One of the most conspicuous features of an airplane flying at high altitude is its white contrails. These contrails, which are formed by the condensation of engine exhaust water vapour, clearly delineate the location of the wing tip vortices. The contrails are often the first — and perhaps the only — exposure most of us have to wing tip vortices (also referred to as “trailing vortices” or, imprecisely, as “wing wake vortices” or “tip wake vortices”). This chapter aims to explain the origin of tip vortices (§X.l) and review their technological relevance (§X.2). The chapter then summarizes lifting line theory, the simplest finite wing theory (§X.3), and synopsizes our knowledge of tip vortex behaviour (§X.4, §X.5).
- Vortex Core
- Wake Vortex
- Delta Wing
- Lead Edge Vortex
- Aspect Ratio Wing
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Tax calculation will be finalised at checkout
Purchases are for personal use onlyLearn about institutional subscriptions
Unable to display preview. Download preview PDF.
Agrawal, S., Barnett, R. M., and Robinson, B. A. 1992 Numerical investigation of vortex breakdown on a delta wing. AIAA J. 30, 584–591.
Arndt, R. E. A. 1983 Cavitation in fluid machinery and hydraulic structures. Ann. Rev. Fluid Mech. 13, 273–328.
Arndt, R. E. A., Arakeri, V. H., and Higuchi, H. 1991 Some observations of tip vortex cavitation. J. Fluid Mech. 229, 269–289.
Arndt, R. E. A. and Keller, A. P. 1992 Water quality effects on cavitation inception in a trailing vortex. J. Fluids Eng. 114, 430–438.
Baker, G. R., Barker, S. J., Bofah, K. K., and Saffman, P. 1974 Laser anemometer measurement of trailing vortices in water. J. Fluid Mech. 65, 325–336.
Bandyopadhyay, P. R., Stead, D. J. and Ash, R. L. 1990 The organized structure of a turbulent trailing vortex. 21st Fluid Dynamics, Plasma Dynamics, and Lasers Conference, Seattle, WA.
Batchelor, G. K. 1964 Axial flow in trailing line vortices. J. Fluid Mech. 20, 645–658.
Bertin, J. J. and Smith, M. L. 1989 Aerodynamics for Engineers. Prentice-Hall.
Betz, A. 1932 Verhalten von wirbelsystemen. Z. Angew. Math. Mech. 12, 164–174 (also NACA TM-713, 1933).
Betz, A. 1919 On airfoil theory with special consideration of rectangular wings. Ph.D. thesis, Gottingen.
Brazil, J. 1994 FAA ignored warnings of 757 jet turbulence. Los Angeles Times, Sunday June 5, 1.
Brown, G. 1988 personal communication.
Campbell, J. F., Chambers, J. R., and Rumsey, C. L. 1989 Observation of airplane flowfields by natural condensation effects. J. Aircraft 26, 593–604.
Carlin, G., Dadone, L., and Spencer, R. 1989 Results of an experimental investigation of blade tip vortex modification devices. NASA CR-181853.
Chen, C.-L. and McCroskey, W. J. 1988 Numerical simulation of helicopter multi-bladed rotor flow. AIAA paper 88-0046.
Chevalier, H. 1973 Flight test studies of the formation and dissipation of trailing vortices. J. Aircraft 10, 14–18.
Chigier, N. A. 1974 Vortexes in aircraft wakes. Scientific American March, 76–83.
Chigier, N. A. and Corsiglia, V. R. 1972 Wind tunnel studies of wing wake turbulence. J. Aircraft 9, 820–825.
Chow, J. S., Zilliac, G. G., and Bradshaw, P. 1993 Measurements in the near-field of a turbulent wingtip vortex. Proceedings of the AIAA 31st Aerospace Sciences Meeting.
Chow, J. S., Zilliac, G. G., and Bradshaw, P. 1991 Initial rollup of a trailing wing tip vortex. Proceedings of the FAA Wake Vortices Conference, Washington, D.C.
