Showing papers on "Vortex published in 1977"
TL;DR: A series of experiments designed to reveal the properties of high Reynolds number vortex rings, using flow-visualization and laser-Doppler techniques, has uncovered several interesting and unexpected results as mentioned in this paper.
Abstract: A series of experiments designed to reveal the properties of high Reynolds number vortex rings, using flow-visualization and laser-Doppler techniques, has uncovered several interesting and unexpected results. Starting at the beginning of the motion, at a nozzle, and proceeding downstream, these include the following.
A formation process that is strongly Reynolds number dependent.The amount of vorticity that appears downstream is very close to that predicted by a simple ‘slug’ model. However flow-visualization studies show that such a model is an oversimplification and that an excess of ring vorticity is probably cancelled by the ingestion of vorticity of opposite sign at the nozzle lip.(iii) A new, bimodal form of vortex-core instability has been observed at moderate but not high Reynolds numbers.Azimuthal inhomogeneities in the breaking of these, and the normal instability waves, create an ‘axial’ flow along the vortex core in the turbulent ring. This axial flow takes the form of a propagating wave that has many characteristics of a solitary wave. It is hypothesized that this axial flow prevents further ring instability.The long-term behaviour of the turbulent ring is marked by dramatic changes in its growth rate, which are probably related to changes in the ‘organization’ of the vortex core. The descriptive turbulent-ring model developed in Maxworthy (1974) is substantially confirmed by these experiments and by observation of ring propagation through a stratified ambient fluid.
373 citations
TL;DR: In this article, the axisymmetric and spiral vortex breakdowns to imposed flow transients reported previously are confirmed, and are traced to the shedding of starting and stopping vortices from swirl vanes.
Abstract: Flow visualization studies and laser Doppler anemometer measurements on swirling water flows reveal six distinct types of very large amplitude disturbance modes of the vortex core. Three, ’’axisymmetric’’ and spiral vortex breakdowns, and the ’’double helix,’’ have been described by others. A definite order of evolution in parameter space (Reynolds number and circulations) occurs, and is described. Puzzling responses of the axisymmetric and spiral vortex breakdowns to imposed flow transients reported previously are confirmed here, and are traced to the shedding of starting and stopping vortices from swirl vanes. Conclusions bearing upon the validity of some theories of vortex breakdown are possible from the data.
368 citations
01 Jan 1977
TL;DR: In this paper, the extent of mixing in two-dimensional free turbulent shear flows was measured using a concentration probe with a frequency response of 100 kHz and a spatial resolution of 0.1 mm.
Abstract: The extent of molecular mixing in several two-dimensional free turbulent shear flows was measured using a concentration probe with a frequency response of 100 kHz and a spatial resolution of 0.1 mm. The flows investigated were (i) a shear layer in which the gases on either side of the layer are of unequal density, (ii) a shear layer in which the gases on either side of the layer are of equal density, and (iii) a wake in which the gases on either side of the wake are of unequal densities. The extent of mixing was measured as a function of Reynolds number for the first case. It was found that at a critical Reynolds number the extent of molecular mixing sharply increased (25%). Power spectral density curves of the concentration time histories also indicated a marked increase in the high frequency fluctuations above this Reynolds number. A shadowgraph investigation of this phenomenon revealed that three-dimensional Taylor-type vortices whose axes of rotation are basically in the flow direction exist in the flow in addition to the two-dimensional large structures previously observed. These Taylor vortices were found to be unstable above the critical Reynolds number and were producing the increase in molecular mixing. The growth and development of the two-dimensional large structures were found to be basically unaffected by this instability. It is proposed that the fully developed turbulence of shear flows is maintained by a combination of the development of the large structures and of the coupling between the large structures and these unstable Taylor vortices. These data were also used to predict results for shear flows in which diffusion-limited chemical reactions have been incorporated.
