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Nonlinear Waves in Two-Layer Systems with Heat Release at the Interface


An influence of a spatial temperature modulation of the heat release/consumption at the interface on nonlinear convective flows in the 47v2 silicone oil - water system, has been investigated. Two types of boundary conditions on lateral walls: periodic boundary conditions corresponding to laterally infinite two-layer system and rigid heat-insulated lateral walls corresponding to the closed cavity, have been considered. It is shown that the spatial modulation can change the sequence of bifurcations and lead to the appearance of new oscillatory regimes. Specifically, pulsating traveling waves changing the direction of propagation, as well as regimes corresponding to period doubling, period-four and period-eight bifurcations, have been obtained.

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  1. Degen, M.M., Colovas, P.W., Andereck, C.D.: Time-dependent patterns in the two-layer Rayleigh-Bénard system. Phys. Rev. E 57, 6647 (1998)

  2. di Bernardo, M., Budd, C.J., Champneys, A.R., Kowalczyk, P., Nordmark, A.B., Tost, G.O., Piiroinen, P.T.: Bifurcations in nonsmooth dynamical systems. SIAM Rev. 50(4), 629 (2013)

  3. Doi, T., Koster, J.N.: Thermocapillary convection in two immiscible layers with free surface. Phys. Fluids A5, 1914 (1993)

  4. Gershuni, G.Z., Zhukhovitsky, E.M.: On monotonic and oscillatory instability of a two-layer immiscible fluids system heated from below. Sov. Phys. Dokl. 27, 531 (1982)

  5. Gilev, A. Y. u., Nepomnyashchy, A.A., Simanovskii, I.B.: Onset of the oscillatory thermogravitational convection in a two-layer system when heating from below. Dynamics of Viscous Fluids, Collection of papers. Sverdlovsk, p. 36 (in Russian) (1987)

  6. Groothuis, H., Zuiderweg, F.G.: Influence of mass transfer on coalescence of drops. Chem. Eng. Sci 12, 288 (1960)

  7. Juel, A., Burgess, J.M., McCormick, W.D., Swift, J.B., Swinney, H.L.: Surface-tension-driven convection patterns in two liquid layers. Physica D 143, 169 (2000)

  8. Levich, V.G., Krylov, V.S.: Surface - tension - driven phenomena. Annu. Rev. Fluid. Mech. 1, 293 (1969)

  9. Nepomnyashchy, A.A., Simanovskii, I.B.: Thermocapillary and thermogravitational convection in a two-layer system with a distorted interface. Fluid Dyn. 19, 494 (1984)

  10. Nepomnyashchy, A.A., Simanovskii, I.B.: Influence of thermocapillary effect and interfacial heat release on convective oscillations in a two-layer system. Phys. Fluids 16, 1127 (2004)

  11. Nepomnyashchy, A.A., Simanovskii, I.B., Legros, J.C.: Interfacial Convection in Multilayer Systems, 2nd edn. Springer, New York (2012)

  12. Rao, C.N.R.: Chemical Applications of Infrared Spectroscopy. Academic, New York (1963)

  13. Renardy, Y.Y.: Pattern formation for oscillatory bulk-mode competition in a two-layer Bénard problem. ZAMP 47, 567 (1996)

  14. Simanovskii, I.B.: The influence of the interfacial heat release on nonlinear convective oscillations in two-layer systems. Phys. Fluids 25, 072106 (1–18) (2013)

  15. Simanovskii, I.B., Nepomnyashchy, A.A.: Convective Instabilities in Systems with Interface. Gordon and Breach, London (1993)

  16. Simanovskii, I.B., Viviani, A., Dubois, F., Legros, J.C.: Nonlinear buoyant-thermocapillary waves in two-layer systems with an interfacial heat release. Micrograv. Sci. Technol. 27(1), 11 (2015)

  17. Simanovskii, I., Viviani, A., Dubois, F., Queeckers, P.: Nonlinear convective flows in a laterally heated two-layer systems with a temperature-dependent heat release/consumption at the interface. Micrograv. Sci. Technol. 30(3), 243 (2018)

  18. Szekely, J.: Fluid Flow Phenomena in Metals Processing. Academic, New York (1979)

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The material of the present paper has been reported at the 12th Asian Microgravity Symposium AMS 2018, 12–16 November 2018 Zhuhai, China.

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Correspondence to Ilya B. Simanovskii.

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Simanovskii, I.B. Nonlinear Waves in Two-Layer Systems with Heat Release at the Interface. Microgravity Sci. Technol. 32, 11–26 (2020).

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  • Instabilities
  • Interface
  • Temperature modulation