Corsiglia, V. R., Schwind, R. G. and Chigier, N. A. 1973 Rapid scanning three-dimensional hot-wire anemometer surveys of wing-tip vortices. J. Aircraft 10, 752–757.
Critchley, J. B. 1991 Wake vortex -the program in the United Kingdom. Proceedings of the FAA Wake Vortices Conference, Washington, D.C.
Crow, S. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172–2179.
Crow, S. C. and Bate, E. R. Jr. 1976 Lifespan of trailing vortices in a turbulent atmosphere. J. Aircraft 13, 476–482.
Dalton, C. and Wong, X. 1990 The vortex roll-up problem using Lamb vortices for the elliptically loaded wing. Computers and Fluids 18, 139–150.
Drummond, A. M., Onno, R., and Panneton, B. 1991 Trajectories and stability of trailing vortices very near the ground. National Research Council of Canada IAR-AN-71
Dunham, R. E. Jr. 1976 Unsuccessful concepts for aircraft wake vortex minimization. NASA SP-409, 221–250.
Eliason, B. G., Gartshore, I. S., and Parkinson, G. V. 1975 Wind tunnel investigation of Crow instability. J. Aircraft 12, 985–988.
Falcão de Campos, J. A. C. 1992 Laser-doppler velocity measurements on tip vortices in non-cavitating and cavitating conditions. ASME Cavitation and Multiphase Flow Forum.
Freymuth, P. 1989 Visualizing the connectivity of vortex systems for pitching wings. J. Fluids Eng. 111, 217–220.
Gilbert, T. 1991 Aerodynamic effects during minimum-interval takeoffs and aerial refuelling. Proceedings of the FAA Wake Vortices Conference, Washington, D.C.
Glauert, H. 1924 A theory of thin airfoils. Brit. Aero. Res. Comm. RM-910
Glegg S. A. L. 1991 Prediction of blade wake interaction noise based on a turbulent vortex model. AIAA J. 29, 1545–1551.
Green, S. I. 1991 Correlating single phase flow measurements with observations of trailing vortex cavitation. J. Fluids Engineering 113, 125–129.
Green, S. 1990 Axial velocity distribution in rectangular planform wing trailing vortices. CSME Mech. Eng. Forum.
Green, S. I. and Acosta, A. J. 1991 Unsteady flow in trailing vortices. J. Fluid Mechanics 227, 107–134.
Green, S.I, Acosta, A. J., and Akbar, R. 1988 The influence of tip geometry on trailing vortex rollup and cavitation. ASME Cavitation and Multiphase Flow Forum.
Greenewalt, C. H. 1975 The flight of birds. Trans. Amer. Phil. Soc. New Series 65, 67 pages.
Hart, D. 1991 Cavitation inception in the tip vortex region of an oscillating hydrofoil. ASME Cavitation and Multiphase Flow Forum.
Hess, J. L. and Smith, A. M. 0. 1967 Calculation of potential flow about arbitrary bodies. Prog. in the Aero. Sci., 1–138.
Higuchi, H., Arndt, R. E. A., Arakeri, V. H., and Killen, J. M. 1989 The structure of tip vortices over a range of cavitation number. 22nd American Towing Tank Conference.
Holl, J. W., Arndt, R. E. A., and Billet, M. 1972 Limited cavitation and the related scale effects problem. JSME Proc. 2nd Int. Symp. Fluid Mech. and Fluidics, Tokyo, Japan, 303–314.
Kaden, H. 1931 Aufwicklung einer unstabilen unstetigkeitsfläche Ingen. Arch. 2, 140–168.
Katz, J. and Galdo, J. B. 1989 The effect of roughness on rollup of tip vortices on a rectangular hydrofoil. J. Aircraft 26, 247–253.
Krasny, R. 1987 Computation of vortex sheet roll-up in the Trefftz plane. J. Fluid Mech. 184, 123–155.