318 citations
TL;DR: In this article, the transmission of sound out of a semi-infinite circular jet pipe in the presence of subsonic flow from the pipe is investigated and a solution satisfying the Kutta condition and causality is found which possesses an instability wave term that dominates within a region of approximately 45° to the downstream jet axis.
Abstract: The transmission of sound out of a semi-infinite circular jet pipe in the presence of subsonic flow from the pipe is investigated. An unstable cylindrical vortex layer attached to the edge of the pipe is considered across which differences in mean subsonic flow, density and temperature are included. A solution satisfying the Kutta condition and causality is found which possesses an instability wave term that dominates within a region of approximately 45° to the downstream jet axis. It is shown that when an exterior flow is imposed the noise level increases upstream whilst the instability wave weakens downstream. The stable part of the solution is shown to agree very well with some recent experimental results.
297 citations
TL;DR: In the mixing of a jet with a cross-stream, it is found that in the near field, defined as the region of the flow from the jet exit to a distance of a few diameters downstream of this exit, a considerable amount of dynamical adjustment takes place as discussed by the authors.
Abstract: In the mixing of a jet with a cross-stream, it is found that in the near field, defined as the region of the flow from the jet exit to a distance of a few diameters downstream of this exit, a considerable amount of dynamical adjustment takes place. This near-field region characterizes the subsequent behaviour and development of the jet, its wake and the cross-stream in the vicinity of this mixing region. The rapid evolution of the flow gives rise to a pair of bound vortices attached to the lee side of the jet boundary, to fast development of the turbulent and mean vorticity, to a vortex-shedding system, and to the largest rates of entrainment of cross-stream flow into the jet. Furthermore, it is found that the geometrical configuration of the boundaries at the jet exit plays an important role in the mixing and development processes.An intrinsic method is proposed for the delineation of the flow boundaries between the jet and the cross-stream. Calculations of mass, momentum and vorticity fluxes have been made. The vorticity flux gives evidence of the rapid stretching and tilting of the vorticity vector field in the near-field region.
244 citations
TL;DR: In this paper, implicit finite-difference procedures for the primitive form of the incompressible Navier-Stokes and the compressible Euler equations are used to compute vortex wake flows.
Abstract: Implicit finite-difference procedures for the primitive form of the incompressible Navier-Stokes and the compressible Euler equations are used to compute vortex wake flows. The partial differential equations in strong conservation-law form are transformed to cluster grid points in regions with large changes in vorticity. In addition to clustering, fourth-order accurate, spatial difference operators are used to help resolve the flowfield gradients. The use of implicit time-differencing permits large time steps to be taken since temporal variations are typically small. Computational efficiency is achieved by approximate factorization. Both two-dimensional and preliminary three-dimensional calculations are described. I. Introduction T HE concentrated vorticity in the near wake of a large aircraft can pose a destructive threat to smaller aircraft within the same airspace. Consequently, experimental and theoretical efforts have been under way to understand, predict (for use in avoidance systems), and possibly reduce the vortex wake hazard. Most theoretical models developed to treat this problem rely on tracing discrete vortices,1"3 but an alternate and potentially more powerful approach is to use finitedifference procedures.4'5 Computer programs based on such methods can ultimately account for flowfield nonlinear effects with few ad hoc assumptions. Implicit finite-difference procedures are developed here to solve the incompressible Navier-Stokes equations and compressible Euler equations for simplified two- and threedimensional, unsteady vortex wake flows. This paper is divided into five interdependent sections. The flowfield and its numerical implications are discussed in Sec. II. The incompressible equations are developed for simulation as a system of first-order partial-differential equations in Sec. Ill, and the finite-difference algorithms are described in Sec. IV. Simulation based on the compressible flow equations is discussed in Sec. V. and, finally, simple wake-vortex flow calculations using both kinds of modeling are presented in Sec. VI.
184 citations
TL;DR: In this article, an application of Kubo's linear response theory is used to study the nonequilibrium situation that results from placing a cluster, of vortices in a weak external velocity field, such as that produced by a distant vortex cluster.
