Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-17T13:55:37.943Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  22 January 2018

Vladimir Shtern
Affiliation:
SABIC Houston, Texas
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Cellular Flows
Topological Metamorphoses in Fluid Mechanics
, pp. 559 - 570
Publisher: Cambridge University Press
Print publication year: 2018

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Acheson, D. G. 1990 Elementary Fluid Dynamics. Oxford, Oxford University Press.CrossRefGoogle Scholar
Ackerberg, R. C. 1965 The viscous incompressible flow inside a cone. J. Fluid Mech. 21, 4781.Google Scholar
Adam, P., Frank, L., Daniel, B. & Yusi, S. 2010 New Developments in Surface Oil Flow Visualization. 27th AIAA Aerodynamic Measurement Technology and Ground Testing Conference: American Institute of Aeronautics and Astronautics, 2010.Google Scholar
Althaus, W., Brucker, C. & Weimer, M. 1995 Breakdown of slender vortices. In Fluid Vortices, ed. Green, S. I., 373426. Dordrecht, Kluver Academic.Google Scholar
Arnold, V. I. 1966 Sur la gćometrie diffćrentielle des gropes de Lie de dimension infinite et ses applications a l’hydrodynamique des fluids parfairts. Ann. Inst Fourier 16, 316361.Google Scholar
Arnold, V. I. 1992 Catastrophe Theory. New York, Springer-Verlag.Google Scholar
Arnold, V. I. & Khesin, B. A. 1998 Topological methods in hydrodynamics. Applied Math. Sci. 125, 175181.Google Scholar
Ashcraft, R. W., Heynderickx, G. J. & Marin, G. B. 2012 Modeling fast biomass pyrolysis in a gas-solid vortex reactor. Chem Eng J. 207, 195208.Google Scholar
Balci, A., Brøns, M., Herrada, M. A. & Shtern, V. N. 2015 Vortex breakdown in a truncated conical bioreactor. Fluid Dyn. Res. 47(6), 065503.CrossRefGoogle Scholar
Balci, A., Brøns, M., Herrada, M. A. & Shtern, V. N. 2016a Patterns of a slow air-water flow in a semispherical container. Eur. J. Mech. B/Fluids 58, 18.Google Scholar
Balci, A., Brøns, M., Herrada, M. A. & Shtern, V. N. 2016b Bifurcations of a creeping air-water flow in a conical container. Teor. Comput.Fluid Dyn. 30, doi: 10.1007/s00162-016-0391-zGoogle Scholar
Barcilon, V. & Pedlosky, J. 1967 On the steady motions produced by a stable stratification in a rapidly rotating fluid. J. Fluid Mech. 29, 673690.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge, Cambridge University Press.Google Scholar
Bejan, A., Al-Homoud, A. A. & Imberger, J., , J. 1981 Experimental study of high-Rayleigh-number convection in a horizontal cavity with different end temperature. J. Fluid Mech. 109, 283299.CrossRefGoogle Scholar
Benjamin, T. B. 1962 Theory of vortex breakdown phenomenon. J. Fluid Mech. 14, 593629.Google Scholar
Bergmann, R., Tophøj, L., Homan, T. A. M., Hersen, P., Andersen, A. & Bohr, T. 2011 Polygon formation and surface flow on a rotating fluid surface. J. Fluid Mech. 679, 415431.CrossRefGoogle Scholar
Beverloo, W. A., Leniger, H. A. & Weldering, J. A. G. 1963 Potentialities of the flat vortex hydrosifter. British Chemical Engineering Journal 8, 678682.Google Scholar
Birikh, R. V. 1966 Thermocapillary convection in a horizontal layer of liquid. J. Appl. Mech. Tech. Phys. 7, 4347.Google Scholar
Birikh, R. V. 1967 On small perturbations of a plane-parallel with a cubic velocity profile. J. Appl. Math. Mech. 30, 432438.Google Scholar
Birikh, R. V. & Pukhnachev, V. V. 2011 An axial convective flow in a rotating tube with a longitudinal temperature gradient. Doklady Physics 56, 4752.CrossRefGoogle Scholar
Blackburn, H. M. & Lopez, J. M. 2002 Modulated rotating waves in an enclosed swirling flow. J. Fluid Mech. 465, 3358.CrossRefGoogle Scholar
Blake, J. 1979 On the generation of viscous toroidal eddies in a cylinder. J. Fluid Mech. 95, 209222.Google Scholar
Bödewadt, U. T. 1940 Die Drehströmung über festem Grund. Z. Angew. Math. Mech. 20, 241253.Google Scholar
Borissov, A. A. & Shtern, V. N. 2010a Turbulent counterflow induced by swirl decay. Int. J. of Energy for Clean Environment 11, 203225.Google Scholar
Borissov, A. A. & Shtern, V. N. 2010b Transparent combustion of kerosene in a vortex combustor with meridional counterflow. Report for ONR Advanced Propulsion Program Review, June 2225, Crystal City, VA.Google Scholar
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, July 5–7, 2010, pp. 297–304.Google Scholar
Bouffanais, R. & Lo Jacono, D. 2009 Unsteady transitional swirling flow in the presence of a moving free surface. Phys. Fluids 21, 064107.CrossRefGoogle Scholar
