Issue
Math. Model. Nat. Phenom.
Volume 16, 2021
Control of instabilities and patterns in extended systems
Article Number 24
Number of page(s) 35
DOI https://doi.org/10.1051/mmnp/2021020
Published online 21 April 2021
  1. G. Ahlers, F.F. Araujo, D. Funfschilling, S. Grossmann and D. Lohse, Non-Oberbeck-Boussinesq Effects in Gaseous Rayleigh-Bénard Convection. Phys. Rev. Lett. 98 (2007) 054501. [Google Scholar]
  2. A.V. Anilkumar, R.N. Grugel, X.F. Shen, C.P. Lee and T.G. Wang, Control of thermocapillary convection in a liquid bridge by vibration. J. Appl. Phys. 73 (1993) 4165–4170. [Google Scholar]
  3. H. Arbell and J. Fineberg, Pattern formation in two-frequency forced parametric waves. Phys. Rev. E 65 (2002) 036224. [Google Scholar]
  4. P. Ashwin and A. Zaikin, Pattern selection: the importance of “how you get there”. Biophys. J. 108 (2015) 1307–1308. [Google Scholar]
  5. H. Ayanle, A.J. Bernoff and S. Lichter. Spanwise modal competition in cross-waves. Physica D 43 (1990) 87–104. [Google Scholar]
  6. T. Azami, S. Nakamura and T. Hibiya, Effect of oxygen on thermocapillary convection in a molten silicon column under microgravity. J. Electrochem. Soc. 148 (2001) G185. [Google Scholar]
  7. L. Bárcena, J. Shiomi and G. Amberg. Control of oscillatory thermocapillary convection with local heating. J. Cryst. Growth 286 (2006) 502–511. [Google Scholar]
  8. B.J.S. Barnard and W.G. Pritchard, Cross-waves. Part 2. Experiments. J. Fluid Mech. 55 (1972) 245–255. [Google Scholar]
  9. O.A. Basaran, H. Gao and P.P. Bhat. Nonstandard inkjets. Annu. Rev. Fluid Mech. 45 (2013) 85–113. [Google Scholar]
  10. J.M. Becker and J.W. Miles. Standing radial cross-waves. J. Fluid Mech. 222 (1991) 471–499. [Google Scholar]
  11. G. Beintema, A. Corbetta, L. Biferale and F. Toschi. Controlling Rayleigh-Bénard convection via reinforcement learning. J. Turbul. (2020) 1–21. [Google Scholar]
  12. R. Bellman and R.H. Pennington, Effects of surface tension and viscosity on Taylor instability. Quart. Appl. Math. 12 (1954) 151–162. [Google Scholar]
  13. H. Bénard, Les tourbillons cellulaires dans une nappe liquide. Rev. Gén. Sciences Pure Appl. 11 (1900) 1261–1271, 1309–1328. [Google Scholar]
  14. T.B. Benjamin and F. Ursell. The stability of a plane free surface of a liquid in vertical periodic motion. Proc. Roy. Soc. Lond. A 225 (1954) 505–515. [Google Scholar]
  15. J. Berg and A. Acrivos. The effect of surface active agents on convection cells induced by surface tension. Chem. Eng. Sci. 20 (1965) 737–745. [Google Scholar]
  16. K. Beyer, I. Gawriljuk, M. Günther, I. Lukovsky and A. Timokha. Compressible potential flows with free boundaries. Part I: Vibrocapillary equilibria. Z. Angew. Math. Mech. 81 (2001) 261–271. [Google Scholar]
  17. K. Beyer, M. Günther and A. Timokha, Variational and finite element analysis of vibroequilibria. Comput. Methods Appl. Math. 4 (2004) 290–323. [Google Scholar]
  18. D. Beysens, Vibrations in space as an artificial gravity? Europhysics News 37 (2006) 22–25. [Google Scholar]
  19. N.K. Bezdenezhnykh, V.A. Briskman, D.V. Lyubimov, A.A. Cherepanov and M.T. Sharov. Control of stability of a fluid interface by means of vibrations, electric and magnetic fields, In Third All-Union Seminar on Hydromechanics and Heat and Mass Transfer in Zero Gravity, Abstracts of Papers (in Russian). (1984) 18–20. [Google Scholar]
  20. T. Bickel, Effect of surface-active contaminants on radial thermocapillary flows. Eur. Phys. J. E. 42 (2019) 131. [EDP Sciences] [Google Scholar]
  21. E. Bodenschatz, W. Pesch and G. Ahlers, Recent developments in Rayleigh-Bénard convection. Annu. Rev. Fluid Mech. 32 (2000) 709–778. [Google Scholar]
  22. J.C. Brice, Crystal growth. Blackie and Son (1986). [Google Scholar]
  23. A. Burkert and D.N.C. Lin, Thermal instability and the formation of clumpy gas clouds. Astrophys. J. 537 (2000) 270–282. [Google Scholar]
