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Instability and convection in fluid layers: A report on Euromech 106

Published online by Cambridge University Press:  19 April 2006

E. J. Hopfinger ,
P. Atten  and
F. H. Busse
E. J. Hopfinger
Affiliation:
Institut de Mécanique (Laboratoire associé au. C.N.R.S.), Université de Grenoble, France
P. Atten
Affiliation:
Laboratoire d'Electrostatique, C.N.R.S., Grenoble, France
F. H. Busse
Affiliation:
Institute of Geophysics and Planetary Physics University of California, Los Angeles
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Abstract

The 106th Euromech Colloquium on instability and convection driven by body forces in fluid layers was held in Grenoble from 11 to 14 September 1978 with the first two authors acting as chairmen. There were sixty-five participants coming from fifteen different countries and having widely different backgrounds. Fifty-seven papers were presented during the four full days of the meeting and are discussed in this report with the purpose of giving an up-to-date view of current research in convection.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 92 , Issue 2 , 28 May 1979 , pp. 217 - 240
Copyright
© 1979 Cambridge University Press

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References

Acheson, D. J. 1976 On over-reflexion. J. Fluid Mech. 77, 433–472.Google Scholar
Acheson, D. J.* Hydrodynamic instabilities provoked by bottom-heavy gradients.
Acheson, D. J. 1978 On the stability of toroidal magnetic fields and differential rotation in stars. Phil. Trans. Roy. Soc. A 289, 459–500.Google Scholar
Adrian, R. J. 1975 Turbulent convection in water over ice. J. Fluid Mech. 69, 753–781.Google Scholar
Ahlers, G. 1974 Low temperature studies of the Rayleigh-Bénard instability and turbulence. Phys. Rev. Lett. 33, 1185–1188.Google Scholar
Ahlers, G. 1975 The Rayleigh-Bénard instability at helium temperatures. In Fluctuations, Instabilities and Phase Transitions (ed. T. Riste), vol. B 11, pp. 181–193. New York: Plenum Press.
Ahlers, G. & Behringer, R. P. 1978 Evolution of turbulence from the Rayleigh-Bénard instability. Phys. Rev. Lett. 40, 712–716.Google Scholar
André, J. C., De Moor, G., Lacarrère, P. & Du Vachat, R. 1976 Turbulence approximation for inhomogeneous flows. I. The clipping approximation. J. Atmos. Sci. 33, 476–481.Google Scholar
André, J. C., De Moor, G., Lacarrère, P. & Du Vachat, R.* Convection turbulente. Simulation numérique d'une expérience de laboratoire.
Antoranz, J. C. & Velarde, M. G. 1978 Soret-driven convective instability with rotation. Phys. Lett. A 65, 377–379.Google Scholar
Atten, P. & Lacroix, J. C. 1979 Nonlinear hydrodynamic stability of liquids subjected to unipolar injection. J. Mécan. (in press).Google Scholar
Azouni, M. A. 1977 Instabilités thermoconvectives entre 0 °C et 4 °C. Lett. Heat Mass Transfer 4, 445–452.Google Scholar
Azouni, M. A.* Hydrodynamic instabilities in a fully confined water layer under its density maximum.
Baranowski, B.* The electrochemical analogue of Bénard instability.
Benjamin, T. B. 1978 Bifurcation phenomena in steady flows of a viscous fluid. Proc. Roy. Soc. A 359, 1–26.Google Scholar
Berge, P.* Experimental evidence of the behaviour of convective velocity in Rayleigh-Bénard instability: Different transitions toward turbulence.
Berkovsky, B. M., Fertman, V. E., Sinitsyn, A. K. & Barkov, Yu. I. 1978 A theoretical and experimental study of thermal disturbances propagating in a fluid layer heated from below. J. Fluid Mech. 89, 173–190.Google Scholar
Bois, P. A.* Instabilité linéaire convective dans l'atmosphère. Théorie asymptotique.
