Showing papers on "Vortex published in 1983"

An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder

Abstract: This paper describes an experimental investigation of transport processes in the near wake of a circular cylinder at a Reynolds number of 140000. The flow in the first eight diameters of the wake was measured using X-array hot-wire probes mounted on a pair of whirling arms. This flying-hot-wire technique increases the relative velocity component along the probe axis and thus decreases the relative flow angle to usable values in regions where fluctuations in flow velocity and direction are large. One valuable fringe benefit of the technique is that rotation of the arms in a uniform flow applies a wide range of relative flow angles to the X-arrays, making them inherently self-calibrating in pitch. An analog circuit was used to generate an intermittency signal, and a fast surface-pressure sensor was used to generate a phase signal synchronized with the vortex-shedding process. The phase signal allowed sorting of the velocity data into 16 populations, each having essentially constant phase. An ensemble average for each population yielded a sequence of pictures of the instantaneous mean flow field, with the vortices frozen as they would be in a photograph. In addition to globally averaged data for velocity and stress, the measurements yield non-steady mean data (in the sense of an average a t constant phase) for velocity, intermittency, vorticity, stress and turbulent-energy production as a function of phase for the first eight diameters of the near wake. The stresses were resolved into a contribution from the periodic motion and a contribution from the random motion at constant phase. The two contributions are found to have comparable amplitudes but quite different geometries, and the time average of their sum (the conventional global Reynolds stress) therefore has a quite-complex structure. The non-steady mean-vorticity field is obtained with good resolution as the curl of the non-steady mean-velocity field. Less than half of the shed circulation appears in the vortices, and there is a slow decay of this circulation for each shed vortex as it moves downstream. In the discussion, considerable emphasis is put on the topology of the non-steady mean flow, which emerges as a pattern of centres and saddles in a frame of reference moving with the eddies. The kinematics of the vortex-formation process are described in terms of the formation and evolution of saddle points between vortices in the first few diameters of the near wake. One important conclusion is that a substantial part of the turbulence production is concentrated near the saddles and that the mechanism of turbulence production is probably vortex stretching at intermediate scales. Entrainment is also found to be closely associated with saddles and to be concentrated near the upstream-facing interface of each vortex.

Small-scale structure of the Taylor–Green vortex

Abstract: The dynamics of both the inviscid and viscous Taylor–Green (TG) three-dimensional vortex flows are investigated. This flow is perhaps the simplest system in which one can study the generation of small scales by three-dimensional vortex stretching and the resulting turbulence. The problem is studied by both direct spectral numerical solution of the Navier–Stokes equations (with up to 256 3 modes) and by power-series analysis in time. The inviscid dynamics are strongly influenced by symmetries which confine the flow to an impermeable box with stress-free boundaries. There is an early stage during which the flow is strongly anisotropic with well-organized (laminar) small-scale excitation in the form of vortex sheets located near the walls of this box. The flow is smooth but has complex-space singularities within a distance $\hat{\delta}(t)$ of real (physical) space which give rise to an exponential tail in the energy spectrum. It is found that $\hat{\delta}(t)$ decreases exponentially in time to the limit of our resolution. Indirect evidence is presented that more violent vortex stretching takes place at later times, possibly leading to a real singularity ( $\hat{\delta}(t) = 0$ ) at a finite time. These direct integration results are consistent with new temporal power-series results that extend the Morf, Orszag & Frisch (1980) analysis from order t 44 to order t 80 . Still, convincing evidence for or against the existence of a real singularity will require even more sophisticated analysis. The viscous dynamics (decay) have been studied for Reynolds numbers R (based on an integral scale) up to 3000 and beyond the time t max at which the maximum energy dissipation is achieved. Early-time, high- R dynamics are essentially inviscid and laminar. The inviscidly formed vortex sheets are observed to roll up and are then subject to instabilities accompanied by reconnection processes which make the flow increasingly chaotic (turbulent) with extended high-vorticity patches appearing away from the impermeable walls. Near t max the small scales of the flow are nearly isotropic provided that R [gsim ] 1000. Various features characteristic of fully developed turbulence are observed near t max when R = 3000 and R λ = 110: a k − n inertial range in the energy spectrum is obtained with n ≈ 1.6–2.2 (in contrast with a much steeper spectrum at earlier times); th energy dissipation has considerable spatial intermittency; its spectrum has a k −1+μ inertial range with the codimension μ ≈ 0.3−0.7. Skewness and flatness results are also presented.