  24. V. Bychkov, M. Modestov, V. Akkerman and L.-E. Eriksson, The Rayleigh-Taylor instability in inertial fusion, astrophysical plasma and flames. Plasma Phys. Controlled Fusion 49 (2007) B513–B520. [Google Scholar]
  25. R.V. Cakmur, D.A. Egolf, B.B. Plapp and E. Bodenschatz. Bistability and competition of spatiotemporal chaotic and fixed point attractors in Rayleigh–Bénard convection. Phys. Rev. Lett. 79 (1997) 1853–1856. [Google Scholar]
  26. J.R. Carpenter, E.W. Tedford, M. Rahmani and G.A. Lawrence, Holmboe wave fields in simulation and experiment. J. Fluid Mech. 648 (2010) 205–223. [Google Scholar]
  27. J.K. Castelino, D.J. Ratliff, A.M. Rucklidge, P. Subramanian and C.M. Topaz. Spatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems. Physica D 409 (2020) 132475. [Google Scholar]
  28. Y.-J. Chen, R. Abbaschian and P.H. Steen. Thermocapillary suppression of the Plateau–Rayleigh instability: a model for long encapsulated liquid zones. J. Fluid Mech. 485 (2003) 97–113. [Google Scholar]
  29. C.-H. Chun and W. Wuest, Experiments on the transition from the steady to the oscillatory Marangoni-convection of a floating zone under reduced gravity effect. Acta Astronaut. 6 (1979) 1073–1082. [Google Scholar]
  30. I. Cisse, G. Bardan and A. Mojtabi, Rayleigh Bénard convective instability of a fluid under high-frequency vibration. Int. J. Heat Mass Transf . 47 (2004) 4101–4112. [Google Scholar]
  31. S.H. Davis. The stability of time-periodic flows. Annu. Rev. Fluid Mech., 8 (1976) 57–74. [Google Scholar]
  32. Y. Ding and P. Umbanhowar, Enhanced Faraday pattern stability with three-frequency driving. Phys. Rev. E 73 (2006) 046305. [Google Scholar]
  33. S. Douady, Experimental study of the Faraday instability. J. Fluid Mech. 221 (1990) 383–409. [Google Scholar]
  34. P. Drazin, Dynamical Meteorology | Kelvin–Helmholtz Instability, In G.R. North, J. Pyle and F. Zhang, editors, Encyclopedia of Atmospheric Sciences. Academic Press, Oxford, second edition (2015) 343–346. [Google Scholar]
  35. R. Dressler and N. Sivakumaran. Non-contaminating method to reduce Marangoni convection in microgravity float zones. J. Cryst. Growth 88 (1988) 148–158. [Google Scholar]
  36. T. Driessen, P. Sleutel, J. Dijksman, R. Jeurissen and D. Lohse. Control of jet breakup by a superposition of two Rayleigh–Plateau-unstable modes. J. Fluid Mech. 749 (2014) 275–296. [Google Scholar]
  37. V. Duclaux, C. Clanet and D. Quéré, The effects of gravity on the capillary instability in tubes. J. Fluid Mech. 556 (2006) 217–226. [Google Scholar]
  38. W.S. Edwards and S. Fauve. Parametrically excited quasicrystalline surface waves. Phys. Rev. E 47 (1993) R788–R791. [Google Scholar]
  39. W.S. Edwards and S. Fauve, Patterns and quasi-patterns in the Faraday experiment. J. Fluid Mech. 278 (1994) 123–148. [Google Scholar]
  40. J.M. Ezquerro, A. Bello, P. Salgado Sanchez, A. Laveron-Simavilla and V. Lapuerta, The Thermocapillary Effects in Phase Change Materials in Microgravity experiment: Design, preparation and execution of a parabolic flight experiment. Acta Astronaut. 162 (2019) 185–196. [Google Scholar]
  41. J.M. Ezquerro, P. Salgado Sanchez, A. Bello, J. Rodriguez, V. Lapuerta and A. Laveron-Simavilla, Experimental evidence of thermocapillarity in phase change materials in microgravity: measuring the effect of Marangoni convection in solid/liquid phase transitions. Int. Commun. Heat Mass Transf . 113 (2020) 104529. [Google Scholar]
  42. O. Faltinsen and A. Timokha. Sloshing. Cambridge Univ. Press (2009). [Google Scholar]
  43. M. Faraday, On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 121 (1831) 299–340. [Google Scholar]
  44. J. Fernandez, P. Salgado Sánchez, I. Tinao, J. Porter and J.M. Ezquerro, The CFVib experiment: control of fluids in microgravity with vibrations. Microgravity Sci. Technol. 29 (2017) 351–364. [Google Scholar]
  45. J. Fernández, I. Tinao, J. Porter and A. Laverón-Simavilla, Instabilities of vibroequilibria in rectangular containers. Phys. Fluids 29 (2017) 024108. [Google Scholar]
