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  • Cited by 45
Publisher:
Cambridge University Press
Online publication date:
November 2012
Print publication year:
2012
Online ISBN:
9781139226516

Book description

This book discusses the physical mechanisms that drive counterflows, examining how they emerge, develop, become double and multiple counterflows and comprise both global and local circulations. Counterflows play an important role in nature and technology. A natural example is the Gulf Stream and the opposite flow in the ocean depths. Technological applications include hydrocyclones, vortex tubes and vortex combustors. These elongated counterflows are wildly turbulent but survive intense mixing, a seeming paradox. Local counterflows, whose spatial extent is small compared with that of surrounding flows, occur behind bluff bodies and in swirling streams. The latter are often referred to as vortex breakdown bubbles, which occur in tornadoes and above delta wings. Most scale counterflows are cosmic bipolar jets. Most miniature counterflows occur in capillary menisci of electrosprays and fuel atomisers.

Reviews

'This book is very interesting and well written. Each chapter is clearly developed and the problems are well treated from both the theoretical and the practical points of view. It will be useful to all researchers interested in various problems related to counterflows.'

Mirela Kohr Source: Mathematical Reviews

'The unique feature of the book is the attention to one special area of fluid dynamics, namely, counterflows. This makes the book an excellent reference for anyone who would like to know more about counterflows. It is also a rich source of special topics for inclusion in a graduate-level course in fluid dynamics.'

Majid Molki Source: Heat Transfer Engineering

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Contents

References

Abramov, A. A. 1961 On the transfer of the boundedness condition for some systems of linear ordinary differential equations. Zh. Vychisl. Mat. Mat. Fiz. 1, 733–737.
Abramovitz, M. & Stegun, I. 1964 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Books of Mathematics.
Akatnov, N. I. 1953 Propagation of plane laminar jet near rigid wall. Trans. Leningrad Polytechnical Inst. Mashgiz, 24–34.
Anna, S. L. & Mayer, H. C. 2006 Microscale tip streaming in a micro-fluidic flow focusing device. Phys. Fluids 18, 121512.
Ardalan, K., Draper, K., & Foster, M. R. 1995 Instabilities of the Type I Long’s vortex at large flow force. Phys. Fluids 7, 365–373.
Aref, H. 1983 Integrable, chaotic and turbulent vortex motion in two-dimensional flows. Ann. Rev. Fluid Mech. 15, 345–389.
Arnol’d, V. I. 1992 Catastrophe Theory. Springer-Verlag.
Bachiller, R. 1996 Bipolar molecular outflows from young stars and protostars. Ann. Rev. Asron. Astrophys. 34, 111–154.
Backstein, S. 1994 Experiments on vortex breakdown. Vortex Flows in Aerodynamics. RWTH Aachen University of Technology, Germany.
Bailey, A. G. 1988 Electrostatic Spraying in Liquids. Wiley.
Baker, E. T. & German, C. R. 2004 On the global distribution of hydrothermal vent fields. 245–266 in Mid-Ocean Ridges: Hydrothermal Interactions Between the Lithosphere and Oceans. American Geophysical Union, Washington, DC.
Banks, W. H. H., Drazin, P. G. & Zaturska, M. B. 1988 On perturbations of Jeffery-Hamel flows. J. Fluid Mech. 186, 359–581.
Barcilon, V. & Pedlosky, J. 1967 On the steady motions produced by a stable stratification in a rapidly rotating fluid. J. Fluid Mech. 29, 673–690.
Barrero, A., Gañán-Calvo, A. M., Dávila, J., Palacio, A. & Gómez-GonzálezE. 1998 Low and high Reynolds number flows inside Taylor cones. Phys. Rev. E, 58, 7309–7314.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Batchelor, G. K. & Gill, A. E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14, 529–551.
Bayley, A. G. 1988 Electrostatic spraying of liquids. Wiley.
Bénard, H. 1900 Les turbilllons cellulaires dans une nappe liquid. Revue Gan. Sci. Pur. Appl. 11, 1261–1271 and 1309–1328.
Benjamin, T. B. 1962 Theory of vortex breakdown phenomenon. J. Fluid Mech. 14, 593–629.
Berman, A. A. 1958 Laminar flow in an annulus with porous walls. J. Appl. Phys. 29, 71–76.
Billant, P., Chomaz, J.-M. & Huerre, P. 1998 Experimental study of vortex breakdown in swirling jets. J. Fluid Mech. 376, 183–219.
Birikh, R. V. 1966 Thermocapillary convection in a horizontal layer of liquid. J. Appl. Mech. Tech. Phys. 7, 43–47.
Birikh, R. V. & Pukhnachev, V. V. 2011 An axial convective flow in a rotating tube with a longitudinal temperature gradient. Doklady Physics 56, 47–52.
Bödewadt, U. T. 1940 Die Drehströmung über festem Gründer. Z. Angew. Math. Mech. 20, 241–253.
Boguslavskii, E. M. & Ivanski, V. G. 1987 SU Patent 1542544 A1, 02.12. 1987.
Bojarevics, V., Freibergs, J. A., Shilova, E. I. & Shcherbinin, E. V. 1989 Electrically Induced Vortical Flows. Kluwer.
Borissov, A. A., Kuibin, P. A. & Okulov, V. L. 1993 Flame shapes in swirl flows. Russ. J. Eng. Thermophys. 3, 243.
Borissov, A. & Shtern. V. 2010 Combustion Apparatus and Methods, US Patent application 13/199,704 filed on 09.08.2011.