Liu, H.-T., Hwang, P. A., and Srnsky, R. A. 1992 Physical modelling of ground effects on vortex wakes. J. Aircraft 29, 1027–1034.
Logan, A. H. 1971 Vortex velocity distributions at large downstream distances. J. Aircraft 8, 930–932.
Margason, R. J. and Lamar, J. E. 1968 Vortex lattice Fortran program for estimating subsonic aerodynamic characteristics of complex planforms. NASA TND-4739.
Martin, R. M., Elliott, J. W., and Head, D. R. 1984 Comparison of experimental and analytical predictions of rotor blade vortex interactions using model scale acoustic data. AIAA 84-2269.
McCormick, B. W. 1962 On cavitation produced by a vortex trailing from a lifting surface. ASME J. Basic Eng. 84, 369–379.
Milne-Thomson, L. M. 1958 Theoretical Aerodynamics. Dover.
Moore, D. W. 1974 A numerical study of the roll-up of a finite vortex sheet. J. Fluid Mech. 63, 225–235.
Munk, M. 1919 Isoperimetric problems in the theory of flight. Ph.D. thesis, Gottingen.
O’Connor, L. 1992 Wingtip turbines promise to reduce drag. Mech. Eng. 114, 122.
Page, R. D., Clawson, K. L., Garodz, L. J., and Rudis, R. P. 1991 Report on tower fly-by testing. Proceedings of the FAA Wake Vortices Conference. Washington, D.C.
Parks, P. C. 1971 A new look at the dynamics of vortices with finite cores. Aircraft Wake Turbulence and its Detection, (ed. J. H. Olsen), Plenum Press.
Peyret, R. and Taylor, T. D. 1983 Computational Methods for Fluid Flow. Springer-Verlag.
Platzer, G. P. and Souders, W. G. 1979 Tip vortex cavitation delay with application to marine lifting surfaces -a literature survey. DTNSRDC-79/051.
Poling, D. R., Dadone, L., and Telionis, D. P. 1989 Blade-vortex interaction. AIAA J. 27, 694–699.
Pouagare, M. and Delaney, R. A. 1985 Study of three-dimensional viscous flows in an axial compressor cascade including tip leakage effects using a simple-based algorithm. J. Turbomach. 108, 51–58.
Prandtl, L. 1919 Tragflugeltheorie. Gottingen Nachrichten, II Mitteilung, 107–137.
Prandtl, L. 1922 Applications of Modern Hydrodynamics to Aeronautics. NACA TR 116.
Ran, B. and Katz, J. 1992 Measurements of cavitation inception and associated pressure fluctuations in the near field of a turbulent jet. ASME Cavitation and Multiphase Flow Forum.
Rao, J. S. 1987 Turbomachine blade vibration. Shock and Vibration Digest 19, 3–10.
Rinoue, K. and Stollery, J. L. 1994 Experimental studies of vortex flaps and vortex plates. J. Aircraft 31, 322–329.
Robins, R. E. and Delisi, D. P. 1993 Potential hazard of aircraft wake vortices in ground effect with crosswind. J. Aircraft 30, 201–206.
Rom, J. 1991 High Angle of Attack Aerodynamics: Subsonic, Transonic, and Supersonic. Springer-Verlag.
Rossow, V. 1991 Prospects for alleviation of hazard posed by lift-generated wakes. Proceedings of the FAA Wake Vortices Conference, Washington, D.C.
Saffman, P. G. 1991 Approach of a vortex pair to a rigid free surface in viscous fluid. Phys. Fluids A 3, 984–985.
Sami, S., Carmody, T., and Rouse, H. 1967 Jet diffusion in the region of flow establishment. J. Fluid Mech. 27, 231–251.
Sarpkaya, T. 1992 Interaction of a turbulent vortex with a free surface. Proceedings of the Nineteenth Symposium on Naval Hydrodynamics, Seoul, South Korea.
