Showing papers on "Vortex published in 1981"

New aspects of turbulent boundary-layer structure

Abstract: Flow visualization studies of the zero-pressure-gradient turbulent boundary layer over the Reynolds-number range 500 2000, say) the layer appears to consist very largely of elongated hairpin vortices or vortex pairs, originating in the wall region and extending through a large part of the boundary-layer thickness or beyond it; they are for the most part inclined to the wall at a characteristic angle in the region of 40–50°. Large-scale features, which exhibit a slow overturning motion, appear to consist mainly of random arrays of such hairpin vortices, although there is some evidence of more systematic structures.At low Reynolds numbers (Reθ < 800, say) the hairpin vortices are very much less elongated and are better described as horseshoe vortices or vortex loops; large-scale features now consist simply of isolated vortex loops (at the very lowest Reynolds numbers), or of several such loops interacting strongly, and show a relatively brisk rate of rotation.

Motion of an Elliptic Vortex in a Uniform Shear Flow

Abstract: Motion of an elliptic vortex of uniform vorticity in a uniform straining and vorticity flow is solved exactly. The elliptic shape is preserved and the area of the vortex is conserved but the axis ratio of the ellipse changes in general. Depending on the magnitudes of the vorticity in the vortex and the strain and the vorticity of the shear flow, this vortex exhibits various types of motion such as rotation and nutation around its centre. When the strain is very strong, the vortex is always elongated infinitely in the direction of the strain. A stationary elliptic vortex can exist in a weaker straining flow.

Instability and transition in rotating disk flow

Abstract: The stability of three dimensional rotating disk flow and the effects of Coriolis forces and streamline curvature were investigated It was shown that this analysis gives better growth rates than Orr-Sommerfeld equation Results support the numerical prediction that the number of stationary vortices varies directly with the Reynolds number

The stability of vortices in a rotating, stratified fluid

Abstract: Axisymmetric flows with a two-layer density stratification are produced by releasing either a constant flux of fluid from a point source or a constant volume of fluid into a rotating environment with a different density. In both experiments the density interface intersects one horizontal boundary, forming a front. Transition to non-axisym-metric flow is observed and can be described by two parameters: θ, the square of the ratio of the internal Rossby radius of deformation to the horizontal length scale of the flow, and δ, the fraction of the total fluid depth occupied by the layer inside the front. For θ [Lt ] 1 and δ > 10−1 unstable disturbances obtain most of their energy from the potential energy of the flow, whilst for δ < 10−1 extraction of kinetic energy from the basic shear becomes the dominant driving mechanism. When the front intersects the free surface, n = 2 is the minimum azimuthal wavenumber for an unstable disturbance. At large amplitude of the growing waves, baroclinic and barotropic processes combine to form n vortex dipole structures which entrain buoyant fluid from the original vortex and propagate radially over the free surface. Vortices are also produced by the continuous release of fluid from a confined source at its own density level in a region of constant density gradient. As in the two-layer case the axisymmetric vortex grows to a critical size and then becomes unstable to a disturbance with wavenumber n = 2, producing, at large amplitude, two vortex pairs.

London approach to anisotropic type-II superconductors

Abstract: The London equations with a phenomenlogical mass tensor are used to analyze the vortex structure near the lower critical field. The anisotropy results in a transverse magnetic field in the Abrikosov vortex. This field attenuates exponentially at large distances from the vortex axis. The strongly anisotropic attenuation length is evaluated. The line energy is found in the London approximation.

A vortex filament moving without change of form

Abstract: The motion of a very thin vortex filament is investigated using the localized induction equation. A family of vortex filaments which move without change of form are obtained. They are expressed in terms of elliptic integrals of the first, second and third kinds. In general they do not close and have infinite lengths. In some particular cases they take the form of closed coils which wind a doughnut. There exist a family of closed vortex filaments which do not travel in space but only rotate around a fixed axis. Our solutions include various well-known shapes such as the circular vortex ring, the helicoidal filament, the plane sinusoidal filament, Euler's elastica and the solitary-wave-type filament. It is shown that they correspond to the travelling wave solution of a nonlinear Schrodinger equation.