  46. G.B. Field, Thermal instability. Astrophys. J. 142 (1965) 531–567. [Google Scholar]
  47. J. Fröhlich, P. Laure and R. Peyret, Large departures from Boussinesq approximation in the Rayleigh–Bénard problem. Phys. Fluids A 4 (1992) 1355–1372. [Google Scholar]
  48. T. Funada and D.D. Joseph, Viscous potential flow analysis of Kelvin–Helmholtz instability in a channel. J. Fluid Mech. 445 (2001) 263–283. [Google Scholar]
  49. G. Gandikota, D. Chatain, S. Amiroudine, T. Lyubimova and D. Beysens, Frozen-wave instability in near-critical hydrogen subjected to horizontal vibration under various gravity fields. Phys. Rev. E 89 (2014) 012309. [Google Scholar]
  50. R.F. Ganiev, V.D. Lakiza and A.S. Tsapenko, Dynamic behavior of the free liquid surface subject to vibrations under conditions of near-zero gravity. Sov. Appl. Mech. 13 (1977) 499–503. [Google Scholar]
  51. Y. Gaponenko, A. Mialdun and V. Shevtsova, Pattern selection in miscible liquids under periodic excitation in microgravity: Effect of interface width. Phys. Fluids 30 (2018) 062103. [Google Scholar]
  52. Y. Gaponenko, V. Yasnou, A. Mialdun, A. Nepomnyashchy and V. Shevtsova, Hydrothermal waves in a liquid bridge subjected to a gas stream along the interface. J. Fluid Mech. 908 (2021) A34. [Google Scholar]
  53. Y.A. Gaponenko, M.M. Torregrosa, V. Yasnou, A. Mialdun and V. Shevtsova, Interfacial pattern selection in miscible liquids under vibration. Soft Matter 11 (2015) 8221–8224. [Google Scholar]
  54. Y. Garrabos, D. Beysens, C. Lecoutre, A. Dejoan, V. Polezhaev and V. Emelianov, Thermoconvectional phenomena induced by vibrations in supercritical SF6 under weightlessness. Phys. Rev. E 75 (2007) 056317. [Google Scholar]
  55. C.J.R. Garrett, On Cross-waves. J. Fluid Mech. 41 (1970) 837–849. [Google Scholar]
  56. I. Gavrilyuk, I. Lukovsky and A. Timokha, Two-dimensional variational vibroequilibria and Faraday’sdrops. Z. Angew. Math. Phys. 55 (2004) 1015–1033. [Google Scholar]
  57. A. Gelfgat, P. Bar-Yoseph and A. Solan, Effect of axial magnetic field on three-dimensional instability of natural convection in a vertical Bridgman growth configuration. J. Cryst. Growth 230 (2001) 63–72. [Google Scholar]
  58. G.Z. Gershuni and E.M. Zhukhovitskii, Free thermal convection in a vibrational field under conditions of weightlessness. Sov. Phys. Dokl. 24 (1979) 894–896. [Google Scholar]
  59. A.V. Getling, Rayleigh-Bénard convection, World Scientific (1998). [Google Scholar]
  60. D. Gligor, P. Salgado Sánchez, J. Porter and V. Shevtsova, Influence of gravity on the frozen wave instability in immiscible liquids. Phys. Rev. Fluids 5 (Aug 2020) 084001. [Google Scholar]
  61. P.M. Gresho and R.L. Sani, The effects of gravity modulation on the stability of a heated fluid layer. J. Fluid Mech. 40 (1970) 783–806. [Google Scholar]
  62. S. Haefner, M. Benzaquen, O. Bäumchen, T. Salez, R. Peters, J.D. McGraw, K. Jacobs, E. Raphaël and K. Dalnoki-Veress, Influence of slip on the Plateau–Rayleigh instability on a fibre. Nat. Commun. 6 (2015) 7409. [Google Scholar]
  63. T. Havelock, LIX. Forced surface-waves on water. Phil. Mag. 8 (1929) 569–576. [Google Scholar]
  64. M. Haynes, E. Vega, M. Herrada, E. Benilov and J. Montanero, Stabilization of axisymmetric liquid bridges through vibration-induced pressure fields. J. Colloid Interface Sci. 513 (2018) 409–417. [Google Scholar]
  65. H. Helmholtz, On discontinuous movements of fluids. Philos. Mag. 36 (1868) 337–346. [Google Scholar]
  66. J. Holmboe, On the behavior of symmetric waves in stratified shear layers. Geofys. Publ. 24 (1962) 67–113. [Google Scholar]
  67. L.E. Howle, Active control of Rayleigh–Bénard convection. Phys. Fluids 9 (1997) 1861–1863. [Google Scholar]
  68. I. Mutabazi, J. E. Wesfreid and E. Guyon, editors, Dynamics of spatio-temporal cellular structures. Vol. 207 of Springer Tracts in Modern Physics, Springer-Verlag, New York (2006). [Google Scholar]