Integrable, chaotic, and turbulent vortex motion in two-dimensional flows

Abstract: Vortex dynamics would appear to be exempt from Hardy 's pe ssimi stic verdict On one hand, the evolution of vorticity, and thu s the motion s of vortice s, are essential ingredient s of virtually any real flow Hence vortex dynamic s i s of profound practical importance On the other hand, vortex motion ha s always constituted a mathematically sophi sticated branch of fluid mechanics that continue s to invite the application of novel analyti­ cal techniques Indeed it i s ne ither dull nor commonplace Thi s central role of vorticity in fluid mechanic s i s not difficult to understand A s we know, any velocity field, v, can be split into a sum of two field s, one with the same divergence a s v, and no curl, and one with the same curl a s v and vani shing divergence Thi s important re sult i s due to Stoke s and to Helmholtz ( 1 858 ; see Sommerfeld 1964) In incompre ssi ­ ble flow , a s we deal with exclu sively here, the fir st part i s irrotational and divergencefree and thu s leads to the linear problem o f po tential flow , The second part, however , derive s directly from the vorticity o f the field ' v In the dynamics of thi s part lie s the essence of the problem

Structure of a turbulent separation bubble

Abstract: Flow in the separation bubble formed along the sides of a blunt flat plate with right-angled corners has been studied in terms of extensive single- and two-point measurements of velocity and surface-pressure fluctuations. The cross-correlations between the surface-pressure and velocity fluctuations are found to be useful for the study of large-scale vortex structure in the bubble. Large-scale vortices are shed downstream from the separation bubble with a frequency of about 0.6U∞/xR, where U∞ is the approaching velocity and xR is the time-mean length of the bubble. On top of this regular vortex shedding, there exists a large-scale unsteadiness in the bubble. Vortices which are much larger than the regular vortices are shed with frequencies less than about 0.2U∞/xR. The large-scale unsteadiness is accompanied by enlargement and shrinkage of the bubble and also by a flapping motion of the shear layer near the separation line. The intermittent nature of the flow in the bubble is clarified in some detail. The distributions of the cross-correlations between the pressure and velocity fluctuations demonstrate the vortex structure in the reattaching zone. The longitudinal distance between the vortices is estimated to be (0.7–0.8) xR and their convection velocity is about 0.5U∞ near the reattachment line. The cross-correlations also suggest the existence of a longitudinal counter-rotating system in the bubble. The distance between the axes of the rotation is of the order of 0.6xR. Variations of timescales, lengthscales and phase velocities of the vortices are presented and discussed.

The nonlinear development of Görtler vortices in growing boundary layers

Abstract: The Growth of Gortler vortices in boundary layers on concave walls is investigated. It is shown that for vortices of wavelength comparable to the boundary-layer thickness the appropriate linear stability equations cannot be reduced to ordinary differential equations. The partial differential equations governing the linear stability of the flow are solved numerically, and neutral stability is defined by the condition that a dimensionless energy function associated with the flow should have a maximum or minimum when plotted as a function of the downstream variable X. The position of neutral stability is found to depend on how and where the boundary layer is perturbed, so that the concept of a unique neutral curve so familiar in hydrodynamic-stability theory is not tenable in the Gortler problem, except for asymptotically small wavelengths. The results obtained are compared with previous parallel-flow theories and the small-wavelength asymptotic results of Hall (1982a, b), which are found to be reasonably accurate even for moderate values of the wavelength. The parallel-flow theories of the growth of Gortler vortices are found to be irrelevant except for the small-wavelength limit. The main deficiency of the parallel-flow theories is shown to arise from the inability of any ordinary differential approximation to the full partial differential stability equations to describe adequately the decay of the vortex at the edge of the boundary layer. This deficiency becomes intensified as the wavelength of the vortices increases and is the cause of the wide spread of the neutral curves predicted by parallel-flow theories. It is found that for a wall of constant radius of curvature a given vortex imposed on the flow can grow for at most a finite range of values of X. This result is entirely consistent with, and is explicable by the asymptotic results of, Hall (1982a).

