No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
An Assessment of Dominant Mechanisms in Vortex-Wake Decay
Abstract
Predicting the transport and decay of the organized vortex system for various aircraft types, flight modes, and meteorological conditions requires clear identification of the various significant factors and mechanisms involved in the transport/decay process. Outside of the ground effect, the dominant factors include the circulation and core characteristics of the vortices, the turbulence in the wake and in the environment, and the thermal stability of the environment. The environmental factors are sometimes dominant; the vortex wakes from an airplane operating in two different meteorological regimes can differ by an order of magnitude in decay and by an order of magnitude in descent distance. Thus any theory of vortex-wake decay in the real atmosphere must consider the meteorological factors, and field observations on decay must be interpreted with consideration of these factors.
... (1974) and later by Saffman (1978). In figs 1 and 2 in MacCready (1971), some beautiful photographs of this cascade in contrail breakup are presented. Unfortunately, exploiting this instability has not yet proven to be very effective. ...
... In extreme cases, one member of the pair seems to disappear and the remaining vortex may persist for several minutes, e.g. see fig. 3 in MacCready (1971). Wind shear is a natural candidate for an explanation of the loss of symmetry and the unequal behaviour of the two filaments. ...
The shape and stability of two–dimensional, uniform patches of vorticity in incompressible inviscid fluid are calculated.
The object of the study is to investigate th effect of wind shear on trailing vortices. The wind shear is modelled by simple shea with velocities in the plane perpendicular to the trailing vorticity. The first portion o this study models the trailing vortices as a pair of uniform straight counter–rotatin line vortices which are essentially point vortices. They move under their self–induce velocities and the external shear. It is shown that the equations for the positions o the vortices can be solved exactly, and they move on parabolic trajectories with th horizontal and vertical separations kept constant. The trajectories are weakly unstable infinitesimal disturbances grow algebraically in time. But, apart from the effec of wind shear on the horizontal displacement and an asymmetry of the streamlines wind shear has no significant effect on the motion of the vortex pair under the poin vortex approximation. The situation is different when the finite size of the trailingvorte cores is taken into account. Following a method originally suggested in personal communication from Jimenez, Schwarz functions are used to find the shap of steady flows and their stability to infinitesimal two–dimensional disturbances. It i found that the vortex patches may be deformed significantly, or very slightly, dependin upon the sense of rotation of the trailing vortex relative to the sense of rotatio in the external simple shear. When co–rotating, the patch remains circular to a goo approximation, as would a single co–rotating patch in a uniform shear, a case whic can be solved exactly. But when counter–rotating, the patch may be significantl deformed into a long, thin shape, perpendicular to the line joining the centroids o the patches. The configuration is unstable to small disturbances but the eigenfunctio corresponding to a deformation of the co–rotating vortex patch is small compare with that for the counter–rotating patch. This type of asymmetric behaviour is seen i the observations and suggests that the asymmetric properties are due to wind shear although other explanations may be significant. It is shown that the heavy numerica calculations which are required by the Schwarz function approach for two or mor patches can be bypassed by use of an approximation called the elliptic patch model which gives equations of Hamiltonian form for the position of the vortex centroid an the orientation of the elliptical patch which models the vortices. The Moore–Saffma dispersion relation for steady states can be shown to be a consequence of the model.
Atmospheric stratification affects the downward motion of an aircraft vortex wake and may influence the persistence and stability of the vortex pair configuration. Observations of actual wakes have shown significant variation in the distance to which they descend and in their lifetimes under different degrees of atmospheric stability. This behavior has been modeled analytically in this paper as a pair of infinite vortices in an inviscid, compressible, stably stratified atmosphere with entrainment characterized by a single parameter which is related to the difference between the density in a particular region of the wake and that external to the wake. It has been found that the motion of such a vortex system is governed by a parameter Q which depends on the initial circulation and vortex spacing, on the atmospheric stability, and on the entrainment parameter.
The nature of the transport follows one of two patterns, depending on whether Q is less than or greater than a critical value Qcrit. If Q < Qcrit, the circulation decreases more rapidly than the momentum and the vortices separate as they descend to an equilibrium level. If Q > Qcrit, the momentum of the vortices decreases more rapidly than the circulation and, after an initial period of slow divergence, the vortices attempt to converge as they descend. In both cases, the descent takes place in a well-defined characteristic time which depends solely on the atmospheric density gradient.
Smoke-marked trailing vortices were generated by a light aircraft under a hierarchy of measured atmospheric stability and turbulence levels and their motion and decay was recorded photographically. Decay from both sinuous vortex interaction and core bursting type instabilities occurred, with bursting being the dominant mode. Turbulence had a strong effect on wake life, with time-to-breakup for both modes varying as ϵ1/3, where ϵ is the turbulent dissipation rate. Observed lifetimes ranged from 6 sec in light-to-moderate turbulence to more than SO sec in calm, stable air. One exceptionally long-lived solitary vortex was observed for more than 3 min. Atmospheric stratification had a weak influence on wake life and its effect on wake descent could not be determined, since descent was often stopped by a rolling of the plane of the vortices. The observed data correlates well with a new theory for time-to-breakup. © 1973, American Institute of Aeronautics and Astronautics, Inc., All rights reserved.