Borissov, A., Shtern. V., Gonzalez, H. & Yrausquin, A. 2010 Volume distributed high-temperature-air combustion for turbine. Proc. of 8th International Symposium on High Temperature Air Combustion and Gasification, Poznan, Poland, 5–7 July 2010, pp. 297–304.
Borissov, A., Shtern, V. & HussainF. 1998 Modeling flow and heat transfer in vortex burners. AIAA Journal 36, 1665–1670. © AIAA 1998.
Bradlaw, R. 1993 A flow visualization study of some flow patterns found in the vortex breakdown produced in a closed cylindrical container. BSME Honors thesis (University of Houston, Houston).
Braginskii, S. I. 1964 Kinematic models of the Earth’s hydromagnetic dynamo. Geomagn, Aeron. 4, 572–583.
Bratukhin, Yu. K. & Maurin, L. M. 1967 Thermocapillary convection in a fluid filling a half-space. J. Appl. Math. Mech. 31, 605–608.
Brons, M., Voigt, L. K. & Sorensen, J. N. 1999 Streamline topology of steady axisymmetric vortex vreakdown in a cylinder with co- and counter-rotating end-covers. J. Fluid Mech. 401, 275–292.
Brons, M., Voigt, L. K. & Sorensen, J. N. 2001 Topology of voretex breakdown bubbles in a cylinder with rotating bottom and free surface. J. Fluid Mech. 428, 133–148.
Brown, G. L. & Lopez, J. M. 1990 Axisymmetric vortex breakdown, Part 2. Physical Mechanisms. J. Fluid Mech. 221, 553–576.
Brüker, C. & Althaus, W. 1992 Study of vortex breakdown by particle tracking velocimetry (PIV). Exp. Fluids, 13, 339–349.
Burggraf, O. R. & Foster, M. R. 1977 Continuation or breakdown in tornado-like vortices. J. Fluid Mech. 80, 685–704.
Busse, F. H. 1970 Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44, 441–460.
Busse, F. H. 1975 Patterns of convection in spherical shells. J. Fluid Mech. 72, 67–85.
Chandrasekhar, S. 1981 Hydrodynamic and Hydromagnetic Stability. Dover.
Chossat, P. 1979 Bifurcation and stability of convective flows in a rotating or not rotating spherical shell. SIAM J. Appl. Math. 37, 624–647.
Cooke, J. C. 1952 On Pohlgaussen’s method with application in a swirl problema of Taylor. J. Aerospace Sci. 19, 486–490.
Cowling, T. G. 1933 The magnetic field of Sunspots. MNRAS 94, 39–48.
Cowling, T. G. 1957 Magnetodynamics. Interscience.
Davies-Jones, R. P. 1982 Tornado dynamics. In Thunderstorms: A Social, Scientific and Technological Documentary (ed. E. Kessler), vol. 2, 297–361.
Dean, W. R. 1934 Note on the divergent flow of fluid. Phil. Mag. 18, 759–777.
Dean, W. R. & Montagnon, P. E. 1949 On the steady motion of a viscous fluid in a corner. Proc. Camb. Phil. Soc. 45, 389–394.
Deem, G. S. & Zabusky, N.  J. 1978 Vortex waves: stationary ‘V-states’, interactions, reccurence and breaking. Phys. Rev. Lett. 13, 859–862.
Donnelly. R. J. & Fultz, D. 1960 Experiments on the stability of viscous flow between rotating cylinders. II. Visual observations. Proc. R. Soc. London A 258, 101–123.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Earnshaw, P. R. 1961 An experimental investigation the structure of the leading-edge vortex. Aeronaut. Res. Council Rep. 22, 876.
Eckert, E. R. G. & Drake, Jr. R. M. 1972 Analysis of Heat and Mass Transfer. McGraw-Hill.
Escudier, M. P. 1984 Observation of the flow produced in a cylindrical container by a rotating endwall. Exp. Fluids, 2, 189–196.
Escudier, M. P. 1988 Vortex breakdown: observations and explanations. Progr. Aerospace Sci. 25, 189 (1988).
Fenn, J. B., Mann, M., Meng, C. K., Wono, C. F. & Whitehouse, C. 1989 Electrospray ionization for mass spectrometry of large molecules. Science 246, 64–71.
Fernandez de la Mora, J. 1992 The effect of charge emission from electrified liquid cones. J. Fluid Mech. 243, 561–574.
Fernandez de la Mora, J. 2007 The fluid dynamics of Taylor cones. Annu. Rev. Fluid Mech. 39, 217–243.
Fernandez-Feria, R. 1996 Viscous and inviscid instabilities of non-parallel self-similar axisymmetric vortex cores. J. Fluid Mech. 323, 339–365.
Fernandez-Feria, R. 1999 Nonparallel stability analysis of Long vortex. Phys. Fluids 11, 1114–1126.
Fernandez-Feria, R., Fernandez de la Mora, J. & Barrero,A. 1995 Solution breakdown in a family of self-similar nearly inviscid axisymmetric vortices. J. Fluid Mech. 305, 77–91.
Fernandez-Feria, R., Fernandez de la Mora, J., Perez-Saborid, M. & Barrero, A. 1999 Conically similar swirling flows at high Reynolds numbers. Quarterly J. Mech. Appl. Math. 52, 1–53.
Ferrari, A. 1998 Modeling extragalactic jets. Ann. Rev. Asron. Astrophys. 36, 539–598.
Foster, M. R. & Duck, P. W. 1982 The inviscid stability of Long’s vortex. Phys. Fluids 25, 1715–1718.
Foster, M. R. & Jackmin, F. T. 1992 Non-parallel effects in the stability of Long’s vortex. J. Fluid Mech. 244, 289–306.