The evolution of an elliptic vortex ring

Abstract: The evolution of a vortex ring in an ideal fluid under self-induction from a flat and elliptic configuration is followed numerically using the cut-off approximation (Crow 1970) for the velocity at the vortex. Calculations are presented for four different axes ratios of the initial ellipse. A particular choice is made for the core size and vorticity distribution in the core of the vortex ring. When the initial axes ratio is close to 1, the vortex ring oscillates periodically. The periodicity is lost as more eccentric cases are considered. For initial axes ratio 0·2, the calculations suggest a break-up of the ring through the core at one portion of the ring touching that at another, initially distant, portion of the ring.Results from quantitative experiments, conducted at moderate Reynolds number with the vortex rings produced by puffing air through elliptic orifices, are compared with the calculations. The agreement is fairly good and it is found that a vortex ring produced from an orifice of axes ratio 0·2 breaks up into two smaller rings. The relevance of the results to the vortex trail of an aircraft is discussed.

A visual study of turbulent spots

Abstract: From the results of a flow visualization experiment, certain physical characteristics of a turbulent spot are suggested by the authors. The spot was artificially initiated at a point by a small intermittent wall jet. The authors also carried out experiments behind vibrating trip wires and observed the ‘signatures’ or ‘footprints’ of the A-shaped vortices seen by other workers. The fact that these ‘signatures’ are also observed in a turbulent spot leads one to suspect that these spots consist essentially of an array of A-shaped vortices. The formation of the spot is subsequently described in terms of three-dimensional disturbances of the cross-stream vortex filaments.The basic structure of the turbulent spot proposed here is similar to the suggested structure of fully developed turbulent boundary layers first put forward by Theodorsen (1955) and more recently by Bandyopadhyay & Head (1979).

Turbulent uniform flow around cylinders of finite length

Abstract: Experimental results are presented which demonstrate the effects of the free end of a circular cylinder on the mean and fluctuating pressures, mean drag force, and the phenomenon of vortex shedding when the cylinder was exposed to uniform flow. The work was carried out at Reynolds number of 0.7 x 105, and turbulence level of 0.9%. The results of the pressure measurements indicated the presence of a suppressed two-dimensional region on the lower part of the cylinder. The functional relationship between the absolute maximum fluctuating pressure coefficient and cylinder length/diameter ratio was obtained. The accuracy of the drag measurements was checked by integrating the pressure profiles, and excellent agreement between the integrated pressure data and the direct measurement was obtained. The vortex shedding measurements suggested the possible existence of three distinct sets of vortex rows with different frequencies. In the lower region, vortex loops were shed with a frequency such that it yielded a Strouhal number appropriate to an infinitely long cylinder.

Dynamics of Two-Dimensional Solitary Vortices in a Low- β Plasma with Convective Motion

Abstract: Numerical studies of the Hasegawa-Mima equation, derived in the context of drift waves but equivalent to the quasi-geostrophic vortex potential equation for Rossby waves, show the stable properties of solitary vortices which are two dimensional, localized, steady and translating solutions of this same equation. A solitary vortex can propagate only in the direction ( x -direction) perpendicular to the density gradient. When this solitary vortex solution is inclined at some angle with respect to the x -axis, its propagation direction oscillates in the x and y plane. In two dimensional collisions, i.e. head-on collision and overtaking, solitary vortices interact two-dimensionally and recover their initial shapes at the end of both types of collisions.