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, TX).Google Scholar
Brady, P. T., Herman, M. & Lopez, J. M. 2012a Two-fluid confined flow in a cylinder driven by a rotating end wall. Phys. Rev. E 85, 016306.Google Scholar
Brady, P. T., Herman, M. & Lopez, J. M. 2012b Addendum to “Two-fluid confined flow in a cylinder driven by a rotating end wall.” Phys. Rev. E 85, 067301.CrossRefGoogle Scholar
Branicki, M. & Moffatt, H. K. 2006 Evolving eddy structures in oscillatory Stokes flows in domains with sharp corners. J. of Fluid Mech. 551, 6392.Google Scholar
Brøns, M. 1994 Topological fluid dynamics of interfacial flows. Phys. Fluids 6, 27302737.Google Scholar
Brøns, M. 2007 Streamline topology: Patterns in fluid flows and their bifurcations. Advances in Applied Mechanics 41, 142.Google Scholar
Brøns, M., Voigt, L. K. & Sorensen, J. N. 1999 Streamline topology of steady axisymmetric vortex breakdown in a cylinder with co- and counter-rotating end-covers. J. Fluid Mech. 401, 275292.Google Scholar
Brøns, 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, 133148.Google Scholar
Brown, G. L. & Lopez, J. M. 1990 Axisymmetric vortex breakdown, Part 2. Physical mechanism. J. Fluid Mech. 221, 553576.CrossRefGoogle Scholar
Burggraf, O. R. & Foster, M. R. 1977 Continuation or breakdown in tornado-like vortices. J. Fluid Mech. 80, 685704.Google Scholar
Busse, F. H. 1970 Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44, 441460.CrossRefGoogle Scholar
Carrión, L., Herrada, M. A. & Shtern, V. N. 2016 Instability of a water-spout flow. Phys. Fluids 28, 034107.Google Scholar
Carrión, L., Herrada, M. A. & Shtern, V. N. 2017a Topology and stability of a water-soybean-oil swirling flow. Phys. Rev. Fluids 2, 024702.Google Scholar
Carrión, L., Herrada, M. A. & Shtern, V. N. 2017b Topology changes in a water-oil swirling flow. Phys. Fluids 29, 032109.Google Scholar
Carrión, L., Herrada, M. A., Shtern, V. N. & López-Herrera, J. M. 2017 Patterns and stability of a whirlpool flow. Fluid Dyn. Res. 49, 025519.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. New York: Dover.Google Scholar
Cormac, D. E., Leal, L. G. & Imberger, J. 1974 Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory. J. Fluid Mech. 65, 209229.CrossRefGoogle Scholar
Dahlstrom, D. A. 1949 Cyclone operating factors and capacities on coal and refuse slurries. Transactions of the American Institute of Mining, Metallurgical and Petroleum Engine 184, 331344.Google Scholar
Daniels, P. G., Blythe, P. A. & Simpkins, P. G. 1987 Onset of multicellular convection in a shallow laterally heated cavity. Proc. R. Soc. London A 411, 327350.Google Scholar
Dean, W. R. & Montagnon, P. E. 1949 On the steady motion of a viscous liquid in a corner. Math. Proc. of Cambridge Phil. Soc. 45, 389394.CrossRefGoogle Scholar
Devenport, W. J., Rife, M. C., Liapis, S. I. & Follin, G. J. 1996 The structure and development of a wing-tip vortex. J. Fluid Mech. 312, 67106.Google Scholar
De Wilde, J. 2014 Gas–solid fluidized beds in vortex chambers. Chemical Engineering and Processing: Process Intensification 11, 256290.Google Scholar
Doi, T. & Koster, J. N. 1993 Thermocapillary convection in two immiscible liquid layers with free surface Phys. Fluids A 5, 19141927.Google Scholar
Donaldson, C. du P. 1961 The magnetohydrodynamic vortex power generator, basic principles and practical problems. Proceedings of the Second Symposium on the Engineering Aspects of Magnetohydrodynamics March 9–10, 1961, Philadelphia.Google Scholar
Donaldson, C. du P. & Williamson, G. G. 1964 An Experimental Study of Turbulence in a Driven Vortex. Aeron. Res. Assoc. of Princeton, Rept. No. ARAP TM-64-2.Google Scholar
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, 101123.Google Scholar
Drazin, P. & Read, W. 1981 Hydrodynamic stability. Cambridge, Cambridge University Press.Google Scholar
Ekatpure, R. P., Suryawanshi, V. U., Heynderickx, G. J., de Broqueville, A. & Marin, G. B. 2011 Experimental investigation of a gas-solid rotating bed reactor with static geometry. Chem. Eng. Process 50, 7784.Google Scholar
Eral, H. B., ’t Mannetje, D. J. C. M. & Oh, J. M. 2013 Contact angle hysteresis: A review fundamentals and applications. Colloid & Polymer Sci. 291, 247260.Google Scholar
Escudier, M. P. 1984 Observation of the flow produced in a cylindrical container by a rotating endwall. Exp. Fluids 2, 189196.Google Scholar
