external effects of background flows involving strain and rotation. Solutions of these asymptotic equations revealing various aspects of this competition are analyzed in detail through both theory and numerical simulation. An application is also presented for the nonlinear stability of a columnar vortex to suitable perturbations in a straining, rotating, background environment. [ABSTRACT FROM AUTHOR]

It is generally shown that the dynamics of three-dimensional nonviscous flows possesses invariant two-dimensional structures if these flows are invariant under translations along their vorticity field directions. In such a two-dimensional fluid, the vorticity field direction is fixed in time everywhere, while its intensity obeys a scalar equation similar to that in the two-dimensional line-vortex case. The most general flow having such a two-dimensional structure is perhaps the helically invariant flow. Expressed in terms of some generalized coordinates according to its spatial symmetry, the dynamics of such a flow admits a Hamiltonian description. A general steady-state condition for such a flow is also derived. Furthermore, using Boltzmann statistics, the equilibrium distribution of the intensity of the vorticity field is shown to satisfy a nonlinear partial differential equation, similar to the sinh-Poisson equation for the line-vortex case. [ABSTRACT FROM AUTHOR]

The exterior flow of a Kida ellipse that has a large chaotic zone is studied. The spatial variability that is characterized by the separation rate of nearby particles in the chaotic region is determined. In order to quantify this variability, a method for calculating the finite time spreading rate is developed. By examining the individual particle trajectories, it is seen that particles that have a high spreading rate are particles that pass near a stagnation point of the flow. The effect of the addition of vorticity to particles in the exterior flow is examined. [ABSTRACT FROM AUTHOR]

The flow field in the polar region between a rotating and stationary, co- or counter-rotating sphere was studied numerically by a steady-state axisymmetric finite-element code and experimentally by flow visualization using a photochromic dye excited by a UV laser. The experimental results show that at a critical Reynolds number a steady axisymmetric vortex breakdown bubble forms at the polar axis, as predicted by the computation. At higher values of the Reynolds number, and depending on the gap, the eccentricity of the spheres along the axis of rotation, and their rotation ratio, further unsteady structures are observed experimentally, viz., an axially oscillating bubble, or a three-dimensional irregular structure. [ABSTRACT FROM AUTHOR]

A model for the selection of vortex roll-up patterns in finite-aspect-ratio, two-dimensional wakes at low to moderate Reynolds number is studied. Two primary patterns are found: a chevron pattern encompassing the entire spanwise domain and one with regions adjacent to the side-wall boundaries, which are divorced from the central region by means of dislocation layers. These patterns can be understood in terms of spanwise-propagating phase waves, wave-number shocks, and the criterion for sustained global modes. Selection criteria for the frequency and scale of internal cells in the wake behind tapered cylinders are also discussed. [ABSTRACT FROM AUTHOR]

Vortical structures in a two-dimensional (2-D) nozzle with a bluff-body slot under isothermal flow conditions have been examined experimentally and numerically. For these experiments, a 2-D sheet lighting technique coupled with a chemically reacting system was used to observe the vortical shedding processes. By varying the slot flow (flow from the central bluff-body slot), four different types of vortical structures are observed-separated by regions of stability (transition regions). From the sets of data, a flow map was constructed showing the zones occupied by the four different types of vortical structures and the regions of stability. The Reynolds number of the slot flow varied from 7.2 to 291.8; the Reynolds number of the air flow (flow surrounding the bluff-body slot) varied from 50 to 392. For the numerical calculations, the same range of Reynolds numbers for the slot flow was chosen; the Reynolds number of the air flow was fixed at 392. The numerical scheme used is a modified MAC method. Simulated vortical structures were visualized by calculating the flow streaklines. These streaklines agreed with experimental observations. Flow streamlines also have been constructed numerically to characterize the flow fields, particularly the recirculating flow zones, for each type of vortical structures. [ABSTRACT FROM AUTHOR]