  69. S.V. Jalikop and A. Juel, Steep capillary-gravity waves in oscillatory shear-driven flows. J. Fluid Mech. 640 (2009) 131–150. [Google Scholar]
  70. D.L. Jassby, Evolution and Large-Electric-Field Suppression of the Transverse Kelvin–Helmholtz Instability. Phys. Rev. Lett. 25 (1970) 1567–1570. [Google Scholar]
  71. A.F. Jones, The generation of cross-waves in a long deep channel by parametric resonance. J. Fluid Mech. 138 (1984) 53–74. [Google Scholar]
  72. B.L. Jones, P.H. Heins, E.C. Kerrigan, J.F. Morrison and A.S. Sharma, Modelling for robust feedback control of fluid flows. J. Fluid Mech. 769 (2015) 687–722. [Google Scholar]
  73. R. Jurado, J. Pallarés, J. Gavaldà and X. Ruiz, Effect of reboosting manoeuvres on the determination of the Soret coefficients of DCMIX ternary systems. Int. J. Therm. Sci. 142 (2019) 205–219. [Google Scholar]
  74. M. Jurisch and W. Löser, Analysis of periodic non-rotational W striations in Mo single crystals due to nonsteady thermocapillary convection. J. Cryst. Growth 102 (1990) 214–222. [Google Scholar]
  75. P.L. Kapitza, Dynamic stability of a pendulum when its point of suspension vibrates. Soviet Phys. JETP. 21 (1951) 588–597. [Google Scholar]
  76. R.E. Kelly, Stabilization of Rayleigh–Bénard convection by means of a slow nonplanar oscillatory flow. Phys. Fluids A 4: (1992) 647–648. [Google Scholar]
  77. L. Kelvin, Mathematical and physical papers, IV, hydrodynamics and general dynamics. Cambridge Univ. Press (1910). [Google Scholar]
  78. A. Khait and L. Shemer. Nonlinear wave generation by a wavemaker in deep to intermediate water depth. Ocean Eng. 182 (2019) 222–234. [Google Scholar]
  79. A. Kidess, S. Kenjereš and C.R. Kleijn, The influence of surfactants on thermocapillary flow instabilities in low Prandtl melting pools. Phys. Fluids 28 (2016) 062106. [Google Scholar]
  80. T.S. Krasnopolskaya and G.J.F.V. Heijst, Wave pattern formation in a fluid annulus with a radially vibrating inner cylinder. J. FluidMech. 328 (1996) 229–252. [Google Scholar]
  81. M. Kudo, Y. Akiyama, S. Takei, K. Motegi and I. Ueno, Effect of ambient air flow on thermocapillary convection in a full-zone liquid bridge. Interfacial Phenom. Heat Transf . 3 (2015) 231–242. [Google Scholar]
  82. A. Kudrolli and J.P. Gollub, Patterns and spatio-temporal chaos in parametrically forced surface waves: a systematic survey at large aspect ratio. Physica D 97 (1996) 133–154. [Google Scholar]
  83. A. Kudrolli, B. Pier and J.P. Gollub, Superlattice patterns in surface waves. Physica D 123 (1998) 99–111. [Google Scholar]
  84. K. Kumar, Linear theory of Faraday instability in viscous liquids. Proc. R. Soc. A 452 (1996) 1113–1126. [Google Scholar]
  85. K. Kumar and L.S. Tuckerman, Parametric instability of the interface between two fluids. J. Fluid Mech. 279 (1994) 49–68. [Google Scholar]
  86. L.D. Landau and E.M. Lifshitz, Fluid mechanics. Vol. 6 of Course of Theoretical Physics. Pergamon Books Ltd., second edition, (1987). [Google Scholar]
  87. M. Lappa. Review: Possible strategies for the control and stabilization of Marangoni flow in laterally heated floating zones. Fluid Dyn. Mater. Process. 1 (2005) 171–188. [Google Scholar]
  88. J. Lindl, Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain. Phys. Plasmas 2 (1995) 3933–4024. [Google Scholar]
  89. B.J. Lowry and P.H. Steen, Capillary surfaces: stability from families of equilibria with application to the liquid bridge. Proc. R. Soc. A 449 (1995) 411–439. [Google Scholar]
  90. B.J. Lowry and P.H. Steen, Flow-influenced stabilization of liquid columns. J. Colloid Interface Sci. 170 (1995) 38–43. [Google Scholar]
  91. D. Lyubimov, T. Lyubimova, A. Croell, P. Dold, K. Benz and B. Roux, Vibration-induced convective flows. Microgravity Sci. Technol. 11 (1998) 101–106. [Google Scholar]