A sufficient condition for the instability of columnar vortices

Abstract: The inviscid instability of columnar vortex flows in unbounded domains to three-dimensional perturbations is considered. The undisturbed flows may have axial and swirl velocity components with a general dependence on distance from the swirl axis. The equation governing the disturbance is found to simplify when the azimuthal wavenumber n is large. This permits us to develop the solution in an asymptotic expansion and reveals a class of unstable modes. The asymptotic results are confirmed by comparisons with numerical solutions of the full problem for a specific flow modelling the trailing vortex. It is found that the asymptotic theory predicts the most-unstable wave with reasonable accuracy for values of n as low as 3, and improves rapidly in accuracy as n increases. This study enables us to formulate a sufficient condition for the instability of columnar vortices as follows. Let the vortex have axial velocity W(r), azimuthal velocity V(r), where r is distance from the axis, let Ω be the angular velocity V/r, and let Γ be the circulation rV. Then the flow is unstable if $ V\frac{d\Omega}{dr}\left[ \frac{d\Omega}{dr}\frac{d\Gamma}{dr} + \left(\frac{dW}{dr}\right)^2\right] < 0.$

Structure and dynamics of round turbulent jets

Abstract: Laser‐induced fluorescence and particle streak velocity measurements were conducted to investigate the structure and dynamics of round turbulent jets. The results suggest that the far‐field region of the jet is dominated by large‐scale vortical structures, which appear to be axisymmetric or helical a large part of the time. Entrainment and mixing of the reservoir fluid with the jet fluid is found to be intimately connected with the kinematics of these structures. Unmixed reservoir fluid is found to reach and cross the jet axis.

Vortex shedding from a rectangular prism and a circular cylinder placed vertically in a turbulent boundary layer

Abstract: Measurements of the vortex-shedding frequency behind a vertical rectangular prism and a vertical circular cylinder attached to a plane wall are correlated with the characteristics of the smooth-wall turbulent boundary layer in which they are immersed. Experimental data were collected to investigate the effects of (i) the aspect ratio of these bodies and (ii) the boundary-layer characteristics on the vortex-shedding frequency. The Strouhal number for the rectangular prism and the circular cylinder, defined by S = f c w / U 0 and f c d / U 0 respectively, was found to be expressed by a power function of the aspect ratio h / w (or h / d ). Here f c is the vortex-shedding frequency, U 0 is the free-stream velocity, h is the height, w is the width and d is the diameter. As the aspect ratio is reduced, the type of vortex shedding behind each of the two bodies was found to change from the Karman-type vortex to the arch-type vortex at the aspect ratio of 2·0 for the rectangular prism and 2·5 for the circular cylinder.

Friction on quantized vortices in helium II. A review

Abstract: We present an analysis of recent data on friction and drag on quantized vortices in helium II. From these data, we deduce values of the phenomenological and microscopic coefficients of friction on vortex lines and rings over a wide range of temperatures at the saturated vapor pressure. We demonstrate that the microscopic parameters are unusually sensitive to the input data. We include brief discussions of the vortex core parameter, and present the results of precision fits of a number of thermodynamic and transport properties of He II which are used in mutual friction calculations.

The effects of yaw and finite length upon the vortex wakes of stationary and vibrating circular cylinders

Abstract: The present investigation considers the vortex wakes behind finite-length yawed cylinders that are stationary or vibrating transversly in a uniform flow. In the Reynolds-number range 160–103 a number of three-dimensional and nominally two-dimensional wake flows are observed and attributed to the dominance of end conditions over rather large spans of the cylinder (aspect ratios up to 100).

