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Edward A. Spiegel Department of Astronomy, Columbia University 1328 Pupin Physics Lab, MC 5246 550 West 120th Street New York, NY 10027 phone: 1-212-854-6810 fax: 1-212-854-8121

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Astrofluiddynamics and Astromathematics
Vortices in a Keplerian flow References		A model of a cosmic fractal References
A strange attractor from a model of oscillatory convection References		Nonlinear solitary waves from oscillatory convection at large aspect ratio References
Saddle-loop bifurcation in a third order nonlinear system of ODEs References		Localized oscillations arising in the complex Ginzburg-Landau equation with quintic terms References
Disk Instability References		A bubbling bed of glass beads References Movies
Patterns in bioconvection References		A reconstructed attractor for the solar cycle References
A cave painting of the Solar tachocline References		Large scale convection References
Movies of Fluid Phenomena
A beaker full of small glass beads is made to behave like a fluid when air is blown into a tube at their base		A train of bubbles rising in water forms a vortex in a rotating reference frame
Current Research Subjects

• Theory of chaos
• Solar physics
• Photofluiddynamics
• Convection
• Pattern formation
• Nonlinear stability theory

Selected Publications

• ADS Search for E. Spiegel

• Keplerian disks

  1. "Stellar and jovian vortices", (with T.E. Dowling), in fifth Florida Workshop on Nonlinear Astrophysics, S. Gottesman and J.R. Buchler, eds. Ann. N. Y. Acad. Sci., 617, 190-216 (1990) link
  2. "Spotted Disks", (with A. Bracco, A. Provenzale and P.A. Yecko) in Theory of Black Hole Accretion Disks, M. Abramowicz, G. Bjornsen & J. Pringle, eds., Cambridge Univ. Press (1998) link link
  3. "Particle Aggregation in Keplerian Flows," (with A. Bracco, P.-H. Chavanis and A. Provenzale), Phys. Fluids 11 , 2280 (1999)
  
  

• Cosmic fractal

  1. "Lacunarity and Intermittency in Fluid Turbulence," (with L.A. Smith and J.-D. Fournier), Phys. Lett. A, 114, 465 (1986) link
  2. "The Dimensions of Cosmic Fractals," (with R. Thieberger and L.A. Smith) in The Ubiquity of Chaos, S. Krasner, ed., (AAAS Pubs.) Chap. 16 (1990)
  3. "Cosmic lacunarity," (with A. Provenzale and R. Thieberger) Chaos, 7, 82-88 (1997) link
  4. "Density singularities and cosmic structures," (with G. Murante, A. Provenzale and R. Thieberger), Mon. Not. Roy. astr. Soc., 291, 585-592 (1997) link
  5. "Scaling Regimes in the Distribution of Galaxies," (with G. Murante, A. Provenzale and R. Thieberger) in Nonlinear Dynamics and Chaos in Astrophysics, J.R. Buchler, S.T. Gottesman & H.E. Kandrup, eds., Ann. N. Y. Acad. Sci., 867, 258-267 (1998) link
  
  

• A strange attractor

  1. "A Thermally Excited Nonlinear Oscillator," (with D. W. Moore), Ap. J., 143, 871 (1966)
  2. "Aperiodic Behavior of a Non-Linear Oscillator," (with N. H. Baker and D. W. Moore), Quar. Jour. Mech. and Applied Math., 24, 391 (1971)
  3. "Ordinary Differential Equations with Strange Attractors," (with C. J. Marzec), SIAM J. Applied Math., 38, 387 (1980)
  4. "Chaos in a Finite Macroscopic System," (with A. Arneodo and P.H. Coullet), Phys. Lett. A, 92, 368 (1982)
  
  

• Solitary waves

  1. "Intermittency Through Modulational Instability," (with C.S. Bretherton), Phys. Lett. A, 96, 152 (1983)
  2. "Chaotic Pulse Trains," (with N.J. Balmforth and G.R. Ierley), SIAM J. Applied Math. 54 1291-1234 (1994)
  
  

• Saddle-loop

  1. "Asymptotic Chaos," (with A. Arneodo, P.H. Coullet and C. Tresser), Physica D 14, 327 (1985)
  2. "The Dynamics of Triple Convection," (with A. Arneodo and P.H. Coullet), Geophys. and Astrophys. Fluid Dynamics 31, 1 (1985)
  
  

• Quintic terms

  1. "The Effect of Radiative Transfer on Convective Growth Rates," Ap. J., 139, 959 (1964)
  2. "Asymptotic Chaos," (with A. Arneodo, P.H. Coullet and C. Tresser), Physica D, 14, 327 (1985)
  