The objective of this study is to investigate with a numerical model how coexisting vertical shear and stratification affect the evolution of a vortex pair. Our results show that the Richardson number (the ratio of stratification forces to shear forces) is an important parameter in the evolution. When the Richardson number is large, the vortex pair evolves more or less symmetrically, the left and right vortex decaying equally, or nearly equally, rapidly. In this case, the effect of the shear is small, and stratification dominates the evolution. When the Richardson number is sufficiently small, however, the evolution is dramatically different. Under these conditions, the vortices evolve asymmetrically, and the vortex with rotational sense opposite to that of the mean shear decays while the vortex with the same rotational sense as the mean shear survives.
A brief summary of previous works is followed by an in-depth analysis of velocities, circulations, and decay histories of a number of trailing vortices generated by large aircraft during field tests in Memphis, Tennessee. The results suggest that the decay of trailing vortices is governed by the mutual straining of vortices; intermittent exchange of mass, momentum, and vorticity across the core boundary; rotational damping and restructuring of turbulence in the core; stretching of large turbulent structures, turbulent diffusion, and the interaction of oppositely signed vorticity in the overlapping regions of the vortex pair; and the draining of vorticity from the Kelvin oval.
FM-CW radars have revealed many unique marine boundary layer echoes in
great detail and permit new interpretations when they are operated
simultaneously with other remote sensors. Three different subject areas
and associated observations are presented. First, an FM-CW radar can
provide information on tropospheric radio propagation conditions through
a refractive index profile updating procedure. Mesoscale variations in
radio propagation conditions can be obtained when separated FM-CW radars
are operated simultaneously. Second, highly distinct radar echoes,
created by wing tip vortices, have been observed at a commercial jet
airport. Third, simultaneous observations with two FM-CW radars can
reveal important submesoscale features.
The flow fields of vortices, whether buoyancy-driven or lift-generated, are fascinating fluid-dynamic phenomena which often possess intense swirl velocities and complex time-dependent behavior. As part of the on-going study of vortex behavior, this paper presents a historical overview of research conducted on the structure and modification of the vortices generated by the lifting surfaces of subsonic transport aircraft. Although primarily presented from an experimental point of view, the derivation and use of relatively compact theoretical formulations and concepts are included. Experience with lift-generated wakes has shown that they are so complex that progress requires application of a combined theoretical and experimental research program, because either alone often leads to incorrect conclusions. The primary purpose of the research to be described is to find a way to reduce the hazard potential of lift-generated vortices shed by subsonic transport aircraft in the vicinity of airports during landing and takeoff operations. The information presented points out that the characteristics of lift-generated vortices are related to the aerodynamic shapes that produce them and that various arrangements of surfaces can be used to produce quite different vortex structures. It is concluded that a satisfactory aerodynamic solution to the wake-vortex problem at airports has not yet been found, but a reduction in the impact of the wake-vortex hazard on airport capacity may soon become available through wake-vortex avoidance concepts currently under study.
An exact solution is derived for the trochoidal motion of a single horizontal buoyant vortex drifting under gravity, and a criterion is given for such vortices to persist. Approximate solutions are obtained for the twodimensional drift of buoyant wing-tip vortices descending in a neutrally stable atmosphere where the buoyancy is achieved by injecting hot gas from the engine exhaust or auxiliary burners into the vortex cores. The vortices are found to approach each other as they descend. This effect may accelerate their breakup and thus reduce the period of time when the wake from a large aircraft is dangerous to other aircraft. At low altitudes the ground effect may dominate and cause buoyant wing-tip vortices to separate instead of approach each other. Formulas and graphs are presented for calculating these effects, and sample calculations are applied to the Boeing 747 aircraft. A weakly stable atmosphere should increase the buoyancy and the convergence rate of descending wing-tip vortices, and a method is presented for calculating the combined effect of core heating and atmospheric stability. © 1972 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.
A theoretical study of the optical and physical requirements of marking trailing vortices that emanate from aircraft wings was carried out by considering particulate light-scattering properties, ability of particles to follow trailing vortices, and survival time of particles to vortex dissipation. Liquid droplets undergoing evaporation and molecular dispersion were investigated. Droplets should have lifetimes of about 300 sec. Droplet size should be about 1 micron to maximize light scattering with the minimum mass of liquid required. Droplets of this small size would spiral outward very slowly and essentially remain in the vortex cores. Nontoxic hygroscopic liquids, having an affinity for moisture in the air, have been identified. These liquids have relatively low vapor pressures of order 10 to the -5 mm Hg that would insure droplet persistence long enough to mark trailing vortices.