Oscillating flow over steep sand ripples

Abstract: Although the form and dimensions of steep vortex ripples are well studied in relation to the oscillating flow which generates them, nevertheless the accompanying fluid motion is not yet understood quantitatively. In this paper we present a method of calculation based on the assumption that the sand-water interface is fixed and that the effect of sand in suspension is, to a first approximation, negligible. The method employs a simple conformal transformation of the fluid flow onto the exterior of a polygon, and thence onto the interior of a unit circle. The initial, irrotational flow is represented by a logarithmic vortex at the centre of the circle. Other vortices within the fluid are each represented by a symmetric system of P vortices and their images in the unit circle, P being the number of sides of the original polygon. Typically P is equal to 5. However, P is not limited to integer values but may be any rational number greater than 2 (see § 15). To proceed with the calculation it is assumed that separation of the boundary layer takes place at the sharp crests of the ripples, and that the shed vorticity can be represented by discrete vortices, with strengths given by Prandtl's rule. (For a typical time sequence see figures 7 and 8.) After a complete cycle, a vortex pair is formed, which can escape upwards from the neighbourhood of the boundary. The total momentum per ripple wavelength and the horizontal force on the bottom are expressible very simply in terms of the shed vortices at any instant. The force consists of two parts: an added-mass term which dissipates no energy, and a ‘vortex drag’, which extracts energy from the oscillating flow. The calculation is at first carried out with point vortices, in a virtually inviscid theory. However, it is found appropriate to assume that each vortex has a solid core whose radius expands with time like [e( t − t n )] ½ , where t n denotes the time of birth, and e is a small parameter analogous to a viscosity. The expansion of the vortex tends to reduce the total energy (which otherwise would increase without limit) at a rate independent of e. If the cores of two neighbouring vortices overlap they are assumed to merge, by certain simple rules. Calculation of the effective vortex drag in an oscillating flow yields drag coefficients $\overline{C}_D$ of the order of 10 −1 , in good agreement with the measurements of Bagnold (1946) and of Carstens, Nielson & Altinbilek (1969). The tendency for the highest drag coefficients to occur when the ratio 2 a / L of the total horizontal excursion of the particles to the ripple length is about 1·5 is confirmed. When 2 a / L = 4, the drag falls to about half its value at ‘resonance’.

An experimental investigation of the end effects on the wake of a circular cylinder towed through water at low Reynolds numbers

Abstract: At low Reynolds numbers, three-dimensional features are frequently observed in the vortices shed behind a basically two-dimensional circular cylinder. This paper deals with the dependence of the configuration of the vortices on various end constructions. The cylinder is towed at a uniform speed in a water tank and simple flow visualization is used. It is found that the three-dimensional structure of the wake depends strongly on the flow configuration at each end of the cylinder. The boundary condition imposed on the nascent vortex lines determines the subsequent behaviour of the shed vortices. Consequently, the vortex street can be rendered more nearly two-dimensional by allowing the vortices to link outside the boundary as they approach that boundary normally. This is the case for the water–air interface when the water surface is clean. In the case of a contaminated water surface or of a solid surface acting as a boundary to the vortex street, the vortices link between themselves underneath the water surface and a strong interaction takes place behind the end of the cylinder. The subsequent effect is a bowing of the vortices towards the end of the cylinder. The free-end effect at the bottom end of the cylinder induces a strong bowing of the vortices towards that end and causes the wake to contract. It follows from the effect of surface contamination that the study of vortex wakes by the spreading of some surface contaminants might not necessarily show the true behaviour of the wake below the surface. It is postulated that slantwise shedding arises from a difference in the two end effects.

On the evolution of thunderstorm rotation

Abstract: A vertical velocity field is chosen which imitates that of the initial stages of cloud development as simulated numerically by Wilhelmson and Klemp (1978). Given this, an approximate version of the equation for the vertical component of the vorticity is solved. The vertical velocity is assumed to vary with height as sin πz/H where a is the altitude and H is the depth of the domain. At the level of nondivergence (z=H/2), the solutions indicate the development of a vortex pair which then splits into two vortex pairs one moving to the right of the mean wind and the other to the left (as observed in the numerical model). At lower levels, owing to the convergence in the updraft and divergence in the downdraft, the cyclonic/anticyclonic member of the vortex pair in the rightward/leftward moving storm is greatly enhanced. The vorticity maximum is initially on the maximum gradient of vertical velocity. At mid-levels the maximum vorticity migrates with time close to the position of maximum vertical veloci...