  92. D. Lyubimov, T. Lyubimova and B. Roux, Mechanisms of vibrational control of heat transfer in a liquid bridge. Int. J. Heat Mass Transf . 40 (1997) 4031–4042. [Google Scholar]
  93. D.V. Lyubimov and A.A. Cherepanov, Development of a steady relief at the interface of fluids in a vibrational field. Fluid Dyn. Res. 21 (1986) 849–854. [Google Scholar]
  94. D.V. Lyubimov, A.A. Cherepanov, T.P. Lyubimova and B. Roux, Deformation of gas or drop inclusion in high frequency vibrational field. Microgravity Q. 6 (1996) 69–73. [Google Scholar]
  95. D.V. Lyubimov, A.A. Cherepanov, T.P. Lyubimova and B. Roux, Interface orienting by vibration. C. R. Acad. Sci. Paris, Ser. IIb 325 (1997) 391–396. [Google Scholar]
  96. D.V. Lyubimov, A.O. Ivantsov, T.P. Lyubimova and G.L. Khilko, Numerical modeling of frozen wave instability in fluids with high viscosity contrast. Fluid Dyn. Res. 48 (2016) 061415. [Google Scholar]
  97. D.V. Lyubimov, T.P. Lyubimova and A.A. Cherepanov, Dynamics of Interfaces in Vibrational Fields, Fizmatlit, (2003), in Russian. [Google Scholar]
  98. T. Lyubimova, A. Ivantsov, Y. Garrabos, C. Lecoutre and D. Beysens, Faraday waves on band pattern under zero gravity conditions. Phys. Rev. Fluids 4 (2019) 064001. [Google Scholar]
  99. T. Lyubimova, A. Ivantsov, Y. Garrabos, C. Lecoutre, G. Gandikota and D. Beysens, Band instability in near-critical fluids subjected to vibrationunder weightlessness. Phys. Rev. E 95 (2017) 013105. [Google Scholar]
  100. T.P. Lyubimova, R.V. Scuridin, A. Cröll and P. Dold, Influence of high frequency vibrations on fluid flow and heat transfer in a floating zone. Crys. Res. Technol. 38 (2003) 635–653. [Google Scholar]
  101. S. Madruga and C. Mendoza, Heat transfer performance and melting dynamic of a phase change material subjected to thermocapillary effects. Int. J. Heat Mass Transf . 109 (2017) 501–510. [Google Scholar]
  102. A. Manela and I. Frankel, On the Rayleigh–Bénard problem: dominant compressibility effects. J. Fluid Mech. 565 (2006) 461–475. [Google Scholar]
  103. C. Marangoni, Sull’espansione delle goccie d’un liquido galleggianti sulla superfice di altro liquido, Fratelli Fusi, (1865). [Google Scholar]
  104. M.J. Marr-Lyon, D.B. Thiessen and P.L. Marston, Stabilization of a cylindrical capillary Rayleigh–Plateau limit using acoustic radiation pressure and active feedback. J. Fluid Mech. 351 (1997) 345–357. [Google Scholar]
  105. G. Martin, S. Hoath and I. Hutchings, Inkjet printing – The physics of manipulating liquid jets and drops. J. Phys. Conf. Ser. 105 (2008) 012001. [Google Scholar]
  106. A. Mialdun, I.I. Ryzhkov, D.E. Melnikov and V. Shevtsova, Experimental evidence of thermal vibrational convection in a nonuniformly heated fluid in a reduced gravity environment. Phys. Rev. Lett. 101 (2008) 084501. [Google Scholar]
  107. A.B. Mikishev and A.A. Nepomnyashchy, Large-scale Marangoni convection in a liquid layer with insoluble surfactant under heat flux modulation. J. Adhes. Sci. Technol. 25 (2011) 1411–1423. [Google Scholar]
  108. J. Milesand D. Henderson. Parametrically forced surface waves. Annu. Rev. Fluid Mech. 22 (1990) 143–165. [Google Scholar]
  109. A.I. Mizev and D. Schwabe, Convective instabilities in liquid layers with free upper surface under the action of an inclined temperature gradient. Phys. Fluids 21 (2009) 112102. [Google Scholar]
  110. J. Moehlis, J. Porter and E. Knobloch, Heteroclinic dynamics in a model of Faraday waves in a square container. Physica D 238 (2009) 846–859. [Google Scholar]
  111. F. Moisy, G.-J. Michon, M. Rabaud and E. Sultan, Cross-waves induced by the vertical oscillation of a fully immersed vertical plate. Phys. Fluids 24 (2012) 022110. [Google Scholar]
  112. F. Muldoon, Numerical study of hydrothermal wave suppression in thermocapillary flow using a predictive control method. Comput. Math. Math. Phys. 58 (2018) 493–507. [Google Scholar]