Bouabdallah, A. & Cognet, G.* Instabilités et turbulence dans l’écoulement de Taylor-Couette.
Braginskii, S. I. & Roberts, P. H. 1975 Magnetic field generation by baroclinic waves. Proc. Roy. Soc. A 347, 125–140.Google Scholar
Busse, F. H. 1967 The stability of finite amplitude cellular convection and its relation to an extremum principle. J. Fluid Mech. 30, 625–649.Google Scholar
Busse, F. H. 1975a Patterns of convection in spherical shells. J. Fluid Mech. 72, 67–85.Google Scholar
Busse, F. H. 1975b Nonlinear interaction of magnetic field and convection. J. Fluid Mech. 71, 193–206.Google Scholar
Busse, F. H. 1977 Convection in rotating stars. In Problems of Stellar Convection (ed. E. A. Spiegel & J. P. Zahn), Lecture Notes in Physics, no. 71, pp. 156–175. Springer.
Busse, F. H.* Convection in planetary cores.
Busse, F. H. & Carrigan, C. R. 1976 Laboratory simulation of thermal convection in rotating planets and stars. Science 191, 81–83.Google Scholar
Busse, F. H. & Hood, L. 1979 Generation of differential rotation by convection. (In preparation.)
Busse, F. H. & Whitehead, J. A. 1974 Oscillatory and collective instabilities in large Prandtl number convection. J. Fluid Mech. 66, 67–80.Google Scholar
Caltagirone, J. P. 1976 Thermoconvective instabilities in a porous medium bounded by two concentric horizontal cylinders. J. Fluid Mech. 76, 337–362.Google Scholar
Caltagirone, J. P. & Mojtabi, A.* Stabilité linéaire et énergétique de l’écoulement de convection naturelle dans une couche poreuse annulaire.
Carrigan, C. R. 1977 A study of buoyancy driven flows in rotating fluids motivated by planetary applications. Ph.D. Thesis, University of California.
Carrigan, C. R. & Busse, F. H.* A laboratory study of convection in a rapidly rotating spherical layer.
Castillo, J. L. & Velarde, M. G. 1978 Thermal diffusion and the Marangoni-Bénard instability of a two-component fluid layer heated from below. Phys. Lett. A 66, 489–491.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Childress, S., Levandowsky, M. & Spiegel, E. A. 1975 Pattern formation in a suspension of swimming micro-organisms: Equations and stability theory. J. Fluid Mech. 63, 591–613.Google Scholar
Clever, R. M.* Instabilities of longitudinal convection rolls with shear.
Clever, R. M. & Busse, F. H. 1974 Transition to time dependent convection. J. Fluid Mech. 65, 625–645.Google Scholar
Clever, R. M. & Busse, F. H. 1977 Instabilities of longitudinal convection rolls in an inclined layer. J. Fluid Mech. 81, 107–127.Google Scholar
Clever, R. M., Busse, F. H. & Kelly, R. E. 1977 Instabilities of longitudinal convection rolls in Couette flow. J. Appl. Math. Phys. 28, 771–783.Google Scholar
Donnelly, R. J., Schwartz, K. W. & Roberts, P. H. 1965 Experiments on the stability of viscous flow between rotating cylinders. IV Finite amplitude experiments. Proc. Roy. Soc. A 283, 531–000.Google Scholar
Dubois, M. & Wesfreid, J.* Experiments on Rayleigh-Bénard convection in simple fluids: Critical properties near threshold and penetration effects.
Dubois-Violette, E., de Gennes, P. G. & Parodi, O. 1971 Hydrodynamic instabilities of nematic liquid crystal under A.C. electric fields. J. Phys. 32, 305–317.Google Scholar
Dubois-Violette, E. & Manneville, P. 1978 Stability of the Couette flow in nematic liquid crystals. J. Fluid Mech. 89, 273–303.Google Scholar
Faust, K. M. & Plate, E. J.* Turbulent penetrative convection.