Combustion-Transition Interaction in a Jet Flame

Abstract: The transition between laminar and turbulent flow in a round jet flame is studied experimentally. Comparison is made between transition in nonburning and burning jets and between jet flames with systematic variation in initial Reynolds number and equivalence ratio. Measurements are made using laser anemometry, miniature thermocouples, ionization probes, laser Schlieren, and high-speed cine films. Compared with the cold jet, the jet flame has a longer potential core, undergoes a slower transition to turbulence, has lower values of fluctuating velocity near the burner with higher values further downstream, and contains higher velocity gradients in the mixing layer region although the total jet width does not alter greatly in the first twenty diameters. As in the cold jet, transitional flow in the flame contains waves and vortices and these convolute and stretch the initially laminar interface burning region. Unlike the cold jet, which has Kelvin-Helmholtz instabilities, the jet flame can contain at least two initial instabilities: an inner high-frequency, combustion-driven instability and an outer, low-frequency instability that may be influenced by buoyancy forces.

Numerical Model of Long-Lived Jovian Vortices

Abstract: A nonlinear numerical model of long-lived Jovian vortices has been constructed. We assume that the measured zonal velocity profile ubar(y) extends into the adiabatic interior, but that the eddies and large oval structures are confined to a shallow stably stratified upper layer. Each vortex is stationary with respect to the shear flow ubar(y) at a critical latitude yc, that is close to the latitude of the vortex center, in agreement with observed flows on Jupiter. Our model differs from the solitary wave model of Maxworthy and Redekopp in that the stratification is not large in our model (the radius of deformation is less than the latitudinal scale of the shear flow), and therefore stationary linear wave solutions, neutral or amplified, do not exist. The solutions obtained are strongly nonlinear in contrast to the solitary wave solutions which are the weakly nonlinear extensions of ultralong linear waves. Both stable and unstable vortices are found in the numerical experiments. When two stable vortices collide, they merge after a short transient phase to form a larger stable vortex. This merging, rather than the non-interaction behavior predicted by the solitary wave theory, is more in agreement with observations of Jovian vortices. We suggest that the long-lived Jovian vortices maintain themselves against dissipation by adsorbing smaller vortices which are produced by convection.

The turbulent trailing vortex during roll-up

Abstract: The turbulent trailing vortex forming from a rolling-up vortex sheet is considered. The inviscid, asymptotic roll-up of a vortex sheet is briefly reviewed, as are the effects to the sheet of merging by viscous and turbulent diffusion. The merged region is found to rapidly attain a state of equilibrium and similarity variables are used to describe it. The detailed distributions of circulation and Reynolds stress are seen to depend to some extent upon the initial spanwise distribution of circulation on the wing. However, a tiny region which is independent of the wing circulation distribution is found to exist near the point of peak tangential velocity. It is suggested that this region is described by Hoffmann & Joubert's logarithmic relationship. Assuming this to be the limiting form for the distribution of circulation near r1, the radius where the tangential velocity takes its peak value v1, an approximate form for the distribution of circulation is found and this is used to determine the form of the Reynolds-stress distribution. It is found that two modes for the decay of v1 with time are possible: one when r1 is much less than ½s, the wing semi-span, and v1 decays like t−½n; and the other when r1 = O(½s) and v1 may decay like t½(n-2); 0 < n < 1, for elliptic wing loading n ≃ ½.

Nonlinear Taylor vortices and their stability

Abstract: Axisymmetric numerical solutions of the Navier-Stokes equations for flow between rotating cylinders are obtained. The stability of these solutions to non-axisymmetric perturbations is considered and the results of these calculations are compared with recent experiments.