Abstract: Equilibrium statistics of a cluster of a large number of positive two-dimensional point vortices in an infinite region and the associated thermodynamic functions, exhibiting negative temperatures, are evaluated analytically and numerically from a microcanonical ensemble. Extensive numerical simulations of vortex motion are performed to verify the predicted equilibrium configurations. An application of Kubo's linear response theory is used to study the nonequilibrium situation that results from placing a cluster, of vortices in a weak external velocity field, such as that produced by a distant vortex cluster. The weak field causes the cluster to grow in size as if there were an effective positive eddy viscosity. When a number of clusters interact, the effect is for each to grow while the distances between them decrease with time. The latter effect is an exhibit of negative viscosity. The application of this to the motion of the atmosphere is discussed.
174 citations
01 Dec 1977
TL;DR: In this paper, the concept of the generalized principal part of an integral yields a residual term to the vorticity-induced velocity field, and the proper incorporation of this term into the velocity field generated by the discrete vortex lines renders the present vortex lattice method valid for supersonic flow.
Abstract: If the discrete vortex lattice is considered as an approximation to the surface-distributed vorticity, then the concept of the generalized principal part of an integral yields a residual term to the vorticity-induced velocity field. The proper incorporation of this term to the velocity field generated by the discrete vortex lines renders the present vortex lattice method valid for supersonic flow. Special techniques for simulating nonzero thickness lifting surfaces and fusiform bodies with vortex lattice elements are included. Thickness effects of wing-like components are simulated by a double (biplanar) vortex lattice layer, and fusiform bodies are represented by a vortex grid arranged on a series of concentrical cylindrical surfaces. The analysis of sideslip effects by the subject method is described. Numerical considerations peculiar to the application of these techniques are also discussed. The method has been implemented in a digital computer code. A users manual is included along with a complete FORTRAN compilation, an executed case, and conversion programs for transforming input for the NASA wave drag program.
167 citations
TL;DR: In this article, it was shown that textures with vorticity but no vortex core can be easily constructed, so that dissipation of superfluid flow can occur by motion of textures alone without true vortex lines.
Abstract: The characteristic dissipation process for conventional superfluid flow is phase slip-page: motion of quantized vortices in response to the Magnus force, which allows finite chemical potential differences to occur. Topological considerations and actual construction are used to show that in liquid $^{3}\mathrm{He}$-$A$, textures with vorticity but no vortex core can easily be constructed, so that dissipation of superfluid flow can occur by motion of textures alone without true vortex lines, dissipation occurring via the Cross viscosity for motions of $\stackrel{^}{l}$.
153 citations
TL;DR: In this article, the free precession frequency of Her X-1 stars with low oblateness was given as π/(sub p/=psi..cap omega.., where psi is the ratio of moments of inertia of the pinned superfluid to the rigid component of the rest of the star and π is half the superfluid vorticity.
Abstract: Vortex pinning affects neutron stellar free precession by modifying its frequency and geometry, in a gyroscopic effect. For neutron stars with low oblateness, the free precession frequency is given by ..omega../sub p/=psi..cap omega.., where psi is the ratio of moments of inertia of the pinned superfluid to the rigid component of the rest of the star, and ..cap omega.. is half the superfluid vorticity. This poses a severe difficulty on any interpretation of the 35/sup d/ cycle in Her X-1 in terms of neutron stellar wobble, if vortex pinning exists.
152 citations
TL;DR: In this article, a simulation of 2D turbulence in a square region with periodic boundary conditions has been performed using a highly accurate approximation of the inviscid Navier-Stokes equations to which a modified viscosity has been added.
TL;DR: In this article, a recent theoretical description of interactions between surface waves and currents in the ocean is extended to allow density stratification and the interaction leads to a convective instability even when the densities stratification is statically stable.