Escudier, M. P. 1988 Confined vortices in flow machinery vortex breakdown: Observations and explanations. Progr. Aerospace Sci. 25, 189229.Google Scholar
Escudier, M. P., O’Leary, J. & Poole, R. J. 2007 Flow produced in a conical container by a rotating endwall. Int. J. Heat Fluid Flow 28, 14181428.CrossRefGoogle Scholar
Fujimoto, S. & Takeda, Ya. 2009 Topology changes of the interface between two immicible liquid layers by a rotating lid. Phys. Rev. E 80, 015304(R).Google Scholar
Gelfgat, A. Yu., Bar-Yoseph, P. Z. & Solan, A. 1996 Stability of confined swirling flow with and without vortex breakdown. J. Fluid Mech. 311, 136.CrossRefGoogle Scholar
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, 363377.Google Scholar
Gershuni, G. Z. & Zhukhovitsky, E. M. 1976 Convective Stability of Incompressible Fluids. Jerusalem, Keter.Google Scholar
Gershuni, G. Z., Zhukhovitsky, E. M. & Myznikov, V. M. 1974 Stability of plane-parallel convective flow of a liquid in a horizontal layer. J. Appl. Mech. Tech. Phys. 15, 7882.Google Scholar
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, 706708.Google Scholar
Getling, A. V. 1998 Rayleigh-Bénard Convection: Structures and Dynamics. World Scientific ISBN 9810226578.Google Scholar
Ghodraty, M., Kuang, S. B., Yui, A. B., Vince, A., Barnett, G. D. & Barnet, P. J. 2012 CFD study of multiphase flow in classifying cyclone: Effect of cone geometry. Ninth Int. Conf. on CFD in the Mineral and Process Industries CSIRO, Melbourne, Australia.Google Scholar
Gill, A. E. 1966 The boundary layer regime for convection in a rectangular cavity. J. Fluid Mech. 26, 515536.Google Scholar
Goldshtik, M., Husain, H. S. & Hussain, F. 1992a Loss of homogeneity in a suspension by kinematic action. Nature 357, 141142.CrossRefGoogle Scholar
Goldshtik, M., Husain, H. S. & Hussain, F. 1992b Kinematic separation of mixtures. Phys. Rev. A 45, 86118616.Google Scholar
Gupta, A. K., Lilley, D. G. & Sared, N. 1984 Swirl Flows. Tunbridge, Wells, Abacus.Google Scholar
Gürcan, F., Gaskell, P. H., Savage, M. D. & Wilson, M. C. T. 2003 Eddy genesis and transformations of Stokes Flow in a double-lid driven cavity. Proc. Instn Mech. Engrs Part C: J. Mech. Eng. Sci. 217, 353364.Google Scholar
Hall, M. G. 1972 Vortex breakdown. Annu. Rev. Fluid Mech. 4, 125218.Google Scholar
Hall, O., Hills, C. P. & Gilbert, A. D. 2007 Slow flow between concentric cones. Quarterly J. of Mechanics & App. Maths 60, 2748.Google Scholar
Hall, O., Hills, C. P. & Gilbert, A. D. 2009 Non-axisymmetric Stokes flow between concentric cones. Q. J. Mech. App. Maths. 62, 137148.Google Scholar
Happel, J. R. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Boston, Springer.Google Scholar
Hart, J. E. 2000 On the influence of centrifugal buoyancy on rotating convection. J. Fluid Mech. 403, 133151.Google Scholar
Herrada, M. A. & Montanero, J. M. 2016 A numerical method to study the dynamics of capillary fluid systems. J. of Comput. Phys. 306, 137147.CrossRefGoogle Scholar
Herrada, M. A., Pérez-Saborid, M. & Barrero, A. 2000 Effects of compressibility on vortex breakdown. Bull. Am. Phys. Soc. 45, 122.Google Scholar
Herrada, M. A., Pérez-Saborid, M. & Barrero, A. 2004 Nonparallel local spatial stability analysis of pipe entrance swirling flows. Phys. Fluids 16, 21472153.Google Scholar
Herrada, M. & Shtern, V. 2003a Control of vortex breakdown by temperature gradients. Phys. Fluids 15, 34683477.CrossRefGoogle Scholar
Herrada, M. & Shtern, V. 2003b Vortex breakdown control by adding near-axis swirl and temperature gradients. Phys. Rev. E 68, 041202.CrossRefGoogle ScholarPubMed
Herrada, M. A. & Shtern, V. N. 2014a Patterns of a creeping water-spout flow. J. Fluid Mech. 744, 6588.CrossRefGoogle Scholar
Herrada, M. A. & Shtern, V. N. 2014b Air-water centrifugal convection. Phys. Fluids 26, 072102.CrossRefGoogle Scholar
Herrada, M. A. & Shtern, V. N. 2015 Stability of centrifugal convection in a rotating pipe. Phys. Fluids 27, 064106.Google Scholar
Herrada, M. A. & Shtern, V. N. 2016a Velocity reversal via bifurcation in thermal convection. Int. J. Heat Mass Transfer 92, 6675.Google Scholar
Herrada, M. A. & Shtern, V. N. 2016b Stability of thermal convection in a rotating cylindrical container. Phys. Fluids 28, 083601.Google Scholar
Herrada, M. A. & Shtern, V. N. 2016c Convection in air-water layer with side heating. Manuscript.Google Scholar