Foster, M. R. & Smith, P. W. 1989 Stability of Long’s vortex at large flow force. J. Fluid Mech. 206, 405–432.
Fraenkel, L. E. 1962 Laminar flow in symmetrical channels with slightly curved walls. I. On the Jeffery-Hamel solution for the flow between plane walls. Proc. Roy. Soc. London A 267, 119–138.
Fraenkel, L. E. 1963 Laminar flow in symmetrical channels with slightly curved walls. II. An asymptotic series for the stream function. Proc. Roy. Soc. London A 272, 406–428.
Fujii, T. 1963 Theory of steady laminar natural convection above a horizontal line heat source. Int. J. Heat Mass Transfer 6, 597–606.
Fulton, C. D. 1950 Ranque tube. Refr. Eng. 58, 473–479.
Funakoshi, M. & Inoue, S. 1988 Surface waves due to resonant horizontal oscillation. J. Fluid Mech. 192, 219–247.
Gañán-Calvo, A. M. 1998a Generation of steady liquid microthreads and micron-sized monodisperse sprays in gas streams. Phys. Rev. Lett. 80, 285–288.
Gañán-Calvo, A. M. 1998b A perfectly steady fluid micro-thread finds its way through a microscopic hole without touching its walls. The tale of a new nebulizer/emulsifier. J. Aerosol Sci 29, S1071–S1072.
Gaster, M. A. 1962 A note on the relation between temporally-increasing and spatially- increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222–224.
Gelfgat, A. Yu., Bar-Yoseph, P. Z. & Solan, A. 1996 Stability of confined swirling flow with and without vortex breakdown. J. Fluid Mech. 311, 1–36.
Gelfgat, A. Yu., Bar-Yoseph, P. Z. & Solan, A. 2001 Three-dimensional instabilities of axisymmetric flow in a rotating lid-cylinder enclosure. J. Fluid Mech. 438, 363–377.
Georgiou, G. A. & Eagles, P. M. 1985 The stability of flows in channels with small wall curvature. J. Fluid Mech. 159, 259–287.
Gershuni, G. Z. & Zhukhovitsky, E. M. 1976 Convective Stability of Incompressible Fluids. Keter, Jerusalem.
Gershuni, G. Z., Zhukhovitsky, E. M. & Myznikov, V. M. 1975 Stability of plane-parallel convective flow in a horizontal layer relative to spatial perturbations. J. Appl. Mech. Tech. Phys. 15, 706–708.
Glauert, M. B. 1956 The wall jet. J. Fluid Mech. 1, 626–643.
Goldshtik, M. A. 1960 A paradoxical solution of the Navier-Stokes equations. Appl. Math. Mech. (Sov.) 24, 610–621.
Goldshtik, M. A. 1979 On swirling jets. Fluid Dyn., 14, 19–26.
Goldshtik, M. A. 1981 Vortex Flows. Nauka, Novosibirsk.
Goldshtik, M. A. 1990 Viscous flow paradoxes. Ann. Rev. Fluid Mech. 22, 441–472.
Goldshtik, M., Husain, H. S. & Hussain, F. 1992a Loss of homogeneity in a suspension by kinematic action. Nature 357, 141–142.
Goldshtik, M., Husain, H. S. & Hussain, F. 1992b Kinematic separation of mixtures. Phys. Rev. A 45, 8611–8616.
Goldshtik, M. & Hussain, F. 1997 The nature of inviscid vortex breakdown. Phys. Fluids 9, 263–265.
Goldshtik, M., Hussain, F. & Shtern, V. 1991 Symmetry breaking in vortex-source and Jeffery-Hamel flows. J. Fluid Mech. 232, 521–566.
Goldshtik, M. A. & Shtern, V. N. 1977 Hydrodynamic Stability and Turbulence. Nauka, Novosibirsk, USSR (in Russian).
Goldshtik, M. A. & Shtern, V. N. 1988 Conical flows of fluid with variable viscosity. Proc. Roy. Soc. London 419 A, 91–106.
Goldshtik, M. A. & Shtern, V. N. 1989 Loss of symmetry in viscous flow from a linear source. Fluid Dyn. 24, 191–199.
Goldshtik, M. A. & Shtern, V. N. 1990a Collapse in conical viscous flows. J. Fluid Mech. 218, 483–508.
Goldshtik, M. A. & Shtern, V. N. 1990b Free convection near a thermal quadrupole. Int. J. Heat Mass Transfer 33, 1475–1483. © Elsevier 1990.
GoldshtikM. A., ShternV. N. & YavorskyN. I. 1989 Viscous Flows with ParadoxicalFfeatures. Nauka, Novosibirsk, USSR (in Russian).
Goldshtik, M. A., Zhdanova, E. M. & Shtern, V. N. 1985 Occurrence of rotational motion resulting from hydrodynamic instability. Fluid Dynamics 20, 707–714.
Golubitsky, M. & Schaeffer, D. 1982 Bifurcation with O(3) symmetry including applications to the Bénard convection. Com. Pure Appl. Math. 35, 81–111.
Govindarajan, R. & Narasimha, R. 1995 Stability of spatially developing boundary layers in pressure gradients. J.Fluid Mech. 300, 117–147.
Guckenheimer, J. & Holmes, P. J. 1983 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer.
Gupta, A. K., Lilley, D. G. & Sared, N. 1984 Swirl Flows. Abacus, Tunbridge, Wells.
Hall, M. G. 1961 A theory for the core of a leading-edge vortex. J. Fluid Mech. 11, 209–228.
Hall, M. G. 1972 Vortex breakdown. Annu. Rev. Fluid Mech. 4, 125–218.