Abstract: A recent theoretical description of interactions between surface waves and currents in the ocean is extended to allow density stratification. The interaction leads to a convective instability even when the density stratification is statically stable. An unspecified random surface wave field is permitted provided that it is statistically stationary.The instability can be traced to torques produced by variations of a ‘vortex force’. Non-diffusive instabilities produced by this mechanism in water of infinite depth are explored in detail for arbitrary distributions of the destabilizing force. Stability is determined by an eigenvalue problem formally identical to that determining normal modes of infinitesimal internal waves in fluid with a density profile that is not monotone and thereby has a statically unstable region. Some tentative remarks are offered about the problem when dissipation is allowed.Application of the present theory to Langmuir circulations is discussed. Also, according to the present theory, internal wave propagation should be modified by the vortex force arising from the interaction between the surface waves and the current.
TL;DR: An implicit finite difference technique employing orthogonal curvilinear co-ordinates is used to solve the Navier-Stokes equations for peristaltic flows in which both the wall-wave curvature and the Reynolds number are finite as discussed by the authors.
Abstract: An implicit finite-difference technique employing orthogonal curvilinear co-ordinates is used to solve the Navier–Stokes equations for peristaltic flows in which both the wall-wave curvature and the Reynolds number are finite (§2). The numerical solutions agree closely with experimental flow visualizations. The kinematic characteristics of both extensible and inextensible walls (§3) are found to have a distinct influence on the flow processes only near the wall. Without vorticity, peristaltic flow observed from a reference frame moving with the wave will be equivalent to steady potential flow through a stationary wavy channel of similar geometry (§4). Solutions for steady viscous flow (§5) are obtained from simulation of unsteady flow processes beginning from an initial condition of potential peristaltic flow. For nonlinear flows due to a single peristaltic wave of dilatation, the highest stresses and energy exchange rates (§6) occur along the wall and in two instantaneous stagnation regions in the bolus core. A series of computations for periodic wave trains reveals that increasing the Reynolds number from 2[sdot ]3 to 251 yields a modest augmentation in the ratio of flow rate to Reynolds number but induces a much greater increase in the shear stress (§7.1). The transport effectiveness is markedly reduced for pumping against a mild adverse pressure drop (§7.2). Increasing the wave amplitude will lead to the development of travelling vortices within the core region of the peristaltic flow (§7.3).
TL;DR: The behaviour of human and frog red cells, platelets and rigid spheres were studied in the annular vortex formed in steady or pulsatile flow at the sudden concentric expansion of a 151 $\mu$ m into 504 $\mu $ m diameter glass tube.
Abstract: The behaviour of human and frog red cells, platelets and rigid spheres were studied in the annular vortex formed in steady or pulsatile flow at the sudden concentric expansion of a 151 $\mu$ m into 504 $\mu$ m diameter glass tube. During a single orbit the measured particle velocities and paths in steady flow were in good agreement with those calculated for the fluid, predicted by theory to circulate in closed orbits. Over longer periods, however, single blood cells and latex spheres $\mu$ m diameter migrated across the streamlines out of the vortex at a rate depending on the Reynolds number whereas spheres and aggregates of red cells > 30 $\mu$ m diameter remained in the vortex at all Reynolds numbers. Similar behaviour was noted in pulsatile flow when the vortex moved in phase with upstream fluid velocity and particles described spiral orbits of continually changing diameter. With red cell suspensions of 15-45% haematocrit in steady flow, migration of the corpuscles was also observed and resulted in the formation of a particle-free vortex. In pulsatile flow, cells were always present in the vortex, but their concentration which varied periodically was lower than that in the mainstream. The formation of aggregates of latex spheres and human platelets through collisions occurring in orbit, and their migration to the vortex centre was also observed.
TL;DR: In this paper, a two-dimensional line vortices are generated in a water tank of dimensions 15 × 122 × 244 cm and their axes span the 15 cm width of the tank, and the flow is visualized using fluorescein dye.