  

• Disk Instability

  1. "The Gravitational Instability of a Gaseous Slab," (with Z. Qian and M.R.E. Proctor), Stability Applied Analysis of Continuous Media 1, 33, (1990)
  2. "Global Equilibria of Turbulent Accretion Disks," (with N.J. Balmforth, S.P. Meacham and W.R. Young) in Astrophysical Disks, S.F. Dermott, J.H. Hunter, Jr. and R.E. Wilson, eds. Ann. N.Y. Acad. Sci., 675, 53-64, (1992)
  3. "Equilibria of rapidly rotating polytropes," (with N.J. Balmforth and L.N. Howard) Mon. Not. Roy. astr. Soc. 260, 253-272, (1993)
  4. "Autogravity Waves in a Polytropic Layer" (with Z.S. Qian) Geophys. & Astrophys. Fluid Dyn., 74 225-244, (1994)
  5. "Instability of Rapidly Rotating Polytropes," (with N.J. Balmforth and L.N. Howard) SIAM J. Applied Math. 55, 298-331 (1995)
  6. "Sinuous Modes and Steady Warps of Polytropic Discs," (with N.J. Balmforth) in Waves in Astrophysics, G. Contopoulos, J.H. Hunter, Jr. and R.E. Wilson, eds. Ann. N.Y. Acad. Sci. 773, 55-69 (1995)
  7. "Nonlinear ringing of polytropic disks," (with N.J.Balmforth) Physica D 97, 1-28 (1996)
  
  

• Bubbling Beds

  1. "Fluidization on the Moon (?)," (with J. D. Murray and J. C. Theys), Comments on Ap. and Space Physics 1, 165, (1969)
  2. "Photon Bubbles," (with K. H. Prendergast), Comments on Ap. and Space Physics 5, 43, (1973)
  3. "Archimedean Instabilities in Two-Phase Flows," (with W. S. Childress), SIAM Reviews 17, 136, (1975)
  4. "Photohydrodynamic Instabilities of Hot Stellar Atmospheres," in Physique des Mouvements dans les Atmospheres Stellaires, p. 14, Colloques Internationaux du C.N.R.S., No. 250, R. Cayrel and M. Steinberg, eds., (1976)
  5. "Photoconvection," in Problems in Stellar Convection, E.A. Spiegel and J.-P. Zahn, eds., Springer-Verlag, Berlin `Heidelberg' New York, (1977)
  6. "The Radiative Stess Tensor," (with X. Chen), Ap. J. 540, 1069 (2000)
  7. "The Radiative Bulk Viscosity," (with X. Chen), Mon. Not. R. Astron. Soc. 323, 865-871 (2001)
  8. "Topics in Astrophysical Fluid Dynamics" in Mechanics of the 21st Century, W. Gutkowski & T. Kowalewski, eds. (Springer, Dordrecht, The Netherlands) pp. 365-378 (2005)
  9. "Phenomenological Photofluiddynamics" in Stellar fluid dynamics and numerical simulations: from the sun to neutron stars, M. Rieutord and B. Dubrulle, eds. (Les Ulis: EDP Sciences) 127-146 (2006)
  
  

• Patterns in bioconvection

  1. "Archimedean Instabilities in Two-Phase Flows," (with W. S. Childress), SIAM Reviews 17, 136 (1975)
  2. "Pattern Formation in a Suspension of Swimming Microorganisms: Equations and Stability Theory," (with S. Childress and M. Levandowsky), J. Fluid Mech. 63, 591 (1975)
  3. "A Mathematical Model of Pattern Formation by Swimming Microorganisms," (with M. Levandowsky and W. S. Childress and S. H. Hunter) J. Protozool. 22, 296 (1975)
  4. "Nonlinear Solutions of Equations Describing Bioconvection," (with W. S. Childress and M. Levandowsky), Swimming and Flying in Nature I, T.Y.-T. Wu, C. J. Brokaw and C. Brennan, eds. p. 361 (Plenum Press), (1976)
  5. "Pattern Formation in a Suspension of Swimming Microorganisms: Nonlinear Aspects," (with S. Childress), in A Celebration of Mathematical Modeling: The Joseph B. Keller Anniversary Volume, D. Givoli, M. J. Grote and G. C. Papanicoulao, eds. (Kluwer, Dordrecht) 33-52 (2004)
  
  