Fautrelle, Y. 1978 Baroclinic waves in the presence of a magnetic field. J. Méc. 17, 1–34.Google Scholar
Fautrelle, Y.* Baroclinic instability in the presence of a magnetic field.
Fenstermacher, P. R., Swinney, H. L., Benson, S. V. & Gollub, J. P. 1978 In Bifurcation Theory and Applications in Scientific Disciplines (ed. O. Gurel and O. E. Rössler). New York Academy of Sciences.
Galloway, D. J., Proctor, M. R. E. & Weiss, N. O. 1978 Magnetic flux ropes and convection. J. Fluid Mech. 87, 243–261.Google Scholar
Galloway, D. J.* The effects of geometry on convection with magnetic fluxropes.
Giglio, M. & Vendramini, A. 1977 Buoyancy-driven instability in a dilute solution of macro-molecules. Phys. Rev. Lett. 39, 1014–1017.Google Scholar
Giglio, M. & Vendramini, A.* Soret-driven instability in a dilute solution of macromolecules.
Gill, A. E. & Davey, A. 1969 Instabilities of a buoyancy driven system. J. Fluid Mech. 35, 775–798.Google Scholar
Gilman, P. A. 1977 Nonlinear dynamics of Boussinesq convection in a deep rotating spherical shell, I. Geophys. Astrophys. Fluid Dyn. 8, 93–136.Google Scholar
Gollub, J. P. & Benson, S. V.* Laser-Doppler studies of convective instabilities and the transition to turbulence.
Gollub, J. P. & Swinney, H. L. 1975 Onset of turbulence in a rotating fluid. Phys. Rev. Lett. 35, 927–930.Google Scholar
Gough, D. O. 1969 The anelastic approximation for thermal convection. J. Atmos. Sci. 26, 448–456.Google Scholar
Gough, D. O., Spiegel, E. A. & Toomre, J. 1975 Modal equations for cellular convection. J. Fluid Mech. 68, 695–719.Google Scholar
Graham, R. 1975 Macroscopic theory of fluctuations and instabilities in optics and hydrodynamics. In Fluctuations, Instabilities and Phase Transitions (ed. T. Riste), vol. B 11, 215–293. New York: Plenum Press.
Gravas, N. & Martin, B. W. 1978 Instability of viscous axial flow in annuli having a rotating linear cylinder. J. Fluid Mech. 86, 385–394.Google Scholar
Guyon, E., Pieranski, P. & Salan, J. 1978 Cristaux liquides - Convection oscillante dans les nématiques. C. r. hebd. séanc. Acad. Sci., Paris, B 287, 41–43.Google Scholar
Guyon, E., Pieranski, P. & Salan, J.* Heat convection in nematics in the presence of fields.
Haken, H. 1975 Cooperative phenomena in systems far from thermal equilibrium and in non-physical systems. Rev. Mod. Phys. 47, 67–121.Google Scholar
Haken, H.* Bifurcation of limit cycles and quasiperiodic flows in continuous media.
Hall, P. & Walton, I. C. 1977 The smooth transition to a convective régime in a two-dimensional box. Proc. Roy. Soc. A 358, 199–221.Google Scholar
Hame, W. & Muller, U.* Free convective flow in a molten pool with internal heat sources and solidified boundaries.
Hart, J. E. 1971 Transition to a wavy vortex régime in convective flow between inclined plates. J. Fluid Mech. 48, 265–271.Google Scholar
Hide, R., Mason, P. J. & Plumb, R. A. 1977 Thermal convection in a rotating fluid subject to a horizontal temperature gradient: Spatial and temporal characteristics of fully developed baroclinic waves. J. atmos. Sci. 34, 930–950.Google Scholar
Hopfinger, E. J., Atten, P. & Lacroix, J. C.* Coulomb force induced instability and convection in dielectric liquids.
Howard, L. N. 1966 Convection at high Rayleigh number. In Proc. 11th Int. Congress of Applied Mechanics, pp. 1109–1115. Springer.