  113. S. Paolucci and D.R. Chenoweth, Departures from the Boussinesq approximation in laminar Bénard convection. Phys. Fluids 30 (1987) 1561–1564. [Google Scholar]
  114. H.M. Park, M.C. Sung and J.S. Chung, Stabilization of Rayleigh-Bénard convection by means of mode reduction. Proc. R. Soc. A 460 (2004) 1807–1830. [Google Scholar]
  115. M. Pastoor, L. Henning, B.R. Noack, R. King and G. Tadmor, Feedback shear layer control for bluff body drag reduction. J. Fluid Mech. 608 (2008) 161–196. [Google Scholar]
  116. J.R.A. Pearson, On convection cells induced by surface tension. J. Fluid Mech. 4 (1958) 489–500. [Google Scholar]
  117. J.M. Perez-Gracia, J. Porter, F. Varas and J.M. Vega, Oblique cross-waves in horizontally vibrated containers. Fluid Dyn. Res. 46 (2014) 041410. [Google Scholar]
  118. J.M. Perez-Gracia, J. Porter, F. Varas and J.M. Vega, Subharmonic capillary-gravity waves in large containers subject to horizontal vibrations. J. Fluid Mech. 739 (2014) 196–228. [Google Scholar]
  119. C.-T. Pham, S. Perrard and G. Le Doudic Surface waves along liquid cylinders. Part 1. Stabilising effect of gravity on the Plateau–Rayleigh instability. J. Fluid Mech. 891 (2020) A8. [Google Scholar]
  120. J.A.F. Plateau, Statique experimentale et theorique des liquides soumis aux seules forces moleculaires. 2 (1873). Gauthier-Villars. [Google Scholar]
  121. J. Porter, I. Tinao, A. Laverón-Simavilla and C.A. Lopez. Pattern selection in a horizontally vibrated container. Fluid Dyn. Res. 44 (2012) 065501. [Google Scholar]
  122. J. Porter, I. Tinao, A. Laverón-Simavilla and J. Rodríguez, Onset patterns in a simple model of localized parametric forcing. Phys. Rev. E 88 (2013) 042913. [Google Scholar]
  123. J. Porter, C.M. Topaz and M. Silber, Pattern control via multifrequency parametric forcing. Phys. Rev. Lett. 93 (2004) 034502. [Google Scholar]
  124. O. Pouliquen, J.M. Chomaz and P. Huerre, Propagating Holmboe waves at the interface between two immiscible fluids. J. Fluid Mech. 266 (1994) 277–302. [Google Scholar]
  125. D.S. Praturi and S.S. Girimaji, Mechanisms of canonical Kelvin–Helmholtz instability suppression in magnetohydrodynamic flows. Phys. Fluids 31 (2019) 024108. [Google Scholar]
  126. F. Preisser, D. Schwabe and A. Scharmann, Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface. J. Fluid Mech. 126 (1983) 545–567. [Google Scholar]
  127. B. Protas and T. Sakajo, Harnessing the Kelvin–Helmholtz instability: feedback stabilization of an inviscid vortex sheet. J. Fluid Mech. 852 (2018) 146–177. [Google Scholar]
  128. Lord Rayleigh, Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. London Math. Soc. s1-14 (1882) 170–177. [Google Scholar]
  129. Lord Rayleigh, On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side. Phil. Mag., Ser.6 32 (1916) 529–546. [Google Scholar]
  130. Lord Rayleigh Sec. R.S. XIX. On the instability of cylindrical fluid surfaces. London, Edinburgh Dublin Philos. Mag. J. Sci. 34 (1892) (207) 177–180. [Google Scholar]
  131. A.M. Rucklidge, M. Silber and A.C. Skeldon, Three-wave interactions and spatiotemporal chaos. Phys. Rev. Lett. 108 (2012) 074504. [Google Scholar]
  132. P. Salgado Sánchez, J. Fernández, I. Tinao and J. Porter, Vibroequilibria in microgravity: Comparison of experiments and theory. Phys. Rev. E 100 (2019) 063103. [Google Scholar]
  133. P. Salgado Sánchez, Y. Gaponenko, V. Yasnou, A. Mialdun, J. Porter and V. Shevtsova, Effect of initial interface orientation on patterns produced by vibrational forcing in microgravity. J. Fluid Mech. 884 (2020) A38. [Google Scholar]
  134. P. Salgado Sánchez, Y.A. Gaponenko, J. Porter and V. Shevtsova, Finite-size effects on pattern selection in immiscible fluids subjected to horizontal vibrations in weightlessness. Phys. Rev. E 99 (2019) 042803. [Google Scholar]
  135. P. Salgado Sánchez, J. Porter, I. Tinao and A. Laverón-Simavilla, Dynamics of weakly coupled parametrically forced oscillators. Phys. Rev. E 94 (2016) 022216. [Google Scholar]