• A reconstructed attractor for the solar cycle

  1. "Chaos and the Solar Cycle," (with A.N. Wolf) in Chaotic Phenomena in Astrophysics, J.R. Buchler & H. Eichhorn, eds., Ann. N.Y. Acad. Sci., 497, 55 (1987)
  2. "On-off intermittency: A mechanism for bursting" (with N. Platt and C. Tresser)} Phys. Rev. Lett. 70, 279-282, (1993)
  3. "The Intermittent Solar Cycle" (with N. Platt and C. Tresser)} Geophys. & Astrophys. Fluid Dyn. 73, 146-161 (1993)
  4. "The Chaotic Solar Cycle," in Lectures on Solar and Planetary Dynamos, M.R.E. Proctor and A.D. Gilbert, eds., Pubs. Newton Inst. (Cambridge Univ. Press), 245-266 (1994)
  5. "Catastrophes, chaos and cycles" in Past and Present variability of the solar-terrestrial system: Measurement, Data Analysis and Theoretical Models, G. Cini Castagnoli and A. Provenzale Eds, (IOS Press, Amsterdam), 311-324, (1997)
  
  

• The solar tachocline

  1. "Solar Spin-Down Problem," (with L. N. Howard and D. W. Moore), Nature 214, 1297 (1967)
  2. "The Mixing of Lithium," Highlights of Astronomy, L. Perek, ed. (D. Reidel Pub. Co.) p. 261, (1968)
  3. "The Effect of the Convection Zone on Solar Spin-Down," (with F. P. Bretherton), Ap. J. 153, L77 (1968)
  4. "A History of Solar Rotation," Physics of the Solar System, p. 61, S. I. Rasool, ed. Scientific and Technical Information Office, NASA, Washington, D.C. 1972, (NASA SP-300) Library Congress Catalog Card No. 72-600107 (1972)
  5. "The solar tachocline," (with J.-P. Zahn) Astron. & Astrophys., 265, 106-114 (1992)
  6. "Reflections on the Tachocline" in The Solar Tachocline, D. Hughes, R. Rosner & N. Weiss, eds. (Cambridge, 2007)
  
  

• Large scale convection

  1. "The Large-Scale Structure of Compressible Convection," (with M. C. Depassier), Astron. J. 86, 3 (1981)
  2. "Convection With Heat Flux Prescribed on the Boundaries of the System I. Temperature Dependent Material Properties," (with M. C. Depassier), Geophys. and Astrophys. Fluid Dynamics 21, 167 (1982)
  3. "Clustering of plumes in turbulent convection," (with A. Parodi, J. von Hardenberg, G. Pasoni and A. Provenzale) Phys. Rev. Lett. 92, 1954503 (2004)
  
  

• Others

  1. "Patterns of Aperiodic Pulsation," Astrophys. and Space Sci., 210, 33-49 (1993)
  2. "The Intermittent Solar Cycle," with N. Platt, and C. Tresser in Geophys. and Astrophys. Fluid Dyn., 73, 146-161 (1993)
  3. "Topological entropy of one-dimensional maps: approximations and bounds," with N.J. Balmforth and C. Tresser, Phys. Rev. Lett., 72, 80-83 (1994)
  4. "Advection of Vector Fields by Chaotic Flows," with N.J. Balmforth, P. Cvitanovic, G.R. Ierly, and G. Vatay, in Stochastic Processes in Astrophysics, J.R. Buchler and H. E. Kandrup, eds. Ann. N.Y. Acad. Sci., 706, 148-160 (1994)
  5. "Autogravity Waves in a Polytropic Layer," with Z.S. Qian Geophys. and Astrophys. Fluid Dyn., 74, 225-244 (1994)
  6. "Instability in extended systems," with L. Tao, in Proceedings of the Summer Study Program in G.F.D., Woods Hole Oceanographic Institution, R. Salmon, dir., pp. 177-184, WHOI-94-12 (1994)
  7. "Chaotic Pulse Trains," with N.J. Balmforth and G.R. Ierley SIAM J. Applied Mathematics, 54, 1294-1304 (1994)
  
  

• Obscure Publications (with PDFs)

  1. "Fluidization on the Moon," (with J.D. Murray and J.C. Theys) in Comments on Astrophysics and Space Physics, 1, 165 (1969) PDF
  2. "The Intermittent Solar Cycle," (with N. Platt and C. Tresser) in Geophysical & Astrophysical Fluid Dynamics, 73, 147-161 (1993) PDF
  3. "Phenomenological Photofluiddynamics," in Stellar fluid dynamics and numerical simulations: from the sun to neutron stars, M. Rieutord and B. Dubrulle, eds. (Les Ulis: EDP Sciences) 127-146 (2006) PDF

Last updated 21 March 2007	www@astro.columbia.edu