The fluid mechanics of slender wing rock

Abstract: The limit cycle oscillation in roll of very slender delta wings the so called wing rock is caused by asymmetric vortex shedding from the wing leading edges and not by vortex burst The breakdown or burst of the leading edge vortices of a delta wing can lead to static instability with associated roll divergence Vortex burst however can never be the cause of wing rock because it has a dynamically stabilizing effect on the roll oscillations Consequently slender wing rock is only realized for delta wings with more than 74 deg leading edge sweep in which case vortex asymmetry occurs before vortex breakdown A careful analysis of available experimental data reveals the fluid mechanical process that generates slender wing rock A simple analytic method is formulated by which the experimentally observed limit cycle amplitude in roll can be predicted provided that the static aerodynamic characteristics are known e g from static tests

On steady vortex flow in two dimensions. I

Abstract: (1983). On steady vortex flow in two dimensios, II. Communications in Partial Differential Equations: Vol. 8, No. 9, pp. 1031-1071.

Computation of supersonic viscous flows around pointed bodies at large incidence

Abstract: A recently reported parabolized Navier-Stokes method has been extended to compute turbulent supersonic flows around cones and an ogive-cylinder body at large incidence. The algebraic eddy-viscosity turbulence model contained in the code was modified to properly account for the large regions of cross-flow separation that occur in these flows. Extensive comparisons between computed results and experimentally measured flow fields are presented. The results show good agreement for viscous-layer profiles and details of the external leeward-side vortex structure at angles of attack up to three times the cone half angles. Details of the modified turbulence model are presented and discussed.

Trailing vortices in homogeneous and density-stratified media

Abstract: Experiments were conducted with three delta wings and two rectangular wings to investigate the evolution of trailing vortices in stratified and unstratified water. The vortex trajectories were determined as a function of the normalized time V0t/b0, stratification parameter Nb0/V0 and an effective vortex-core size re/b0. The results have shown that the vortices rise only to a finite height as they decay gradually at first and rapidly thereafter under the influence of turbulence, sinusoidal instability, and core bursting. The effect of stratification is to reduce the lifespan of vortices and the maximum height attained by them.

On the structure of wall‐bounded turbulent flows

Abstract: The variable-interval time-averaging (VITA) technique developed by Blackwelder and Kaplan is applied to data obtained from large-eddy simulation of turbulent channel flow in an investigation of the organized structures associated with the bursting phenomenon in the near-wall region. Conditionally averaged velocities, shear stress, pressure, and vorticity are discussed in conjunction with the bursting phenomenon detected by the VITA technique. The conditionally averaged pressure reveals that the ejection process is associated with a localized adverse pressure gradient. In the plane perpendicular to the flow direction, the conditionally averaged vorticity field indicates that a pair of counterrotating streamwise vorticity is being lifted through the ejection process.

The hydrodynamics of rotating superfluids. I. Zero-temperature, nondissipative theory

Abstract: This is the first in a series of papers in which we develop the complete hydrodynamics of rotating superfluid4He, and other superfluids with scalar order parameters, taking into account the elasticity effects of the vortex lattice. The theory is capable of describing the long-wavelength Tkachenko shear waves exhibited by the vortices, as well as all phenomena contained in the usual Bekarevich-Khalatnikov hydrodynamics. In this paper we develop the basic theory, ignoring the normal component of the fluid. The conserved energy, written in terms of macroscopically averaged superfluid and vortex-line velocities, includes an elastic energy associated with shear, compressional, and line-bending deformations of the vortex array. Equations of motion for three-dimensional flow, consistent with the conservation laws for mass, energy, and vorticity, are derived; and Tkachenko modes with line bending, as well as inertial modes associated with the small vortex effective mass, are investigated. In the second paper of this series we extend this description to finite temperatures, to include dynamics of the normal fluid and dissipative effects.

Vortex shedding from a spinning cylinder

Abstract: An experimental investigation of a two‐dimensional turbulent wake behind a spinning cylinder at Re=9000 is carried out to determine the influence of the rotation on the initial development of the flow. Spectral analysis of the velocity data measured in the near wake shows that for peripheral velocities up to the value of the free‐stream velocity, a distinct Karman vortex activity exists within the wake, whereas for greater peripheral velocities, the Karman activity deteriorates and disappears for values in excess of twice the free‐stream velocity.