Herrada, M. A., Shtern, V. N., & López-Herrera, J. M. 2013a Off-axis vortex breakdown in a shallow whirlpool. Phys. Rev. E 87, 063016.Google Scholar
Herrada, M. A., Shtern, V. N., & López-Herrera, J. M. 2013b Vortex breakdown in a water-spout flow. Phys. Fluids 25, 093604.Google Scholar
Herrada, M. A., Shtern, V. N., & Torregrosa, M. M. 2015 The instability nature of the Vogel-Escudier flow. J. Fluid Mech. 766, 590610.Google Scholar
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, 209229.Google Scholar
Hills, C. P. 2001 Eddies induced in cylindrical containers by a rotating end wall. Phys. Fluids 13, 22792286.Google Scholar
Hilsch, R. 1947 The use of the expansion of gases in a centrifugal field as cooling process. Review of Scientific Instruments 18, 108113.CrossRefGoogle Scholar
Hirsch, C. 1997 Numerical Computation of Internal and External Flows, 2nd ed. New York, Wiley.Google Scholar
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, 605624.Google Scholar
Hornbeck, R. W. 1968 Viscous flow in a short cylindrical vortex chamber with a finite swirl ratio. Lewis Research Center, NASA1968. TN D-5132.Google Scholar
Husain, H., Shtern, V. & Hussain, F. 1996 Control of vortex breakdown. Bull. APS 41, 1764, FB.Google Scholar
Husain, H., Shtern, V. & Hussain, F. 1997 Control of vortex breakdown using vortex generators. AIAA 07-1879.Google Scholar
Husain, H., Shtern, V. & Hussain, F. 2003 Control of vortex breakdown by addition of near-axis swirl. Phys. Fluids 15, 271279.Google Scholar
Ismadi, M.-Z. P., Meunier, R., Fouras, A. & Hourigan, K. 2011 Experimental control of vortex breakdown by density effects. Phys. Fluids 23, 034104.Google Scholar
Issa, R. I. 1986 Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62, 4065.Google Scholar
Iwatsu, R. 2005 Vortex breakdown flows in cylindrical geometry, Notes Num. Fluid Mech. & Multidiscipl. Design 90, 141151.CrossRefGoogle Scholar
Jakirlic, S., Hanjalic, K. & Tropea, C. 2002 Modeling rotating and swirling turbulent flows: A perpetual challenge. AIAA Journal 40(10), 19841996.Google Scholar
Kármán, T. 1921 Über laminare und turbulent reibung. Z. angew. Math. und Mech. 1, 233252.Google Scholar
Keller, J. J., Egli, W. & Althaus, R. 1988 Vortex breakdown as a fundamental element of vortex dynamics. Z. Angew. Math. Phys. 39, 404440.Google Scholar
Keller, J. J., Egli, W. & Exley, W. 1985 Force- and loss-free transitions between flow states. Z. Angew. Math. Phys. 36, 856889.Google Scholar
Kelstall, D. F. 1952 A study of the motion of solid particles in a hydrolyc cyclone. Trans. Inst. Chem. Engrs. 30, 87108.Google Scholar
Kendall, J. M. Jr. 1962 Experimental study of a compressible viscous vortex. Cal. Inst. of Tech. Report JPL-TR, 32290.Google Scholar
Kerrebrock, J. L. & Meghreblian, R. V. 1961 Vortex containment for the gaseous-fission rocket. Journal of the Aerospace Sciences 28, 710724.Google Scholar
Khorrami, M. R. 1991 Chebyshev spectral collocation method using a staggered grid for the stability of cylindrical flows. Int. J. Numer. Methods Fluids 12, 825833.Google Scholar
Kirdyashkin, 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, 12051218.CrossRefGoogle Scholar
Kovacevic, J. Z., Pantzali, M. N., Heynderickx, G. J. & Marin, G. B. 2014 Bed stability and maximum solids capacity in a gas–solid vortex reactor: Experimental study. Chem.Eng.Sci. 106, 293303.Google Scholar
Kovacevic, J. Z., Pantzali, M. N., Niyogi, K., Deen, N. G., Heynderickx, G. J. & Marin, G. B. 2015 Solids velocity fields in a cold-flow gas–solid vortex reactor. Chem.Eng.Sci. 123, 220230.Google Scholar
Kulikov, D. V., Mikkelsen, R., Naumov, I. V. & Okulov, V. L. 2014 Diagnostics of bubble-mode vortex breakdown in swirling flow in a large-aspect-ratio cylinder. Tech. Phys. Lett. 40(2), 181184.Google Scholar
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.Google Scholar
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537566.Google Scholar
Launder, B. E. & Spalding, D. B. 1974 The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering 3, 269289.Google Scholar
Leibovich, S. 1978 The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10, 221246.CrossRefGoogle Scholar
Leibovich, S. 1984 Vortex stability and breakdown: Survey and extention. AIAA Journal 22, 11921206.CrossRefGoogle Scholar
Lele, S. K. 1992 Compact finite-difference schemes with spectral-like resolution. Comput. Phys. 103, 1642.Google Scholar
LeVeque, R. 1990 Numerical Methods for Conservation Laws (Lectures in Mathematics, ETH-Zurich). Birkhauser-Verlag.CrossRefGoogle Scholar