Hamel, G. 1916 Spiralförmige Bewegungen zäher Flüssigkeiten. Jahresbericht Deutsch. Math. Verein, 25, 34–60.
Happel, J. & Brenner, H. 1986 Low Reynolds Number Hydrodynamics (4th printing). Martinus Nijhoff, Dordrecht.
Hart, J. E. 2000 On the influence of centrifugal buoyancy on rotating convection. J. Fluid Mech. 403, 133–151.
Hayati, I., Bailey, V. & Tadros, Th. F. 1986a Mechanism of stable jet formation in electrohydro-dynamic atomization. Nature 319, 41–43.
Hayati, I., Bailey, V. & Tadros, Th. F. 1986b Investigation into the mechanism of electrohydrodynamic spraying of liquids. J. Colloid Interface Sci. 117, 22–230.
Herrada, M. A. 2000 Estudio teo´rico y experimental de vo´rtices. Ph.D. thesis, University of Seville.
Herrada, M. A. & Barrero, A. 2002 Self-rotation in electrocapillary flows. Phys. Rev. E, 66, 036311.
Herrada, M. A. & Gañán-Calvo, A. M. 2009 Swirl flow focusing: A novel procedure for the massive production of monodisperse microbubbles. Phys. Fluids 21, 042003.
Herrada, M. A.Gañán-Calvo, A. M., Ojeda-Monge, A., Bluth, B. & Riesco-Chueca, P. 2008 Liquid flow focused by a gas: Jetting, dripping, and recirculation. Phys. Rev. E 78, 036323.
Herrada, M. A., Pe´rez-Saborid, M. & Barrero, A. 2000 Effects of compressibility on vortex breakdown. Bull. Am. Phys. Soc. 45, 122.
Herrada, M. & Shtern, V. 2003a Control of vortex breakdown by temperature gradients. Phys. Fluids 15, 3468–3477. © AIP 2003.
Herrada, M. & Shtern, V. 2003b Vortex breakdown control by adding near-axis swirl and temperature gradients. Phys. Rev., E 68, 041202. © APS 2003.
Herrada, M., Shtern, V. & López-HerreraJ. M. 2011 Two-cell circulation in a liquid meniscus driven by a gas jet. Phys. Fluids, 23, 012003.
Herrmann, J. & Busse, F. H. 1997 Convection in a rotating cylindrical annulus. Part 4. Modulation and transition to chaos at low Prandtl numbers. J. Fluid Mech. 350, 209–229.
Hilsch, R. 1947 The use of the expansion of gases in a centrifugal field as cooling process. Review of Scientific Instruments 18(2), 108.
Hirsch, C. 1997 Numerical Computation of Internal and External Flows, 2nd ed. Wiley.
Homsy, G. M. & Hudson, J. L. 1971 Centrifugal convection and its effect on the asymptotic stability of a bounded rotating fluid heated from below. J. Fluid Mech. 48, 605–624.
Hooper, A. P., Duffy, B. R. & Moffat, H. K. 1982 Flow of fluid of nonuniform viscosity in converging and diverging channels. J. Fluid Mech. 117, 283–304.
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developed flows. Ann. Rev. Fluid Mech. 22, 473–537.
Husain, H., Shtern, V. & Hussain, F. 1996 Control of vortex breakdown. Bull. APS 41, 1764, FB.
Husain, H., Shtern, V. & Hussain, F. 1997 Control of vortex breakdown using vortex generators. AIAA 07–1879. © AIAA 1997.
Husain, H., Shtern, V. & Hussain, F. 2003 Control of vortex breakdown by addition of near-axis swirl. Phys. Fluids 15, 271–279. © AIP 2003.
Hussain, F. & Husain, H. S. 1989 Elliptic jets. Part 1. Characterization of inexited and exited jets. J. Fluid Mech. 208, 257–320.
Iooss, G. & Joseph, D. D. 1981 Elementary Stability and Bifurcation Theory. Springer.
Ismadi, M.-Z. P., Meunier, P., Fouras, A. & Hourigan, K. 2011 Experimental control of vortex breakdown by density effects. Phys. Fluids 23, 034104.
Issa, R. I. 1986 Solution of implicitly discretised fluid flow equations by operator splitting. Comput. Phys. 62, 40–65.
Iudovich, V. I. 1971 The onset of auto-oscillations in a fluid. J. Appl. Math. Mech. 34, 587–603.
Jaluria, Y. 1980 Natural Convection: Heat and Mass Transfer. Pergamon Press.
Jeffery, G. B. 1915 The two-dimensional steady motion of a viscous fluid. Phil. Mag. (6) 29, 455–465.
Joseph, D. D. 1976 Stability of Fluid Motions, Springer-Verlag.
Kambe, T. 1969 The stability of an axisymmetric jet with a parabolic profile. J. Phys. Soc. Jap. 26, 566–575.
Kárman, T. von 1921 Laminare und turbulente Reibang. Z. Angew. Math. Mech. 1, 233–252.
Kawakubo, M., Tsuchia, Y., Sugaya, M. & Matsumura, K. 1978 Formation of a vortex around a sink: A kind of phase transition in a nonequilibrium open system. Phys. Let. A 68, 65–66.
Keller, J. J. 1995 On the interpretation of vortex breakdown. Phys. Fluids 7, 1695–1702.
Keller, J. J., Egli, W. & Althaus, R. 1988 Vortex breakdown as a fundamental element of vortex dynamics. Z. Angew. Math. Phys. 39, 404–440.
Keller, J. J., Egli, W. & Exley, W. 1985 Force- and loss-free transitions between flow states. Z. Angew. Math. Phys. 36, 856–889.