Huppert, H. E. & Linden, P. F.* Heating a stable salinity gradient from below.
Iooss, G.* Properties of a flow bifurcating from a self-oscillating one.
James, I. N. & Jonas, P. R.* Recent combined laboratory and numerical studies of baroclinic waves in an annulus.
Jenkins, J. T. 1978 Flows of nematic liquid crystals. Ann. Rev. Fluid Mech. 10, 197–219.Google Scholar
Jones, C. A. & Moore, D. R.* The stability of axisymmetric convection.
Jones, C. A., Moore, D. R. & Weiss, N. O. 1976 Axisymmetirc convection in a cylinder. J. Fluid Mech. 73, 353–388.Google Scholar
Joseph, D. D. 1976 Stability of fluid motions. I and II. Springer Tracts in Natural Philosophy, vols. 27 and 28. Springer.
Joseph, D. D. 1979 Hydrodynamic stability and birfurcation. To appear in Hydrodynamic Instabilities and the Transition to Turbulence, ed. Swinney and Gollub, Topics in Current Physics. Springer.
Joseph, D. D.* Review of repeated and direct bifurcations into turbulence.
Kelly, R. E. 1978 The onset and development of Rayleigh-Bénard convection in shear flows: A review. In Proc. Int. Conf. Phys. Chem. and Hydrodynamics, pp. 65–79. Hemisphere Publ. Corp.
Klapisz, C., Strauss, B., Van Grunderbeeck, P. & Weill, A.* Convection and similarity in the free convection atmospheric layer.
Krishnamurti, R. 1968a Finite amplitude convection with changing mean temperature. 1. Theory. J. Fluid Mech. 33, 445–455.Google Scholar
Krishnamurti, R. 1968b Finite amplitude convection with changing mean temperature. 2. An experimental test of the theory. J. Fluid Mech. 33, 457–463.Google Scholar
Krishnamurti, R. 1970 On the transition to turbulent convection, II. The transition to time-dependent flow. J. Fluid Mech. 42, 309–320.Google Scholar
Krishnamurti, R. 1973 Some further studies on the transition to turbulent convection. J. Fluid Mech. 60, 285–303.Google Scholar
Krishnamurti, R. 1975a On cellular cloud patterns. Part 2: Laboratory model. J. Atmos. Sci. 32, 1364–1372.Google Scholar
Krishnamurti, R. 1975b On cellular cloud patterns. Part 3: Applicability of the mathematical and laboratory models. J. Atmos. Sci. 32, 1373–1383.Google Scholar
Krishnamurti, R.* A review of convective instability with examples from atmospheric and biological convection.
Kulacki, F. A. & Goldstein, R. J. 1972 Thermal convection in horizontal fluid layer with uniform volumetric energy sources. J. Fluid Mech. 55, 271–287.Google Scholar
Lacroix, J. C., Atten, P. & Hopfinger, E. J. 1975 Electroconvection in a dielectric liquid layer subjected to unipolar injection. J. Fluid Mech. 69, 539–563.Google Scholar
Latour, J., Spiegel, E. A., Toomre, J. & Zahn, J. P. 1976 Stellar convection theory I. The anelastic modal equations. Astrophys. J. 207, 233–243.Google Scholar
Latour, J., Toomre, J. & Zahn, J. P.* Nonlinear penetrative Boussinesq convection.
Legros, J. Cl., Van Hook, W. A. & Thomaes, G. 1968 Convection and thermal diffusion in a solution heated from below. Chem. Phys. Lett. 2, 249–250.Google Scholar
Legros, J. Cl. & Platten, J. K.* Le problème de Bénard à deux constituants: théorie non-linéaire, parois rigides.
Legros, J. Cl. & Platten, J. K.* 1978 Les instabilités hydrodynamiques en convection libre, forcée et mixte. Lecture Notes in Physics, vol. 72. Springer.