Abstract: A new technique for generating a pair of line vortices in the laboratory has been developed. The mean flow of these vortices is highly two-dimensional, although most of the flow field is turbulent. This two-dimensionality permits the study of vortex motions in the absence of the Crow mutual induction instability and other three-dimensional effects. The vortices are generated in a water tank of dimensions 15 × 122 × 244 cm. They propagate vertically and their axes span the 15 cm width of the tank. One wall of the tank is transparent, and the flow is visualized using fluorescein dye. High speed photography is used to study both the transition to turbulence during the vortex formation process and the interaction of the turbulent vortices with a simulated ground plane.Transition occurs first in an annular region surrounding the core of each vortex, starting with a shear-layer instability on the rolled-up vortex sheet. The turbulent region then grows both radially inwards and radially outwards until the entire recirculation cell is turbulent. A ‘relaminarization’ of the vortex core appears to take place somewhat later.The interaction of the vortex pair with the ground plane does not follow the predictions of potential-flow theory for line vortices. Although the total circulation is apparently conserved, the vortices remain at a larger distance from the ground than is expected and eventually ‘rebound’ or move away from the ground. Differences between a free-surface boundary condition and a smooth or rough ground plane are discussed. The ground-plane interaction is qualitatively very similar to that of aircraft trailing vortices observed in recent flight tests.
TL;DR: In this paper, the steady laminar flow is studied by means of a three-dimensional extension of triple-deck theory, so that there is the prospect of separation in the nonlinear motion.
Abstract: A shallow three-dimensional hump disturbs the two-dimensional incompressible boundary layer developed on an otherwise flat surface. The steady laminar flow is studied by means of a three-dimensional extension of triple-deck theory, so that there is the prospect of separation in the nonlinear motion. As a first step, however, a linearized analysis valid for certain shallow obstacles gives some insight into the flow properties. The most striking features then are the reversal of the secondary vortex motions and the emergence of a ‘corridor’ in the wake of the hump. The corridor stays of constant width downstream and within it the boundary-layer displacement and skin-friction perturbation are much greater than outside. Extending outside the corridor, there is a zone where the surface fluid is accelerated, in contrast with the deceleration near the centre of the corridor. The downstream decay (e.g. of displacement) here is much slower than in two-dimensional flows.
TL;DR: In this paper, a general theory is proposed for the small disturbance field in strongly swirling flows in turbomachines, and conditions for propagation of pressure modes in the strongly swirling flow show the effects of rotation to be small if the frequency is large compared to base rotational frequency.
Abstract: A general theory is proposed for the small disturbance field in strongly swirling flows in turbomachines. In contrast to the situation in nonswirling flows, vorticity, pressure, and entropy fields are not independent. Shear disturbances are not purely convected but rather propagate slowly in flows stable in the sense of Rayleigh, and are unstable in flows approaching free vortices. In the course of the propagation, there is an interchange between radial and tangential velocity perturbations. General conditions for propagation of pressure modes in the strongly swirling flow show the effects of rotation to be small if the frequency is large compared to base rotational frequency. Oscillatory shear flows have been observed in experiments in the MIT Blowdown Compressor.
TL;DR: In this paper, a 4 m wide and 7 m tall tornado vortex generator was constructed at Purdue University that operates on a principle similar to that of the earlier machine modeled by Ward (1972).
Abstract: A 4 m wide and 7 m tall tornado vortex generator (including exhaust fan and duct work) has been constructed at Purdue University that operates on a principle similar to that of the earlier machine modeled by Ward (1972). Characteristics of the Purdue simulator are described, as well as the corresponding modifications and improvements that have been made to Ward's machine. Selected photographs of vortex configurations obtained in the simulator demonstrate the ability of the machine to achieve vortex breakdown and multiple vortex configuration. A radial-axial profile of velocity magnitudes (using hot-film anemometry) has been obtained for the state of vortex breakdown characterized by two interlocking helical spiral vortices. This preliminary result shows the potential that the experimental system offers for obtaining quantitative information about the flow field of selected vortex configurations. Multiple vortex phenomena in the thunderstorm-tornado system are examined in light of the laboratory s...