Lewellen, W. S. 1971 A review of confined vortex flows. NASA contractor report CR-1772.Google Scholar
Liow, K. Y. S., Tan, B. T., Thouas, G. & Thompson, M. C. 2009 CFD modeling of the steady-state momentum and oxygen transport in a bioreactor that is driven by a rotating disk. Modern Physics Letters B 23(2), 121127.CrossRefGoogle Scholar
Liow, K. Y. S., Thouas, G., Tan, B. T., Thompson, M. C. & Hourigan, K. 2008 Modeling the transport of momentum and oxygen in an aerial disk-driven bioreactor used for animal tissue or cell culture. IFMBE Proceedings 23, 16721675.Google Scholar
Liu, C. H. & Joseph, D. D. 1978 Stokes flow in conical trenches. SIAM J. Appl. Math. 34, 286296.Google Scholar
Liu, Q. S., Chen, G, & Roux, B. 1993 Thermo-gravitational and thermocapillary convection in a cavity containing two superposed immiscible liquid layers. Int J Heat Mass Transfer 36, 101117.CrossRefGoogle Scholar
Liu, Q. S., Roux, B. & Velarde, M. G. 1998 Thermocapillary convection in two-layer systems. Int J Heat Mass Transfer 41, 14991511.CrossRefGoogle Scholar
Lo Jacono, D., Nazarinia, M. & Brøns, M. 2009 Experimental vortex breakdown topology in a cylinder with a free surface. Phys. Fluids 21, 111704.CrossRefGoogle Scholar
Lo Jacono, D., Sørensen, J. N., Tompson, M. C. & Hourigan, K. 2008 Control of vortex breakdown in a closed cylinder with a small rotating rod. J. Fluids Struct. 24, 12781283.Google Scholar
Long, R. R. 1961 A vortex in an infinite viscous fluid. J. Fluid Mech. 11, 611624.CrossRefGoogle Scholar
Lonnes, S., Hofeldt, D. & Strykovsky, P. 1998 Flame speed control using a countercurrent swirl combustor. AIAA-98–0352, 1–10.Google Scholar
Lopez, J. M. 1990 Axisymmetric vortex breakdown. Part 1. Confined swirling flows. J. Fluid Mech. 221, 533552.Google Scholar
Lopez, J. M. 1995 Unsteady swirling flow in an enclosed cylinder with reflectional symmetry. Phys. Fluid 7, 27002714.Google Scholar
Lopez, J. M. 2012 Three-dimensional swirling flow in a tall cylinder driven by a rotating endwall. Phys. Fluids 24, 014101.Google Scholar
Lucca-Negro, O. & O’Donelly, T. 2001 Vortex breakdown: A review. Progress in Energy and Combustion Science 27, 431481.Google Scholar
Lugt, H. J. & Abboud, M. 1987 Axisymmetric vortex breakdown in a container with a rotating lid. J. Fluid Mech. 179, 179190.Google Scholar
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, 275295.Google Scholar
Madruga, S, Pérez-García, C. & Lebon, G. 2003 Convective instabilities in two superposed horizontal liquid layers heated laterally. Phys. Rev. E 68, 041607.CrossRefGoogle ScholarPubMed
Mahesh, K. 1996 A model for the onset of breakdown in an axisymmetric compressible vortex. Phys. Fluids 8, 33383345.Google Scholar
Maltby, R. L. & Keating, R. F. A. 1962 The surface oil flow technique for use in low speed wind tunnels. In: Flow Visualization in Wind Tunnels Using Indicators, edited by R. L. Maltby. AGARDograph. Elsevier 70, 87109.Google Scholar
Malyuga, V. S. 2005 Viscous eddies in a circular cone. J. Fluid Mech. 522, 101116.Google Scholar
Marques, F. & Lopez, J. M. 2001 Precessing vortex breakdown mode in an enclosed cylinder flow. Phys. Fluids 13, 16791682.CrossRefGoogle Scholar
Mei, R. 1996 Velocity fidelity of flow tracer particles. Experiments in Fluids 22, 113.Google Scholar
Melville, R. 1996 The role of compressibility in free vortex breakdown. AIAA Paper No. 96–2075.Google Scholar
Merzkirch, W. 1987 Flow Visualization (Second Edition). San Diego, Academic Press, 115231.Google Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 118.Google Scholar
Moffatt, H. K., Bajer, K. & Kimura, Y. 2013 IUTAM Symposium on Topological Fluid Dynamics: Theory and Applications. Procedia IUTAM 7, 1260. Elsevier.Google Scholar
Moffatt, H. K. & Tsinober, A. (editors) 1989 Topological Fluid Mechanics. Proc. of IUTAM Symp. Cambridge, UK.Google Scholar
Mougel, J., Fabre, D. & Lacaze, L. 2015 Waves in Newton’s bucket. J. Fluid Mech. 783, 211250.CrossRefGoogle Scholar
Muite, B. K. 2004 The flow in a cylindrical container with a rotating end wall at small but finite Reynolds number. Phys. Fluids 16, 36143626.CrossRefGoogle Scholar
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, 425432.CrossRefGoogle Scholar
Mununga, L., Lo Jacono, D., Sørensen, J. N., Leweke, T., Thompson, M. C. & Hourigan, K. 2014 Control of confined vortex breakdown with partial rotating lids. J. Fluid Mech. 738, 533.Google Scholar