Keller, J. J., Sattelmayer, Th. F. & Thüringer, F. 1991 Double-cone burner for gas turbine type 9 retrofit application. Procedings of the 19th International Congress On Combustion Engines, Florence, Italy, CIMAC.
Khorami, M. R. & Trivedi, P. 1994 The viscous stability analysis of Long’s vortex. Phys. Fluids 6, 2623–2630.
Königl, A. 1986 Stellar and galactic jets: Theoretical issues. Can. J. Phys. 64, 362–368.
Kyrdyashkin, A. G. 1984 Thermogravitational and thermocapillary flows in a horizontal liquid layer under the conditions of a horizontal temperature gradient. Int. J. Heat Mass Transfer 27, 1205–1218.
Lamb, H. 1993 Hydrodynamics. Cambridge University Press.
Lambourne, N. C. & Brayer, D. W. 1961 The bursting of leading edge vortices – Some observations and discussion of the phenomenon. Aeronautical Research Council Reports and Memoranda 3282.
Landau, L. D. 1944a On the exact solution of the Navier-Stokes equations. Dokl. Akad Nauk SSSR 43, 299–301.
Landau, L. D. 1944b On the turbulence problem. Dokl. Akad Nauk SSSR 44, 339–342.
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon Press.
Lasheras, J. C. & Hopfinger, E. J. 2000 Liquid jet instability and atomization in a coaxial gas stream. Annu. Rev. Fluid Mech. 32, 275–342.
Leibovich, S.1984 Vortex stability and breakdown: Survey and extention. AIAA Journal 22, 1192–1206.
Lele, S. K. 1992 Compact finite-difference schemes with spectral-like resolution. Comput. Phys. 103, 16–42.
Lessen, M. & Singh, P. J. 1973 The stability of axisymmetric free shear layers. J. Fluid Mech. 60, 433–457.
LeVeque, R. 1990 Numerical Methods for Conservation Laws (Lectures in Mathematics, ETH-Zurich). Birkhauser-Verlag.
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice Hall.
Lew, H. G. 1956 Asymptotic suction characteristics of the boundary layer over a circular cylinder. J. Aeronaut. Sci. 23, 895–897.
Libby, P. A. & Fox, H. 1963 Some perturbation solutions in laminar boundary-layer theory. J. Fluid Mech. 268, 71–88.
Lo Jacono, D., Sørensen, J. N., Thompson, M. C. & Hourigan, K. 2008 Control of vortex breakdown in a closed cylinder with a small rotating rod. J. Fluids Struct. 24, 1278–1283.
Loitsyansky, L. G. 1966 Mechanics of fluid and gas. Pergamon.
Long, R. R. 1961 A vortex in an infinite viscous fluid. J. Fluid Mech. 11, 611–623.
Lonnes, S., Hofeldt, D. & Strykovsky, P. 1998 Flame speed control using a countercurrent swirl combustor. AIAA-98–0352, 1–10.
Lopez, J. M. 1990 Axisymmetric vortex breakdown. Part 1. Confined swirling flows. J. Fluid Mech. 221, 533–552.
Lopez, J. M. 1995 Unsteady swirling flow in an enclosed cylinder with reflectional symmetry. Phys. Fluids 7, 2700–2714.
Lowson, M. V. 1964 Some experiments with vortex breakdown. J. of Roy. Aeronautical Soc. 68, 347.
Lugt, H. J. & Abboud, M. 1987 Axisymmetric vortex breakdown in a container with a rotating lid. J. Fluid Mech. 179, 179–190.
Lyubimova, T. P., Lyubimov, D. V., Morozov, V. A., Scuridin, R. V., Ben Hadid, H. & Henry, D. 2009 Stability of convection in a horizontal channel subjected to a longitudinal temperature gradient. Part 1. Effect of aspect ratio and Prandtl number. J. Fluid Mech. 635, 275–295.
Mahesh, K. 1996 A model for the onset of breakdown in an axisymmetric compressible vortex. Phys. Fluids 8, 3338–3345.
Martynenko, O. G., Berezovsky, A. A. & Sokovishin, Yu. 1979 Asymptotic Methods in the Theory of Free-convective Heat Transfer. Nauka I Teknika, Minsk (in Russian).
McAlpine, A. & Drazin, P. G. 1998 On the spatio-temporal development of small perturbations of Jeffery-Hamel flows. Fluid Dyn Res. 22, 123–138.
Meissel, E. 1873 Über den Ausfluss der Wasser aus Gefässen in zwei besonderen Fällen nach Eintritt des Beharrungszustandes. Archiv der Mathematik und Physik, Bd. 55.
Melville, R. 1996 The role of compressibility in free vortex breakdown. AIAA Paper No. 96–2075.
Menke, M. & Gursul, I. 1997 Unsteady nature of leading edge vórtices. Phys. Fluids 9, 2960–2966.
Millsaps, K. & Pohlhausen, K. 1953 Thermal distribution in Jeffery-Hamel flows between nonparallel plane walls. J. Aeronaut. Sci. 20, 187–196.
Modest, M. F. 1993 Radiative Heat Transfer. McGraw-Hill.
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1–18.
Moffatt, H. K. 1983 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge Universiy Press.
Moffatt, H. K. & Duffy, B. R. 1980 Local similarity solutions and their limitations. J. Fluid Mech. 96, 299–313.
Mollendorf, J. C. & Gebhart, B. 1973 Thermal buoyancy in round laminar vertical jets. Int. J. Heat Mass Transfer 16, 735–745.
Morris, P. J. 1976 The spatial viscous instability of axisymmetric jets. J. Fluid Mech. 77, 511–529.