  136. P. Salgado Sánchez, V. Yasnou, Y. Gaponenko, A. Mialdun, J. Porter and V. Shevtsova, Interfacial phenomena in immiscible liquids subjected to vibrations in microgravity. J. Fluid Mech. 865 (2019) 850–883. [Google Scholar]
  137. P. Salgado Sánchez, J.M. Ezquerro, J. Fernández and J. Rodriguez, Thermocapillary effects during the melting of phase change materials in microgravity: Heat transport enhancement. Int. J. Heat Mass Transf . 163 (2020) 120478. [Google Scholar]
  138. P. Salgado Sánchez, J.M. Ezquerro, J. Fernández and J. Rodríguez, Thermocapillary effects during the melting of phase-change materials in microgravity: steady and oscillatory flow regimes. J. Fluid Mech. 908 (2021) A20. [Google Scholar]
  139. P. Salgado Sánchez, J.M. Ezquerro, J. Porter, J. Fernández and I. Tinao, Effect of thermocapillary convection on the melting of phase change materials in microgravity: Experiments and simulations. Int. J. Heat Mass Transf . 154 (2020) 119717. [Google Scholar]
  140. A.E. Samoilova and A. Nepomnyashchy, Nonlinear feedback control of Marangoni wave patterns in a thin film heated from below. Physica D 412 (2020) 132627. [Google Scholar]
  141. R. Sattler, S. Gier, J. Eggers and C. Wagner, The final stages of capillary break-up of polymer solutions. Phys. Fluids 24 (2012) 023101. [Google Scholar]
  142. H.A. Schäffer, Second-order wavemaker theory for irregular waves. Ocean Eng. 23 (1996) 47–88. [Google Scholar]
  143. D. Schwabe, Thermocapillary liquid bridges and Marangoni convection under microgravity–Results and lessons learned. Microgravity Sci. Technol. 26 (2014) 1–10. [Google Scholar]
  144. D. Schwabe and A. Scharmann, Some evidence for the existence and magnitude of a critical Marangoni number for the onset of oscillatory flow in crystal growth melts. J. Cryst. Growth 46 (1979) 125–131. [Google Scholar]
  145. D. Sharp, An overview of Rayleigh–Taylor instability. Physica D 12 (1984) 3–18. [Google Scholar]
  146. M. Sheldrake and R. Sheldrake, Determinants of Faraday wave-patterns in water samples oscillated vertically at a range of frequencies from 50-200 Hz. Water 9 (2017) 1–27. [Google Scholar]
  147. V. Shevtsova, Y. Gaponenko, H. Kuhlmann, M. Lappa, M. Lukasser, S. Matsumoto, A. Mialdun, J. Montanero, K. Nishino and I. Ueno, The JEREMI-project on thermocapillary convection in liquid bridges. Part B: Overview on impact of co-axial gas flow. Fluid Dyn. Mater. Process. 10 (2014) 197–240. [Google Scholar]
  148. V. Shevtsova, Y. Gaponenko and A. Nepomnyashchy, Thermocapillary flow regimes and instability caused by a gas stream along the interface. J. Fluid Mech. 714 (2013) 644–670. [Google Scholar]
  149. V. Shevtsova, Y.A. Gaponenko, V. Yasnou, A. Mialdun and A. Nepomnyashchy, Two-scale wave patterns on a periodically excited miscible liquid–liquid interface. J. Fluid Mech. 795 (2016) 409–422. [Google Scholar]
  150. V. Shevtsova, I.I. Ryzhkov, D.E. Melnikov, Y.A. Gaponenko and A. Mialdun, Experimental and theoretical study of vibration-induced thermal convection in low gravity. J. Fluid Mech. 648 (2010) 53–82. [Google Scholar]
  151. J. Shiomi, M. Kudo, I. Ueno, H. Kawamura and G. Amberg, Feedback control of oscillatory thermocapillary convection in a half-zone liquid bridge. J. Fluid Mech. 496 (2003) 193–211. [Google Scholar]
  152. F. Simonelli and J.P. Gollub, Surface wave mode interactions: Effects of symmetry and degeneracy. J. Fluid Mech. 199 (1989) 349–354. [Google Scholar]
  153. W.A. Sirignano and I. Glassman, Flame spreading above liquid fuels: Surface tension driven flows. Combust. Sci. Technol. 1 (1970) 307. [Google Scholar]
  154. A.C. Skeldon and J. Porter, Scaling properties of weakly nonlinear coefficients in the Faraday problem. Phys. Rev. E 84 (2011) 016209. [Google Scholar]
  155. L.A. Slobozhanin and J.M. Perales, Stability of liquid bridges between equal disks in an axial gravity field. Phys. Fluids A 5 (1993) 1305–1314. [Google Scholar]