Murphy, H. D., Coxon, M. & McEligot, D. M. 1978 Symmetric sink flow between parallel plates. J. Fluids Eng. 100, 477484.Google Scholar
Muylaert, I. M. 1980 Effect of compressibility on vortex bursting on slender delta wings. VKJ Project Report 1980-21.Google Scholar
Nepomnyashchy, A., Simanovskii, I. & Legros, J. C. 2012 Interfacial Convection in Multilayer Systems, 2nd ed. Springer, Appl. Math. Sci. 179.Google Scholar
Niyogi, K. 2017 Single and two-phase hydrodynamics in confined vortex technology. PhD thesis. Universiteit Gent. ISNB 978-90-8578-993.2, NUR 962Google Scholar
Niyogi, K., Torregrosa, M., Pantzali, M. N., Shtern, V. N., Heynderickx, G. J. & Marin, G. B. 2017a On near-wall jets in a disc-like gas vortex unit. AIJChE 63, 17401756.Google Scholar
Niyogi, K., Torregrosa, M., Shtern, V. N., Heynderickx, G. J. & Marin, G.B. 2017b. Counterflows and multiple eddies in a gas vortex unit. Manuscript.Google Scholar
Olendraru, C., Sellier, A., Rossi, M. & Huerre, P. 1996 Absolute/convective instability of the Batchelor vortex. C. R. Acad. Sci. Paris 11b, 153159.Google Scholar
Ostroumov, G. A. 1952 Free convection under the conditions of the internal problem. GITL Moscow (in Russian); 1958 NACA Tech. Mem. 1407 (in English).Google Scholar
Pantzali, M. N., Kovacevic, J. Z., Heynderickx, G. J., Marin, G. B. & Shtern, V. N. 2015 Radial pressure profiles in a cold-flow gas-solid vortex reactor. AIChE Journal 61, 41144125.CrossRefGoogle Scholar
Pantzali, M. N., Lozano Bayón, N., Heynderickx, G. J. & Marin, G. B. 2013 Three-component solids velocity measurements in the middle section of a riser. Chem Eng Sci. 9, 412423.Google Scholar
Paolucci, S. 1994 The differently heated cavity. Sadhana 19, 619647.Google Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere Series on Computational Methods in Mechanics and Thermal Science. 1st Edition.Google Scholar
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.Google Scholar
Pereira, J. C. F. & Sausa, J. M. M. 1999 Confined vortex breakdown generated by a rotating cone. J. Fluid Mech. 385, 287323.Google Scholar
Priestman, G. H. 1987 A study of vortex throttles. J. Mech. Eng. Sci. 201, 337343.CrossRefGoogle Scholar
Ramazanov, Yu. A., Kislykh, V. I., Kosyuk, I. P., Bakuleva, N. V. & Shchurikhina, V. V. 2007 Industrial production of vaccines using embryonic cells in gas-vortex gradient-less bioreactors. In New Aspects of Biotechnology and Medicine, ed.Egorov, A. M., New York, Nova Biomedical Books, ISBN: 1-60021-465-7, pp. 8791.Google Scholar
Rayleigh, Lord 1920 Steady motion in a corner of a viscous fluid. Scientific papers 6, 1821.Google Scholar
Roesner, K. G. 1990 Recirculation zones in a cylinder with rotating lid. In Topological Fluid Mech., eds. Moffatt, H. K. & Tsinober, A., 699. Cambridge, University of Cambridge.Google Scholar
Rosales Trujillo, W. & De Wilde, J. 2012 Fluid catalytic cracking in a rotating fluidized bed in a static geometry: A CFD analysis accounting for the distribution of the catalyst coke content. Powder Technology 221, 3646.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge, Cambridge University Press.Google Scholar
Sarpkaya, T. 1971 Vortex breakdown in swirling conical flows. AIAA J. 9, 17921799.CrossRefGoogle Scholar
Sarpkaya, T. 1995 Turbulent vortex breakdown. Phys. Fluids 7, 23012103.CrossRefGoogle Scholar
Savino, J. M. & Keshock, E. G. 1965 Experimental profiles of velocity components and radial pressure distributions in a vortex contained in a short cylindrical chamber. NASA TN D-3072, Oct. 1965.Google Scholar
Schlichting, H. 1933 Laminare Strahlausbreitung. Z. angew. Math. Mech. 13, 260263.CrossRefGoogle Scholar
Schlichting, H. 1960 Boundary Layer Theory. New York, McGraw-Hill.Google Scholar
Schneider, W. 1985 Decay of momentum flux in submerged jets. J. Fluid Mech. 154, 91110.CrossRefGoogle Scholar
Schneider, W., Zauner, E. & Bohm, H. 1987 The recirculatory flow induced by a laminar axisymmetric jet issuing from a wall. Trans. ASME I: J. Fluids Engng. 109, 237241.Google Scholar
Schultz, V., Gorbach, G. & Piesche, M. 2009 Modeling fluid behavior and droplet interactions during liquid–liquid separation in hydrocyclones. Chem. Eng. Sci. 64, 39353952.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Serre, E. & Bontoux, P. 2002 Vortex breakdown in a three-dimensional swirling flow. J. Fluid Mech. 459, 347370.Google Scholar