Müller, K. N. 1958 Zur Theorie des Wirbelstrahles. Z. angew. Math. Mech. 38, 170–187.
Mullin, T., Kobine, J. J., Tavener, S. J. & Cliffe, K. A. 2000 On the creation of stagnation points near a straight and sloped walls. Phys Fluids 12, 425–432.
Mununga, L., Hourigan, K. & Thompson, M. C. 2004 Confined flow vortex breakdown control using a small rotating disk. Phys. Fluids 16, 4750–4753.
Muylaert, I. M. 1980 Effect of compressibility on vortex bursting on slender delta wings. VKJ Project Report1980–21.
Nathan, G. J., Hill, S. J. & Luxton, R. E. 1998 An axisymmetric ‘fluidic’ nozzle to generate jet precession. J. Fluid Mech. 370, 347–380.
Ogawa, A. 1993 Vortex flows. CRC Press.
Oseen, C. W. 1927 Exakter Lösungen der hydrodinamischen Differential-gleichungen. Arkiv fur Matematik, Astr. Fysik. I (14), 1–24, II (22), 1–9.
Ostroumov, G. A. 1952 Free convection under the conditions of the internal problem. GITL Moscow (in Russian); 1958 NACA Tech. Mem. 1407 (in English).
Panton, L. 1996 Incompressible Flow. Wiley.
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.
Paull, R. & Pillow, A. F. 1985 Conically similar viscous flows. Part 3. Characterization of axial causes of swirling flows and one-parameter flow generated by a uniform half-line source of kinematic swirl angular momentum. J. Fluid Mech. 155, 359–380.
Peckham, D. H. & Atkinson, S. A. 1957 Preliminary results of low speed and tunnel tests on a goethic wing of aspect ratio 1.0. Aero. Res. Counc. Tech. Rep. CP-508, TN NO. Aero 254.
Pereira, J. C. F. & Sousa, J. M. M. 1999 Confined vortex breakdown generated by a rotating cone. J. Fluid Mech. 385, 287–323.
Petrunin, A. A. & Shtern, V. N. 1993 Bifurcation in MHD flow generated by electric current discharge. Progress in Astronautics and Aeronautics 149, 116–130. © AIAA 1993.
Pillow, A. F. & Paull, R. 1985 Conically similar viscous flows. Part 1. Basic conservation principles and characterization of axial causes in swirling flows. J. Fluid Mech. 155, 327–342.
Pshenichnikov, A. F. & Yatsenko, S. S. 1974 Convective diffusion from compact source of surface-active matter. Hydrodynamics (Scientific papers of Perm University) 5, 175–181.
Pudritz, R. I. 2000 Jets from accretion discs. Phil.Trans. R. Soc. London A358: 743–759.
Ranque, G. 1933 Expériences sur la Détente Giratoire avec Productions Simultanées d’un Echappement d’air Chaud et d’un Echappement d’air Froid. J. de Physique et Radium 4(7), 112S.
Rayleigh, Lord. 1916 On convection currents in a horizontal layer of fluid, when the highest temperature is on the under side. Phil. Mag. (8) 32, 529–546.
Reynolds, A. J. 1962 Observations of a liquid-into-liquid jet. J. Fluid Mech. 14, 552–556.
Roesner, K. G. 1990 Recirculation zones in a cylinder with rotating lid. In Topological Fluid Mech., edited by H. K. Moffatt & A. Tsinober. University of Cambridge, p. 699.
Rosenhead, L. 1940 The steady two-dimensional radial flow of viscous fluid between two inclined plane walls. Proc. Roy. Soc.London A 175, 436–467.
Rumer, Yu. B. 1953 Convective diffusion in a submerged jet. J. Appl. Math. & Mech. 17, 743–744.
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.
Sagalakov, A. M. & Yudintsev, A. Yu. 1992 Self-oscillation in magnetohydrodynamic flows through a tube of circular cross section in a longitudinal magnetic field. Magnetohydrodynamics 28, 1, 5–10.
Sarpkaya, T. 1971 Vortex breakdown in conical swirling flows. AIAA J. 9, 1792–1799.
Sarpkaya, T. 1995 Turbulent vortex breakdown. Phys. Fluids 7, 2301–2303.
Sarpkaya, T. & Novak, F. 1998 Turbulent vortex breakdown: Experiments in tubes at high Reynolds numbers. In Dynamics of Slender Vortices, Kluwer, Dordrecht, pp. 287–296.
Schlichting, H. 1933 Laminare Strahlausbreitung. Z. angew. Math. Mech. 13, 260–263.
Schlichting, H. 1979 Boundary-Layer Theory. McGraw-Hill.
Schmucker, A. & Gersten, K. 1988 Vortex breakdown and its control on delta wings. Fluid Dyn. Res. 3, 268–271.
Schneider, W. 1981 Flow induced by jets and plumes. J. Fluid Mech. 108, 55–65.
Schneider, W. 1985 Decay of momentum flux in submerged jets. J. Fluid Mech. 154, 91–110.
Schneider, W., Zaunder, R. & Bohm, H. 1987 The recirculatory flow induced by a laminar axisymmetric jet issuing from a wall. Trans. ASME I: J. Fluids Engng 109, 237–241.
Schultz, S., Gorbach, G. and Piesche, M. 2009 Modeling fluid behavior and droplet interactions during liquid–liquid separation in hydrocyclones. Chemical Engineering Science 64, 3935.
Secchiaroli, A., Ricci, R., Montelpare, S. & D’Alessandro, V. 2009 Numerical simulation of turbulent flow in a Ranque-Hilsch vortex-tube. Int. J. of Heat and Mass Transfer 52, 5496.