Analogies between transitional and turbulent boundary layers

Abstract: One of the interesting aspects of transitional and turbulent boundary layers is the development of counter‐rotating streamwise vortices near the wall. The most regular pattern is found in a boundary layer on a concave wall where the generation mechanism is known to be the Gortler instability. The origin of these vortices in other translational and turbulent boundary layers is presently unknown. Since the counter‐rotating vortices are located in a region of strong shear, low‐speed fluid is pumped away from the wall which coalesces into regions of low momentum lying between the vortices. As this pumping action continues, localized inflectional velocity profiles become apparent in the transitional and turbulent boundary layers. The oscillations which develop upon these profiles scale with the local thickness and velocity difference in the same manner as the two‐dimensional steady free shear layer stability problems. The oscillations grow to large amplitude and break down into new turbulence in both the transitional and turbulent boundary layers.

Gravity currents moving along a lateral boundary in a rotating fluid

Abstract: Density currents in a rotating fluid are produced by releasing a volume of buoyant fluid from a lock at one end of a long rotating channel. Coriolis forces hold the current against one wall. It is observed that the velocity and depth of the nose decrease exponentially in time, implying that the nose can effectively come to a halt at a finite distance from the lock. In reality though, the flow regime eventually changes and a viscous wedge-shaped intrusion continues. The high-Reynolds-number currents contain three-dimensional turbulence a short distance behind the nose, but the influence of rotation causes this to become quasi-two-dimensional further upstream. The intrusion and turbulent motions represent a forcing to the lower layer that produces vortex and wave-like motions which penetrate deep into the lower-layer fluid. It is shown that the exponential decay can be attributed to radiation of momentum by these inertial waves.The width l of the turbulent current varies with distance behind the nose, from 0.6 times the local time-dependent deformation radius at the ‘head’ to l ≈ R0 far upstream, where R0 is the initial deformation radius in the lock. The nose of the boundary current is unstable, with billows appearing near the tip of the intruding nose and leading to an intermittent breakup of the ‘head’ structure and oscillations of the nose velocity. These oscillations are rapid, often having frequencies much greater than f (where f = 2Ω is the Coriolis parameter), and, along with the production of the turbulence that is so characteristic of the currents, are attributed to a Kelvin–Helmholtz instability. Rotationally dominated baroclinic waves appear only a very large distance behind the nose.

A viscous vortex pair in ground effect

Abstract: We calculate the flow induced by a vortex pair in a viscous fluid, which is otherwise at rest, in the presence of a plane boundary. This may be either a no-slip or a stress-free boundary. The phenomenon of rebound of the vortices from the boundary occurs for either type of boundary, and an explanation for this is offered in terms of viscous effects.

Vortex-Front Propagation in Rotating Couette-Taylor Flow

Abstract: This Letter reports experimental measurements of the velocity $v$ of a Taylor vortex front propagating into an unstable Couette state in rotating Couette-Taylor flow and of the wavelength selected by this dynamical process. The data are consistent with a constant velocity $v\ensuremath{\propto}{\ensuremath{\epsilon}}^{\frac{1}{2}}$, as predicted from an amplitude equation, but are nearly a factor of 2 smaller than that prediction. Recent dynamic experiments on the onset of Taylor vortex flow by Park, Crawford, and Donnelly are explained in terms of vortex-front propagation.

The roles of inertia and shear-thinning in flow of an inelastic liquid through an axisymmetric sudden contraction

Abstract: The roles of luid inertia and shear-rate dependent viscosity in determining the velocity field in an axisymmetric sudden contraction are assessed by finite-element analysis for a generalized Newtonian fluid with viscosity function given by a Carreau equation. Acting alone, either increasing shear-thinning of the viscosity or increasing fluid inertia suppresses the upstream vortex that surrounds the opening to the small tube. For creeping flows, shear thinning does not produce concavities and off-centered maxima in the axial velocity profile just inside the small tube, even at high Carreau numbers where the velocity field approaches the limiting form for a power-law fluid. Peaks in the axial velocity away from the center of the tube were found only for moderate and high Reynolds numbers and were enhanced by shear thinning, which decreased the viscosity and consequently increased the “local” Reynolds number near the wall of the small tube. The effect of steep velocity gradients near this surface on the accuracy of the finite-element approximations is discussed.