Shankar, P. N. 1997 Three-dimensional eddy structure in a cylindrical container. J. Fluid Mech. 342, 97118.CrossRefGoogle Scholar
Shankar, P. N. 1998 Three-dimensional Stokes flow in a cylindrical container. Phys. Fluids 10, 540549.CrossRefGoogle Scholar
Shankar, P. N. 2005 Moffatt eddies in the cone. J. Fluid Mech. 539, 113135.Google Scholar
Shankar, P. N. 2007 Slow Viscous Flows. London, Imperial College Press.Google Scholar
Shankar, P. N. & Deshpande, M. D. 2000 Fluid mechanics in the driven cavity. Annu. Rev. Fluid Mech. 32, 93136.Google Scholar
Shankar, P. N., Kidambi, R. & Hariharan, J. 2003 Oscillatory eddy structure in a container. J. Fluid Mech. 494, 163185.CrossRefGoogle Scholar
Shtern, V. 2012a Counterflows. Cambridge, Cambridge University Press.Google Scholar
Shtern, V. 2012b A flow in the depth of infinite annular cylindrical cavity. J. Fluid Mech. 711, 667680.CrossRefGoogle Scholar
Shtern, V. 2013 Asymptotic flow in the depth of narrow cavity. Phys. Fluids 25, 083604.Google Scholar
Shtern, V. 2014 Moffatt eddies at an interface. Theor. Comput. Fluid Dyn. 28, 651656.Google Scholar
Shtern, V. & Borissov, A. 2010a Counterflow driven by swirl decay. Phys. Fluids 22, 063601.Google Scholar
Shtern, V. & Borissov, A. 2010b Nature of counterflow and circulation in vortex separators. Phys. Fluids 22, 083601.Google Scholar
Shtern, V., Borissov, A. & Hussain, F. 1997 Vortex-sinks with axial flow. Phys. Fluids 9, 29412959.Google Scholar
Shtern, V. & Hussain, F. 1993 Hysteresis in a swirling jet as a model tornado. Phys. Fluids A5, 21832195.Google Scholar
Shtern, V. & Hussain, F. 1996 Hysteresis in swirling jets. J. Fluid Mech. 309, 144.Google Scholar
Shtern, V. & Hussain, F. 1999 Collapse, symmetry breaking, and hysteresis in swirling flows. Annu. Rev. Fluid Mech. 31, 537566.Google Scholar
Shtern, V., Hussain, F. & Herrada, M. 2000 New features of swirling jets. Phys. Fluids 12, 28682877.CrossRefGoogle Scholar
Shtern, V. N., Torregrosa, M. M. & Herrada, M. A. 2011a Development of a swirling double counterflow. Phys. Rev. E 83, 056322.CrossRefGoogle ScholarPubMed
Shtern, V. N., Torregrosa, M. M. & Herrada, M. A. 2011b Development of colliding counterflows. Phys. Rev. E 84, 046306.Google Scholar
Shtern, V. N., Torregrosa, M. M. & Herrada, M. A. 2012 Effect of swirl decay on vortex breakdown in a confined steady axisymmetric flow. Phys. Fluids 24, 043601.Google Scholar
Shtern, V., Zimin, V. & Hussain, F. 2001 Analysis of centrifugal convection in rotating pipes. Phys. Fluids 13, 22962308.Google Scholar
Simpkins, P. G. & Dudderar, T. D. 1981 Convection in rectangular cavity with differentially heated end walls. J. Fluid Mech. 110, 433456.Google Scholar
Singh, A. 1993 Theoritical and experimental investigations and decelerating flows within two flat discs, IIT Bombay.Google Scholar
Singh, A., Vyas, B. D. & Powle, U. S. 1999 Investigations on inward flow between two stationary parallel disks. Int. J. Heat Fluid Fl. 20, 395401.Google Scholar
Sorensen, J. N., Gelfgat, A. Y., Naumov, I. V. & Mikkelsen, R. 2009 Experimental and numerical results on the three-dimensional instabilities in a rotating disk-tall cylinder flow. Phys. Fluids 21, 054102.CrossRefGoogle Scholar
Sorensen, J. N., Naumov, I. V. & Mikkelsen, R. 2006 Experimental investigation in three-dimensional flow instabilities in a rotating lid-driven cavity. Exp. Fluids 41, 425440.CrossRefGoogle Scholar
Sorensen, J. N., Naumov, I. V. & Okulov, V. L. 2011 Multiple helical modes of vortex breakdown. J. Fluid Mech. 683, 430441.Google Scholar
Sorokin, V. V. 2006 Calculation of compressible flow in a short vortex chamber. J. Eng. Phys. and Thermophysics 79, 9991005.Google Scholar
Sotiropulos, F. & Venticos, Y. 2001 The three-dimensional structure of confined swirling flows with vortex breakdown. J. Fluid Mech. 426, 155175.Google Scholar
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, 257297.CrossRefGoogle Scholar
Sparrow, E. M., Azevedo, L. F. A. & Prata, A. T. 1986 Two-fluid and single fluid natural convection heat transfer in an inclosure. J. Heat Transfer 108, 848852.Google Scholar
Spohn, A., Mory, N. & Hopfinger, E. J. 1993 Observations of vortex breakdown in an open cylindrical container with a rotating bottom. Exp. Fluids 14, 7077.Google Scholar
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, 7399.Google Scholar
Squire, H. B. 1956 Rotating fluids. In Surveys in Mechanics, eds. Batchelor, & Davies, , 139161. Cambridge, Cambridge University Press.Google Scholar