Serre, E. & P.Bontoux, P. 2002 Vortex breakdown in a three-dimensional swirling flow. J. Fluid Mech. 459, 347–370.
Serrin, J. 1972 The swirling vortex. Phil. Trans. R. Soc. Lond. A 271, 325–360.
Shtern, V. 1995 Cosmic jets as a pump for the magnetic field. Phys. Lett. A 206, 96–100. © APS 1995.
Shtern, V. 2004 Instability versus collapse in a flow driven by the radial electric current. Phys. Fluids 16, L17–L19. © AIP 2004.
Shtern, V. & Barrero, A. 1994 Striking features of fluid flows in Taylor cones related to electrosprays. J. Aerosol Sci. 25, 1049–1063. © Elsevier 1994.
Shtern, V. & Barrero, A. 1995 Bifurcation of swirl in liquid cones. J. Fluid Mech. 300, 169–205.
Shtern, V. & Borissov, A. 2010a Counter-flow driven by swirl decay. Phys. Fluids 22, 063601.
Shtern, V. & Borissov, A. 2010b Nature of counterflow and circulation in vortex separators, Phys. Fluids 22, 083601. © AIP 2010.
Shtern, V., Borissov, A. & Hussain, F. 1997 Vortex sinks with axial flow: Solution and applications. Phys. Fluids 9, 2941–2959. © AIP 1997.
Shtern, V., Borissov, A. & Hussain, F. 1998 Temperature distribution in swirling jets. Int. J. Heat Mass Transfer 41, 2455–2467. © Elsevier 1998.
Shtern, V. & Drazin, P. G. 2000 Instability of a free swirling jet driven by a half-line vortex. Proc. R. Soc. Lond. A 456, 1139–1161.
Shtern, V., Torregrosa, M. & Herrada, M. 2011a Development of a swirling double counterflow. Phys. Rev. E 83, 056322. © APS 2011.
Shtern, V., Torregrosa, M. & Herrada, M. 2011b Development of colliding swirling counterflows. Phys. Rev. E 84, 046306. © APS 2011.
Shtern, V., Torregrosa, M. & Herrada, M. 2012 Effect of swirl decay on vortex breakdowm development in a confined steady axisymmetric flow. Phys. Fluids 24, 043601. © AIP 2012.
Shtern, V. & Hussain, F. 1993a Azimuthal instability of diverging flows. J. Fluid Mech. 256, 535–560.
Shtern, V. & Hussain, F. 1993b Hysteresis in a swirling jet as a model tornado. Phys. Fluids A 5, 2183–2195. © AIP 2001.
Shtern, V. & Hussain, F. 1996 Hysteresis in swirling jets. J. Fluid Mech. 309, 1–44.
Shtern, V. & Hussain, F. 1998 Instabilities of conical flows causing steady bifurcations. J. Fluid Mech. 366, 33–85.
Shtern, V. & Hussain, F. 1999 Collapse, symmetry breaking, and hysteresis in swirling flows. Annu. Rev. Fluid Mech. 31, 537–566.
Shtern, V. & Hussain, F. 2001a Generation of collimated jets by a point source of heat and gravity. J. Fluid Mech. 449, 39–59.
Shtern, V. & Hussain, F. 2001b Onset of convection near a point source of heat and gravity. Phys. Rev. Lett. 87, 264301. © APS 2001.
Shtern, V. & Hussain, F. 2003 Effect of deceleration on jet instability. J. Fluid Mech. 480, 283–309.
Shtern, V., Hussain, F. & Herrada, M. 2000 New features of swirling jets. Phys. Fluids 12, 2868–2877. © AIP 2000.
Shtern, V. & Mi, J. 2004 Hysteresis and precession of a swirling jet normal to a wall. Phys. Rev. E 69, 016312. © APS 2004.
Shtern, V., Zimin, V. & Hussain, F. 2001 Analysis of centrifugal convection in rotating pipes. Phys. Fluids 13, 2296–2308. © AIP 2001.
Slezkin, N. A. 1934 On a case of integrability of the full differential equations of viscous fluid motion. Sci. Pap. Moscow Univ. 2, 89–90.
Smulsky, I. I. 1992 Aerodynamics and Processes in Vortex Chambers. Nauka, Novosibirsk.
Snow, J. T. 1982 A review of recent advances in tornado vortex dynamics. Rev. Geophys. Space Phys. 20, 953–964.
Sobey, I. J. & Drazin, P. G. 1986 Bifurcations of two-dimensional channel flows. J. Fluid Mech. 171, 263–287.
Sotiropulos, F. & Venticos, Y. 2001 The three-dimensional structure of confined swirling flows with vortex breakdown. J. Fluid Mech. 426, 155–175.
Sotiropulos, F.Venticos, Y. & Lackey, T. C. 2001 Chaotic advection in three-dimensional stationary vortex-breakdown bubbles: Sil’nikov’s chaos and the devil’s staircase. J. Fluid Mech. 444, 257–297.
Sozou, C. 1971 On fluid motion induced by an electric current source. J. Fluid Mech. 46, 25–32.
Sozou, C. 1992 On solution relating to conical vortices over a plane wall. J. Fluid Mech. 244, 633–644.
Sozou, C., Wilkinson, L. C. & Shtern, V. 1994 On swirling flows in infinite fluid. J. Fluid Mech. 276, 261–271.
Spohn, A., Mory, N. & Hopfinger, E. J. 1993 Observations of vortex breakdown in an open cylindrical container with a rotating bottom. Exp. Fluids 14, 70–77.