Description of velocity measurements made in the wake of wings in the Ames 7 x 10 ft wind tunnel. Distributions of velocity components were measured with a three-wire anemometer up to 12 chord lengths downstream of a CV-990 aircraft model and a rectangular wing. Results show that increasing the drag increases the vortex core radius, reduces the maximum tangential velocities, and increases the magnitude of axial velocity defects. For the rectangular wing, axial velocity changes from a defect (wake flow) for angles of attack less than 9 deg to an excess (jet flow) for angles of attack greater than 9 deg. Wind-tunnel measurements of the near flowfield are compared with flight measurements of the far flowfield.
Flight tests have been conducted by the Federal Aviation Administration (FAA) at both the Environmental Science Services Administration/Atomic Energy Commission (ESSA/AEC) facility, Idaho Falls, Idaho, and the National Aviation Facilities Experimental Center (NAFEC), Atlantic City, New Jersey, during the period 18’February 1970 through 3 August 1970 to gather quantitative data on aircraft vortex wake characteristics using the tower fly-by technique. Aircraft tested included the Boeing 747, 707–300 and 727–100, the Douglas DC-8-63F, DC-8-33 and DC-9-10, the Lockheed C5A, the Convair 880, and the Learjet 24. A 200-foot and a 100-foot tower was used at the ESSA and NAFEC test sites, respectively. Vortex flow visualization for vortex characteristics and movement was provided by colored smoke grenades mounted on the towers and by injecting CORVUS-type smoke oil into the outboard jet engine exhausts of certain aircraft with wing mounted engines.
Atmospheric stratification affects the downward motion of an aircraft vortex wake and may influence the persistence and stability of the vortex pair configuration. Observations of actual wakes have shown significant variation in the distance to which they descend and in their lifetimes under different degrees of atmospheric stability. This behavior has been modeled analytically in this paper as a pair of infinite vortices in an inviscid, compressible, stably stratified atmosphere with entrainment characterized by a single parameter which is related to the difference between the density in a particular region of the wake and that external to the wake. It has been found that the motion of such a vortex system is governed by a parameter Q which depends on the initial circulation and vortex spacing, on the atmospheric stability, and on the entrainment parameter.
The nature of the transport follows one of two patterns, depending on whether Q is less than or greater than a critical value Qcrit. If Q < Qcrit, the circulation decreases more rapidly than the momentum and the vortices separate as they descend to an equilibrium level. If Q > Qcrit, the momentum of the vortices decreases more rapidly than the circulation and, after an initial period of slow divergence, the vortices attempt to converge as they descend. In both cases, the descent takes place in a well-defined characteristic time which depends solely on the atmospheric density gradient.
Trailing vortices do not decay by simple diffusion. Usually they undergo a symmetric and nearly sinusoidal instability, until eventually they join at intervals to form a train of vortex rings. The present theory accounts for the instability during the early stages of its growth. The vortices are idealized as interacting lines; their core diameters are taken into account by a cutoff in the line integral representing self-induction. The equation relating induced velocity to vortex displacement gives rise to an eigenvalue problem for the growth rate of sinusoidal perturbations. Stability is found to depend on the products of vortex separation and cutoff distance times the perturbation wavenumber.
A series of 36 diffusion trials were conducted in four widely differing terrains and meteorological regimes. Objective of the program was to extend the results obtained in the Dallas Tower Program to other terrain and meteorological conditions.
An experimental study was carried out on a rectangular wing in the NASA-Ames 7- by 10-Foot Wind Tunnel. Flow visualization studies were made using a tuft grid and smoke. Preliminary studies showed that the introduction of a bluff body into the trailing vortex downstream of the wing resulted in modification of the vortex. Further studies showed that a small vertical panel, termed a vortex dissipater, mounted on the wing upper surface near the wing tip also caused modification of the vortex. Both the smoke and tuft grid visualization studies indicated that the dissipater caused a significant reduction in the maximum tangential velocities in the trailing vortex. Additional studies using a hot wire anemometer showed significant reductions in the magnitude of the tangential velocities, increases in the cross-sectional dimensions of the core of the dissipated vortex and changes in the turbulence structure. Limited flight tests with a dissipater fitted to a Convair 990 wing tip and using a Lear jet aircraft as a probe indicated that the rolling acceleration and the degree of roll control required was less in the modified vortex than in the unmodified vortex.
Aircraft Wakes and Diffusion Enhancement
- T B Smith
- P B Maccready
- TB Smith
Contrail Studies for Jet Aircraft
- T B Smith
- K M Beesmer
- TB Smith
Vertical Diffusion from a Low Altitude Line Source - Dallas Tower Studies
- P B Maccready
- T B Jr
- M A Smith
- Wolf
- PB Maccready Jr
Cluster Diffusion in the Inertial Subrange
- P B Maccready
- B L Jr
- L Niemann