Stevens, J. L., Lopez, J. M., & Cantwell, B. J. 1999 Oscillatory flow states in an enclosed cylinder with a rotating endwall. J. Fluid Mech. 389, 101118.Google Scholar
Tan, B. T., Liow, K. Y. S., Mununga, L. T., Thompson, M. C. & Hourigan, K. 2009 Simulation of the control of vortex breakdown in a closed cylinder using a small rotating disk. Phys. Fluids 21, 024104.CrossRefGoogle Scholar
Thompson, J. F., Thames, F. C. & Mastin, C. M. 1982 Boundary-fitted coordinate systems for numerical solution of partial differential equations – A review. J. Comput. Phys. 47, 1108.CrossRefGoogle Scholar
Topøj, L., Mougel, J., Bohr, T. & Fabre, D. 2013 Rotating polygon instability of a swirling free surface flow. Phys. Rev. Lett. 110, 194502.Google Scholar
Trigub, V. N. 1985 The problem of breakdown of a vortex line. J. Appl. Math. Mech. 95, 166171.Google Scholar
Tsai, J.-C., Tao, C.-Y., Sun, Y.-C., Lai, C.-Y., Huang, K.-H., Juan, W.-T. & Huang, J.-R. 2015 Vortex-induced morphology on a two-fluid interface and transitions. Phys. Rev. E 92, 031002(R).Google Scholar
Tsuji, H., Gupta, A., Hasegava, T., Katsuki, M., Kishimoto, K. & Morita, M. 2003 High Temperature Air Combustion. Boca Raton, London, New York, Washington D.C., CRS Press.Google Scholar
Valentine, D. T. & Jahnke, C. C. 1994 Flow induced in a cylinder with both endwalls rotating. Phys. Fluids 6, 27022710.CrossRefGoogle Scholar
Van Leer, B. 1979 Towards the ultimate conservative difference scheme. V. A. second-order sequel to Godunov’s method. J. Comput. Phys. 32, 101136.CrossRefGoogle Scholar
Vatistas, G. H., Fayed, M. & Soroardy, J. U. 2008 Strongly swirling turbulent sink flow between two stationary disks. Journal of Propulsion and Power 24, 296301.Google Scholar
Villers, D. & Platten, J. K. 1988 Thermal convection in superposed immiscible liquid layers. Appl. Sci. Res. 45, 145151.Google Scholar
Villers, D. & Platten, J. K. 1990 Influence of the interfacial tension gradient on thermal convection in superposed immiscible liquid layers. Appl. Sci. Res. 47, 177191.Google Scholar
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.Google Scholar
Wakiya, S. 1976 Axisymmetric flow of a viscous fluid near the vertex of a body. J. Fluid Mech. 78, 737747.CrossRefGoogle Scholar
Wang, S. & Russak, Z. 1997 The dynamics of a swirling flow in a pipe and transition to axisymmetric vortex breakdown. J. Fluid Mech. 340, 177223.Google Scholar
Weidman, P. D. & Calmidi, V. 1999 Instantaneous Stokes flow in a conical apex aligned with gravity and bounded by a stress-free surface. SIAM J. Appl. Math. 59, 15201531.Google Scholar
Werle, H. 1963 La Hoille Blanche 28, 330 (photo reproduced from Panton, R. I. 1996 Incompressible Flow. p. 569. New York: Wiley & Sons).Google Scholar
Williamson, G. G. & McCune, J. E. 1961 A preliminary study of the structure of turbulent vortices. Aeronautical Research Association of Princeton Inc. 1961–32.Google Scholar
Wilson, M. C. T., Gaskell, P. H. & Savage, M. D. 2005 Nested separatrices in simple shear flows: The effect of localized disturbances on stagnation lines. Phys. of Fluids 17, 093601.CrossRefGoogle Scholar
Wormley, D. N. 1969 An analytical model for the incompressible flow in short vortex chambers. Journal of Basic Engineering 91, 264272.Google Scholar
Yoo, J. Y. & Joseph, D. D. 1978 Stokes flow in a trench between concentric cylinders. SIAM J. Appl. Math. 34, 247285.CrossRefGoogle Scholar
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, 389392.Google Scholar
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.Google Scholar
Yuan, J. & Piomelli, U. 2015 Numerical simulation of a spatially developing accelerating boundary layer over roughness. J. Fluid Mech. 780, 192214.Google Scholar
Zauner, E. 1985 Visualization of the viscous flow induced by a round jet. J. Fluid Mech. 154, 111120.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Vladimir Shtern
  • Book: Cellular Flows
  • Online publication: 22 January 2018
  • Chapter DOI: https://doi.org/10.1017/9781108290579.011
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Vladimir Shtern
  • Book: Cellular Flows
  • Online publication: 22 January 2018
  • Chapter DOI: https://doi.org/10.1017/9781108290579.011
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Vladimir Shtern
  • Book: Cellular Flows
  • Online publication: 22 January 2018
  • Chapter DOI: https://doi.org/10.1017/9781108290579.011
Available formats
×