Sarpkaya, T. 1989 Computational methods with vortices. J. Fluids Eng. 111, 5–52.
Sarpkaya, T. 1983 Trailing vortices in homogeneous and density-stratified media. J. Fluid Mech. 136, 85–109.
Sarpkaya, T. and Daly, J. J. 1987 Effect of ambient turbulence on trailing vortices. J. Aircraft 24, 399–404.
Schreier, J., 1982 Fluctuating forces and rotor noise due to main rotor -tail rotor interaction. Association Aeronautique et Astronautique de France, 8th European Rotorcraft Forum.
Schrenk, O. 1940 Simple approximation method for obtaining spanwise lift distribution. NACA TM-948.
Shekarriz, A., Fu, T. C, Katz, J., Liu, H.L., and Huang, T.T. 1992 Study of junction and tip vortices using particle displacement velocimetry. AIAA J. 30, 145–152.
Shekarriz, À., Fu, T. C, Katz, J., and Huang, T.T. 1993 Near-field behavior of a tip vortex. AIAA J. 31, 112–118.
Simonich, J. C., McCormick, D. C, and Lavrich, P. L. 1993 Role of leading-edge vortex flows in prop-fan interaction noise. J. Aircraft 30, 255–261.
Singh, P. I. and Uberoi, M. S. 1976 Experiments on vortex stability. Physics of Fluids 19, 1181–1188.
Smith, J. H. B. 1986 Vortex Flows in Aerodynamics. Ann. Rev. Fluid Mech. 18, 221–242.
Spreiter, J. R. and Sacks, A. H. 1951 The rolling up of the trailing vortex sheet and its effect on the downwash behind wings. J. Aero. Sci. 18, 21–32.
Srinivasan, G. R., Baeder, J. D., Obayashi, S., and McCroskey, W. J. 1992 Flow-field of a lifting rotor in hover: A Navier-Stokes simulation. AIAA J. 30, 2371–2378.
Srinivasan, G. R., McCroskey, W. J., Baeder, J. D., and Edwards, T. A. 1986 Numerical simulation of tip vortices of wings in subsonic and transonic flows. AIAA 86-1095.
Stahl, W. H., Mahmood, M., and Asghar, A. 1992 Experimental investigations of the vortex flow on delta wings at high incidence. AIAA J. 30, 1027–1033.
Stinebring, D. R., Farrell, K. J., and Billet, M. L. 1991 The structure of a three dimensional vortex at high Reynolds number. J. Fluids Eng. 113, 496–503.
Teske, M. E., Bilanin, A. J., and Barry, J. W. 1993 Decay of aircraft vortices near the ground. AIAA J. 31, 1531–1533.
Thomas, A. S. W. 1985 Aircraft viscous drag reduction technology. Lockheed Horizons 19, 22–32.
Thompson, D. H. 1975 Experimental study of axial flow in wing tip vortices. J. Aircraft 12 990–991.
Tu, E. L. 1994 Vortex-wing interaction of a close-coupled canard configuration. J. Aircraft 31, 314–321.
Wake, B. E. and Sankar, N. L. 1989 Solutions of the Navier-Stokes equations for the flow about a rotor blade. J. American Helicopter Society 34, 13–23.
Webber, G. W. and Dansby, T. 1983 Wing tip devices for energy conservation and other purposes -experimental and analytical work in progress at the Lockheed-Georgia Company. Can. Aero. Space J. 29, 105–120.
Werlé, H. 1974 Le tunnel hydrodynamique au service de la recherche aérospatiale. ONERA-156. (see also van Dyke, M. 1982 An Album of Fluid Motion. Parabolic.)
Editors and Affiliations
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Green, S.I. (1995). Wing Tip Vortices. In: Green, S.I. (eds) Fluid Vortices. Fluid Mechanics and Its Applications, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0249-0_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4111-9
Online ISBN: 978-94-011-0249-0
eBook Packages: Springer Book Archive