Lekkerkerker, H. N. W. 1977 Oscillatory convective instabilities in nematic liquid crystals. J. Phys. Lett. L 38, 277–281.Google Scholar
Libchaber, A. & Maurer, J. 1978 Local probe in a Rayleigh-Bénard experiment in liquid helium. J. Phys. Lett. L 39, 369–372.Google Scholar
Linde, H. & Schwartz, P.* Dissipative structures and nonlinear kinetics of the Marangoni instability.
Malkus, W. V. R. 1954 Discrete transitions in turbulent convection. Proc. Roy. Soc. A 225, 185–195.Google Scholar
Manneville, P.* Stability on the cylindrical Couette flow in nematic liquid crystals.
Martin, B. W.* Instability of viscous axial flow in an annulus with a rotating inner cylinder.
Massaguer, J. M. & Zahn, J. P.* Nonlinear anelastic convection in a highly stratified medium.
Maurer, J. & Libchaber, A.* Local probe in a Rayleigh-Bénard experiment in liquid helium.
McClimans, T. A. & Steen, J. E.* Double diffusion at the freezing point in fjords.
Moore, D. R. & Weiss, N. O. 1973 Nonlinear penetrative convection. J. Fluid Mech. 61, 553–581.Google Scholar
Mucha, Z., Peradzynski, Z. & Baranowski, A. 1977 Instability of continuous optical discharge. Bull. Acad. Pol. Sci. Ser. Sci. Tech. (Poland) 25, 361–367.Google Scholar
Oertel, H.* Time-dependent wave mode convection.
Oertel, H. & Buhler, K. 1978 A special differential interferometer used for heat convection investigations. Int. J. Heat Mass Transfer 21, 1111–1115.Google Scholar
Orszag, S. & Krell, L. 1978 Transition to turbulence in plane Poisseuille and plane Couette flow. Preprint.
Palm, E. 1975 Nonlinear thermal convection. Ann. Rev. Fluid Mech. 7, 39–61.Google Scholar
Palm, E.* On heat and mass flux through snow.
Pantaloni, J. & Bailleux, R.* Experimental results on Bénard convection in molten salt layers: the role of solidification at an open interface and the difference with Bénard-Marangoni instability of an oil layer.
Peradzynski, Z.* Instability of convective flow due to a strong thermal source.
Pieranski, P., Dubois-Violette, E. & Guyon, E. 1973 Heat convection in liquid crystals heated from above. Phys. Rev. Lett. 30, 736–739.Google Scholar
Pieranski, P. & Guyon, E. 1974 Instability of certain shear flows in nematic liquids. Phys. Rev. A 9, 404–417.Google Scholar
Platten, J. K. & Chavepeyer, G. 1977 Non-linear two-dimensional Bénard convection with Soret effect: Free boundaries. Int. J. Heat Mass Transfer 20, 113–122.Google Scholar
Platten, J. K. & Legros, J. Cl.* Simulations numériques de la convection de Rayleigh-Bénard: Exposants critiques, longueur de pénétration, temps d'amortissement.
Pomeau, Y.* Unsteadiness and turbulence near the onset of convection.
Prigogine, I., Legros, J. Cl. & Platten, J. K.* Critère général de stabilité thermo-dynamique hors de l’équilibre.
Prigogine, I. & Rice, S. A. 1975 Proc. Conf. Instabilities and Dissipative Structures in Hydrodynamics. Adv. Chem. Physics, 32. Wiley.Google Scholar
Proctor, M. R. E.* The bifurcation problem for Rayleigh-Bénard convection with magnetic fields.
Proctor, M. R. E. & Galloway, D. J. 1979 The dynamic effect of the flux ropes on Rayleigh-Bénard convection. J. Fluid Mech. In press.Google Scholar
Ribotta, R.* Penetration length of a vortex into a subcritical region.
Roesner, K. G.* Numerical simulation of accelerated spherical gap flow at critical Reynolds numbers.