TL;DR: In this paper, the authors studied the two-dimensional flow of an incompressible liquid between two infinitely close concentric spheres, due to an initial distribution of the vorticity differing from zero.
Abstract: The article discusses the two-dimensional flow of an incompressible liquid between two infinitely close concentric spheres, due to an initial distribution of the vorticity differing from zero. The concept of point singularities (vortices, sources, and sinks) at a sphere is introduced. Equations of motion are obtained for point vortices, as well as invariants of the motion, known for the plane case [1]. The simplest case of the mutual motion of a pair of vortices is considered. Equations are obtained for the motion of point vortices at a rotating sphere. Integral invariants for the continuous distribution of the vorticity are obtained, having the dynamic sense of the total kinetic energy and the momentum of the liquid at the sphere. The effect of the topology of the sphere on the dynamics of the vorticity is noted, and a comparison is made with the plane case.
TL;DR: In this article, a plate at 60° incidence impulsively started from rest in an otherwise stationary incompressible fluid is numerically studied through the use of the discrete-vortex approximation, in which the shear layers emanating from the edges of the plate are represented by an array of discrete vortices introduced into the flow field at appropriate time intervals at some fixed points near the edges.
Abstract: Unsteady separated flow behind an inclined flat plate is numerically studied through the use of the discrete-vortex approximation, in which the shear layers emanating from the edges of the plate are represented by an array of discrete vortices introduced into the flow field at appropriate time intervals at some fixed points near the edges of the plate. The strengths of the nascent vortices are chosen so as to satisfy the Kutta condition at the edges of the plate. Numerical calculations are performed for a plate at 60° incidence impulsively started from rest in an otherwise stationary incompressible fluid, by systematically changing the distance between the location of the nascent vortices and the edges of the plate. The temporal changes in the drag force, the rate of vorticity transport at both edges of the plate and the velocity of the separated shear layers are given together with the flow patterns behind the plate on the basis of this model. The results of the computation show that the vortex street behind the plate inclines as a whole towards the direction of the time-averaged lift force exerted on the plate. It is also predicted from the calculations that the vortex shedding at one edge of the plate will not occur at the mid-interval of the successive vortex shedding at the other edge. The predicted flow patterns are not inconsistent with a few experimental observations based on the flow-visualization technique.
TL;DR: In this article, the structural damping and the fluid dynamic reaction or damping in phase opposition with the cylinder's velocity were measured for three cylinders in a wind tunnel and the nonlinear dependence of the lift force on the cylinder amplitude confirms the wake-oscillator hypothesis put forward by several previous investigators.
TL;DR: An axisymmetric numerical model has been developed to simulate Ward's (1972) laboratory experiments as mentioned in this paper, and it is shown that the core radius is independent of the Reynolds number at high Reynolds number.
Abstract: An axisymmetric numerical model has been developed to simulate Ward's (1972) laboratory experiments. It was shown by Davies-Jones (1976) that this experiment is more geophysically relevant than all previous experiments in that Ward's experiment exhibits both dynamical and geometrical similarity to actual tornadoes. Major results are 1) the core size versus inflow angle relationship agrees very nearly with Ward's measurements, 2) the numerical and laboratory surface pressure patterns are in agreement, and 3) it is demonstrated that the core radius is independent of the Reynolds number at high Reynolds number (Ward's data also exhibit this behavior). Based on this axisymmetric model some speculation concerning the nature of the asymmetric multiple vortex phenomenon is made. Furthermore, the numerical model allows the examination of the interior flow field. As a consequence, an explanation is offered in Section 6 for the double-walled structure sometimes observed in natural vortices. The experiments...
TL;DR: In this article, it was shown that a flux vortex, in the presence of a sufficiently large current density applied parallel to its axis, is unstable against the growth of helical perturbations.