Spohn, A., Mory, M. & Hopfinger, E. J. 1998 Experiments on vortex breakdown in a confined flow generated by a rotating disc. J. Fluid Mech. 370, 73–99.
Spotar’, S. Yu.Chohar’, I. A., Lukashov, V. V. & Prozorov, D. S. 1995 Method and device for local ventilation. Russian Patent N 2046258.
Spotar’, S. Yu. & Terekhov, V. I. 1987 Two spontaneously alternating regimes in a vortex flow above a plane. J. Appl. Mech. Tech. Phys. 2, 68–70.
Squire, H. B. 1952 Some viscous fluid flow problem. 1. Jet emerging from a hole in a plane jet. Phil. Mag. 43, 942–945.
Squire, H. B. 1956 Rotating fluids. In Surveys in Mechanics, edited by G. K. Batchelor & R. M. Davies, Cambridge University Press, pp. 139–161.
Squire, H. B. 1965 The growth of vortex in turbulent flow. Aero. Quart. 16, 302–306.
Stuart, J. T. 1966 A simple corner flow with a suction. Q. J. Mech. Appl.Math. 19, 217.
Suryo, R. & Basaran, O. A. 2006 Tip streaming from a liquid drop forming from a tube in a co-flowing outer fluid. Phys. Fluids 18, 082102.
Tam, K. K. 1996 Linear stability of the non-parallel Bickley jet. Can. Appl. Math. Quart. 3, 99–110.
Tan, B. T., Liow, K. Y. S., Mununga, L., Thompson, M. C. & Hourigan, K. 2009 Simulation of the control of vortex breakdown in a closed cylinder usinga small rotating disk. Phys. Fluids 21, 024104.
Taylor, G. I. 1950 The boundary layer in the converging nozzle of a swirl atomizer. Q. J. Mech. Appl. Maths 3, 129–139.
Taylor, G. I. 1964 Desintegration of water drops in an electric field. Proc. R. Soc. Lond. A 280, 383–397.
Torrance, K. E. 1979 Natural convection in thermally stratified enclosures with localized heating from below. J. Fluid Mech. 95, 477–495.
Tsuji, H., Gupta, A., Hasegava, T., Katsuki, M., Kishimoto, K. & Morita, M. 2003 High Temperature Air Combustion, CRS Press.
Uriba, F. J., Diaz, E., Bravo, A., Peralta Fabi, R. & Soto, R. 1989 Bifurcation diagram for Jeffery-Hamel flow. Winter Meeting on Statistical Physics. World Scientific.
Valentine, D. T. & Jahnke, C. C. 1994 Flow induced in a cylinder with both endwalls rotating. Phys. Fluids 6, 2702–2710.
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic Press.
Van Leer, J. B. 1979 Towards the ultimate conservative difference scheme V; A second-order sequel to Godunov’s sequel. Comput. Phys. 32, 101–136.
Viilu, A. 1962 An experimental determination of the minimum Reynolds number for instability in a free jet. J. Appl. Mech. 29, 506–508.
Vogel, H. U. 1968 Experimentelle Ergebnisse über die laminare Strömung in einem Zylindrischen Gehäuse mit darin rotierender Scheibe,’’ Max-Planck-Institut für Strömungsforschung, Göttigen, Bericht. 6.
Wang, C. V. 1971 Effect of spreading of material of the surface of a liquid. Int. J. Nonlinear Mech. 6, 255–262.
Wang, C. V. 1991 Exact solutions of the steady-state Navier-Stokes equations. Ann. Rev. Fluid Mech. 23, 159–177.
Wang, S. & Russak, Z. 1997 The dynamics of a swirling flow in a pipe and transition to axisymmetric vortex breakdown. J. Fluid Mech. 340, 177–223.
Widnall, S. E. & Sullivan, J. P. 1972 On the stability of vortex rings. Proc. R. Soc. London A 332, 323–353.
Williams, F. A. 1984 Combustion Theory, 2nd ed. Addison-Wesley.
Wuest, W. 1955 Asymptotische absaugegrenzschichten an langsangestromten zylindrischen Korpern. Ing. Arch. 23, 198–208.
Yasuhara, M. 1957 On the asymptotic solution of the laminar compressible boundary layer over a circular cylinder with uniform suction. J. Phys. Soc. Jpn. 12, 102–112.
Yatseev, V. N. 1950 On a class of exact solutions of the viscous fluid motion equations. Sov. Phys. J. Exp. Theor. Phys. 20, 1031–1034.
Yih, C. -H. 1951 Fee convection due to a point source of heat. Proc. 1st U.S. Nat. Congr. Appl. Math., 941–947.
Yih, C. -H., Wu, F., Garg, A. K. & Leibovich, S. 1982 Conical vortices: A class of exact solutions of the Navier-Stokes equations. Phys. Fluids 25, 2147–2157.
Young, D. L., Sheen, H. J. & Hwu, T. Y. 1995 Period-doubling route to chaos for a swirling flow in an open cylindrical container with a rotating disk. Exp. Fluids 18, 389–392.
Yu, P., Lee, T. S., Zeng, Y. & Low, H. T. 2006 Effects of conical lids on vortex breakdown in an enclosed cylindrical chamber. Phys. Fluids 18, 117101.
Zauner, E. 1985 Visualization of the viscous flow induced by a round jet. J. Fluid Mech. 154, 111–120.
Zeleny, J. 1914 The electrical discharge from liquid points, and a hydrostatic method of measuring the electric intensity at their surfaces. Physical Review 3 (2), 69–91.
Zeleny, J. 1917 Instability of electrified liquid surfaces. Physical Review 10 (1), 1–6.

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