Ruelle, D. & Takens, F. 1971 On the nature of turbulence. Comm. Math. Phys. 20, 167–192.Google Scholar
Schatzman, E. 1977 Turbulent transport and lithium destruction in main sequence stars. Astron. Astrophys. 56, 211.Google Scholar
Schatzman, E.* On the possible existence of turbulence in rotating stars.
Schinkel, W. M. M.* Natural convection in inclined air-filled enclosures: An interferometric study.
Schneider, W. & Keck, H.* Thermoconvective waves.
Schwabe, D., Scharmann, A., Preisser, F. & Oeder, R. 1978 Experiments on surface tension driven flow in floating zone melting. J. Cryst. Growth. 43, 305–312.Google Scholar
Schwabe, D., Scharmann, A. & Preisser, F.* Instability of surface tension driven flow.
Soward, A. M. 1977 On the finite amplitude thermal instability in a rapidly rotating fluid sphere. Geophys. Astrophys. Fluid Dyn. 9, 19–74.Google Scholar
Sproston, J. L.* Electroconvection in insulating liquids.
Steppeler, J. 1978 Fluid computations using infinitesimal functionals. Comp. Fluids. (In the Press.)Google Scholar
Steppeler, J.* A variational approach to Bénard convection with applications to cumulus convection.
Tritton, D. J.* High Rayleigh number convection of a very viscous fluid heated from below.
Tritton, D. J. & Zarraga, M. N. 1968 Convection in horizontal layers with internal heat generation: Experiments. J. Fluid Mech. 30, 21–31.Google Scholar
True, H.* Bifurcation and stability of the convective boundary layer at a vertical wall with a stable temperature gradient.
Turner, J. S. 1965 The coupled turbulent transport of salt and heat across a sharp density interface. Int. J. Heat Mass Transfer 8, 759–767.Google Scholar
Turner, J. S. 1974 Double-diffusive phenomena. Ann. Rev. Fluid Mech. 6, 37–56.Google Scholar
Velarde, M. G.* Thermal diffusion and convective instability of binary fluid layers.
Velarde, M. G. & Schechter, R. S. 1972 Thermal diffusion and convective stability. II. An analysis of the convective fluxes. Phys. Fluids. 15, 1707–1714.Google Scholar
Walton, I. C.* The smooth transition to a convective regime in a two-dimensional box.
Wesfreid, J., Berge, P. & Dubois, M. 1979 Induced pretransitional Rayleigh-Bénard convection. Phys. Rev. (to be published).Google Scholar
Wesfreid, J., Pomeau, Y., Dubois, M., Normand, C. & Berge, P. 1978 Critical effects in Rayleigh-Bénard convection. J. Phys. Lett. 39, 725–731.Google Scholar
Whitehead, J. A. & Parsons, B. 1978 Observations of convection at Rayleigh numbers up to 760,000 in a fluid with large Prandtl number. Geophys. Astrophys. Fluid Dyn. 9, 201–217.Google Scholar
Whitehead, J. A.* Time dependent high Prandtl number convection.
Willis, G. E. & Deardorff, J. W. 1970 The oscillatory motions of Rayleigh convection. J. Fluid Mech. 44, 661–672.Google Scholar
Willis, G. E. & Deardorff, J. W. 1974 A laboratory model of the unstable planetary boundary layer. J. atmos. Sci. 31, 1297–1307.Google Scholar
Wimmer, M. 1976 Experiments on a viscous fluid flow between concentric rotating spheres. J. Fluid Mech. 78, 317–335.Google Scholar
Zahn, J. P., Toomre, J., Spiegel, E. A. & Gough, D. D. 1974 Nonlinear cellular motions in Poiseuille channel flow. J. Fluid Mech. 64, 319–345.Google Scholar
Zeman, O. & Lumley, J. L. 1976 Modeling buoyancy driven mixed layers. J. atmos. Sci. 33, 1974–1988.Google Scholar