Abstract: It is shown that a flux vortex, in the presence of a sufficiently large current density applied parallel to its axis, is unstable against the growth of helical perturbations. This instability, which has an analog in magnetohydrodynamics, may play a critical role in current-carrying type-II superconductors subjected to longitudinal magnetic fields.
TL;DR: In this paper, the authors propose a theory to describe the motion and thermodynamics of superfluids when a large number of quantized vortex lines are present and when the phenomena under study are on scales large compared with the vortex line spacing.
Abstract: There are two well known theories to describe the motion and thermodynamics of superfluids when a large number of quantized vortex lines are present and when the phenomena under study are on scales large compared with the vortex line spacing. These works have been criticised on the grounds that their governing equations for the smoothly varying, spatially averaged, fields do not satisfy the accepted invariance principles basic to modern continuum mechanics. This paper demonstrates one way in which such theories can arise from a properly invariant continuum approach and indicates the presence of hitherto unconsidered terms that bring them closer to the generally accepted microscopic picture. The resulting theory has applications both to rotating helium II in the laboratory, and to rotating neutron stars (pulsars).
TL;DR: In this paper, an experimental study was carried out on the interaction of two vortex rings moving in air side by side along their parallel axes and the behavior of two rings was observed by a flow visualization method and the three-dimensional structure of the cross-linking of the two vortex filaments was studied.
Abstract: Experimental studies were carried out on the interaction of two vortex rings moving in air side by side along their parallel axes. The behavior of two rings was observed by a flow visualization method and the three-dimensional structure of the cross-linking of the two vortex filaments was studied. This phenomena were classified into three patterns, depending on the initial speeds of two rings. (1) At lower speed, two rings merge into one distorted ring. (2) At higher speed, it splits into two rings again after merging, (3) At still higher speed, they merge, split and merge again into one ring before they diffuse away. Theory of virtual momentum was examined in the case of this interaction of two vortex rings.
TL;DR: In this paper, the authors define a tornado-like vortex as one for which the axial velocity falls to zero for sufficiently large radius, and seek to clarify the conditions under which the solution of the quasi-cylindrical flow equations can be continued indefinitely or breaks down at a finite height.
Abstract: Laboratory experiments on swirling flows through tubes often exhibit a phenomenon called vortex breakdown, in which a bubble of reversed flow forms on the axis of swirl. Mager has identified breakdown with a discontinuity in solutions of the quasicylindrical flow equations. In this study we define a tornado-like vortex as one for which the axial velocity falls to zero for sufficiently large radius, and seek to clarify the conditions under which the solution of the quasi-cylindrical flow equations can be continued indefinitely or breaks down at a finite height. Vortex breakdown occurs as a dynamical process. Hence latent-heat effects, though doubtless important to the overall structure and maintenance of the tornado, are neglected here on the scale of the breakdown process. The results show that breakdown occurs when the effective axial momentum flux (flow force) is less than a critical value; for higher values of the flow force, the solution continues indefinitely, with Long's (1962) similarity solution as the terminal state. When applied to the conditions of the 1957 Dallas tornado, the computed breakdown location is in agreement with Hoecker's analysis of the observations.
TL;DR: In this paper, a numercial study was made of the interaciton of two-dimensional al, time-dependent, inviscid vortical regions, and it was found that discrete boundaries, which depend on the structure and spacing of the vortices, distinguish merging from non-merging situations.
Abstract: The several wake vortices that originate from aircraft wingtips, flap edges, engine pylons, etc. usually merge, in the far field to form a single pair, whose structure determines the hazard posed to encountering aircraft. In order to gain an understanding of the process whereby vortices merge and disperse, a numercial study was made of the interaciton of two-dimension al, time-dependent, inviscid vortical regions. It was found that discrete boundaries, which depend on the structure and spacing of the vortices, distinguish merging from nonmerging situations. Furthermore, certain arrays of finite vortex cores that alternate in sign were found to undergo division and merging that may be useful in alleviating the hazard posed by aircraft wakes. AR b CL Ce Ct c c de d/