  156. W.D. Smyth, G.P. Klaassen and W.R. Peltier, Finite amplitude holmboe waves. Geophys. Astrophys. Fluid Dyn. 43 (1988) 181–222. [Google Scholar]
  157. W.D. Smyth and W.R. Peltier, Instability and transition in finite-amplitude Kelvin–Helmholtz and Holmboe waves. J. Fluid Mech. 228 (1991) 387–415. [Google Scholar]
  158. J.W. Strutt, VI. On the capillary phenomena of jets. Proc. R. Soc. London 29 (1879) 71–97. [Google Scholar]
  159. R.S. Subramanian and R. Balasubramanian, The Motion of Bubbles and Drops in Reduced Gravity. Cambridge University Press, Cambridge (2001). [Google Scholar]
  160. A. Swaminathan, S. Garrett, M. Poese and R. Smith, Dynamic stabilization of the Rayleigh-Bénard instability by acceleration modulation. J. Acoust. Soc. Am. 144 (2018) 2334–2343. [Google Scholar]
  161. S. Taneda, Visual observations of the flow around a half-submerged oscillating circular cylinder. Fluid Dyn. Res. 13 (1994) 119–151. [Google Scholar]
  162. G.I. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. A 201 (1950) 192–196. [Google Scholar]
  163. U. Thiele, J.M. Vega and E. Knobloch, Long-wave Marangoni instability with vibration. J. Fluid Mech. 546 (2006) 61–87. [Google Scholar]
  164. S.A. Thorpe, Experiments on the instability of stratified shear flows: miscible fluids. J. Fluid Mech. 46 (1971) 299–319. [Google Scholar]
  165. I. Tinao, J. Porter, A. Laverón-Simavilla and J. Fernández, Cross-waves excited by distributed forcing in the gravity-capillary regime. Phys. Fluids 26 (2014) 024111. [Google Scholar]
  166. C.M. Topaz, J. Porter and M. Silber, Multifrequency control of Faraday wave patterns. Phys. Rev. E 73 (2004) 066206. [Google Scholar]
  167. C.M. Topaz and M. Silber, Resonances and superlattice pattern stabilization in two-frequency forced Faraday waves. Physica D 172 (2002) 1–29. [Google Scholar]
  168. M. Troitiño, P. Salgado Sánchez, J. Porter and D. Gligor, Symmetry breaking in large columnar frozen wave patterns in weightlessness. Microgravity Sci. Technol. 32 (2020) 907–919. [Google Scholar]
  169. A.M. Turing, The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B 237 (1952) 37–72. [Google Scholar]
  170. L. Turyn, The damped Mathieu equation. Q. Appl. Math. 51 (1993) 389–398. [Google Scholar]
  171. W.B. Underhill, S. Lichter and A.J. Bernoff, Modulated, frequency-locked and chaotic cross-waves. J. Fluid Mech. 225 (1991) 371–394. [Google Scholar]
  172. F. Varas and J.M. Vega, Modulated surface waves in large-aspect-ratio horizontally vibrated containers. J. Fluid Mech. 579 (2007) 271–304. [Google Scholar]
  173. J.T. Waddell, C.E. Niederhaus and J.W. Jacobs, Experimental study of Rayleigh–Taylor instability: Low Atwood number liquid systems with single-mode initial perturbations. Phys. Fluids 13 (2001) 1263–1273. [Google Scholar]
  174. J. Walker, L.M. Witkowski and B. Houchens, Effects of a rotating magnetic field on the thermocapillary instability in the floating zone process. J. Cryst. Growth 252 (2003) 413–423. [Google Scholar]
  175. G.H. Wolf, The dynamic stabilization of the Rayleigh-Taylor instability and the corresponding dynamic equilibrium. Z. Physik 227 (1969) 291–300. [Google Scholar]
  176. G.H. Wolf, Dynamic stabilization of the interchange instability of a liquid-gas interface. Phys. Rev. Lett. 24 (1970) 444–446. [Google Scholar]
  177. V. Yasnou, Y. Gaponenko, A. Mialdun and V. Shevtsova, Influence of a coaxial gas flow on the evolution of oscillatory states in a liquid bridge. Int. J. Heat Mass Transf . 123 (2018) 747–759. [Google Scholar]
  178. S. Zen’kovskaya, V. Novosyadlyi and A. Shleikel’, The effect of vertical vibration on the onset of thermocapillary convection in a horizontal liquid layer. J. Appl. Math. Mech. 71 (2007) 247–257. [Google Scholar]
  179. W. Zhang and J. Viñals, Pattern formation in weakly damped parametric surface waves. J. Fluid Mech. 336 (1997) 301–330. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.