Evolution and breakdown of a vortex street in two dimensions

Abstract: The initial-value problem defined by two parallel vortex sheets of opposite sign is studied. Strictly two-dimensional, incompressible, nearly inviscid dynamics is assumed throughout. The roll-up of the sheets into a vortex street is simulated numerically using 4096 point vortices. Much longer runs than in previous work are performed, and it is found that only for a finite range of values of the ratio, h/λ, of sheet separation to perturbation wavelength, does a long-lived vortex street emerge. For h/λ [gsim ] 0·6 a pairing transition within each row intervenes. For h/λ [lsim ] 0·3 we find oscillatory modes.Using up to 16384 point vortices, we also study the breakdown of the metastable street to a two-dimensional, turbulent shear flow. The vortex blobs that made up the street may merge with others of the same sign after the breakdown, but otherwise persist throughout the turbulent regime. Neither their disintegration nor amalgamation with vortices of opposite sign was observed. Using dimensional arguments we derive the relevant scaling theory, and show that it applies to a flow started from two random vortex sheets. The resulting turbulence is not self-similar. For the turbulent flow that follows from the breakdown of a regular vortex street two length scales with different power-law growth in time appear to be necessary. The important differences in the asymptotic structure of flows initialized from random and regular sheets leads us to question the idea of universality. The influence of the symmetry of the initial perturbation on the subsequent development is also considered.

The structure of trailing vortices generated by model rotor blades

Abstract: Hot-wire anemometry to analyze the structure and geometry of rotary wing trailing vortices is studied. Tests cover a range of aspect ratios and blade twist. For all configurations, measured vortex strength correlates well with maximum blade-bound circulation. Measurements of wake geometry are in agreement with classical data for high-aspect ratios. The detailed vortex structure is similar to that found for fixed wings and consists of four well defined regions--a viscous core, a turbulent mixing region, a merging region, and an inviscid outer region. A single set of empirical formulas for the entire set of test data is described.

Uniaxial type-II superconductors near the upper critical field

Abstract: The problem of a uniaxial type-II superconductor near the upper critical field is considered in the framework of the Ginzburg-Landau equations with a phenomenological mass tensor. The currents are shown to flow in planes which are in general no longer orthogonal to the direction of the vortex axes as in the isotropic case; the inclination angle is obtained in terms of anisotropic masses. The magnetic field has a component normal to the vortex axes; equations are derived which relate the transverse and axial fields. The average value of the transverse field (the transverse induction) vanishes. The constitutive relation between the induction and the magnetization is obtained. The components of the magnetization normal and parallel to the vortex direction are simply related in terms of the effective masses.

Leading edge vortex flap for wings

Abstract: A series of flaps (21) along the leading edge of a highly swept-back wing (20) for a supersonic airplane; wherein, the spanwise series of the flaps (21) comprise a double-flap chordwise having fore and aft flap segments (22, 24). When the leading edge double-flap is positioned at a forward and downward angle-of-deflection relative to the wing (20), the fore-flap segment (22) is further positioned at an angle-of-deflection relative to the aft-flap segment (24). This difference in the deflection angles, between the fore-flap segment (22) and the aft-flap segment (24), creates a vortex flow region ahead of the wing leading edge; and this vortex functions to control separation of an upper surface boundary layer airflow, over the remainder of the upper surface of the wing (20). Also, the vortex flow will move in a spanwise direction outboard toward the tip of a swept-back wing (20), while remaining forward or ahead of the upper surface of the aft-flap segment (24). Additional embodiments relate to various other arrangements for creating a leading edge vortex flow to maintain attached flow over the remainder of the upper surface of the wing.

On the Point Vortex Method

Abstract: The discretization of the integrodifferential equation governing the evolution of a vortex sheet leads to a representation of the sheet by point vortices. It is shown, by examination of the special case of a uniform circular vortex sheet, that the chaotic motion which often arises when the point vortex representation is used is due to the amplification of numerically introduced disturbances. The mechanism is a discrete form of Helmholtz instability. The linear smoothing method of Longuet-Higgins and Cokelet (1976) and the repositioning method of Fink and Soh (1978) are shown to reduce the instability.

A numerical study of two-dimensional shock vortex interaction

Abstract: The numerical analysis of shock vortex interaction in a two-dimensional channel is discussed in this paper. The Euler equations and the two-step MacCormack scheme are employed in this numerical analysis. The comparison of the numerical results with the theoretical analyses and experimental results in the literature has provided unique insights into the dynamics of the transient interaction process and the needs for further theoretical developments. The results are useful in applications to problems in aeroacoustics and the transient aerodynamics of high performance aircraft.