Multiple solutions, oscillons and strange attractors in thermoviscoelastic marangoni convection

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Abstract

Through numerical solution of the governing time-dependent and non-linear Navier-Stokes equations cast in the framework of the Oldroyd-B model, the supercritical states of thermal Marangoni-Bénard convection in a viscoelastic fluid are investigated for increasing values of the relaxation time while keeping fixed other parameters (the total viscosity of the fluid, the Prandtl number and the intensity of the driving force, Ma=300). A kaleidoscope of patterns is obtained revealing the coexistence of different branches of steady and oscillatory states in the space of parameters in the form of multiple solutions. In particular, two main families of well-defined attractors are identified, i.e. multicellular steady states and oscillatory solutions. While the former are similar for appearance and dynamics to those typically produced by thermogravitational hydrodynamic disturbances in layers of liquid metals, the latter display waveforms ranging from pervasive standing waves to different types of spatially localised oscillatory structures (oscillons). On the one hand, these localised phenomena contribute to increase the multiplicity of solutions and, on the other hand, give rise to interesting events, including transition to chaos and phenomena of intermittency. In some intervals of the elasticity number, the interference among states corresponding to different branches produces strange attractors for which we estimate the correlation dimension by means of the algorithm originally proposed by Grassberger and Procaccia.
Original languageEnglish
Article number104104
Number of pages19
JournalPhysics of Fluids
Volume30
Issue number10
DOIs
Publication statusPublished - 19 Oct 2018

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Marangoni convection
strange attractors
Fluids
fluids
Prandtl number
intermittency
liquid metals
Liquid metals
standing waves
free convection
Chaos theory
Relaxation time
Navier-Stokes equation
Navier Stokes equations
chaos
casts
Elasticity
waveforms
disturbances
Hydrodynamics

Keywords

  • oscillons
  • multiple solutions
  • strange attractors
  • thermal convection

Cite this

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title = "Multiple solutions, oscillons and strange attractors in thermoviscoelastic marangoni convection",
abstract = "Through numerical solution of the governing time-dependent and non-linear Navier-Stokes equations cast in the framework of the Oldroyd-B model, the supercritical states of thermal Marangoni-B{\'e}nard convection in a viscoelastic fluid are investigated for increasing values of the relaxation time while keeping fixed other parameters (the total viscosity of the fluid, the Prandtl number and the intensity of the driving force, Ma=300). A kaleidoscope of patterns is obtained revealing the coexistence of different branches of steady and oscillatory states in the space of parameters in the form of multiple solutions. In particular, two main families of well-defined attractors are identified, i.e. multicellular steady states and oscillatory solutions. While the former are similar for appearance and dynamics to those typically produced by thermogravitational hydrodynamic disturbances in layers of liquid metals, the latter display waveforms ranging from pervasive standing waves to different types of spatially localised oscillatory structures (oscillons). On the one hand, these localised phenomena contribute to increase the multiplicity of solutions and, on the other hand, give rise to interesting events, including transition to chaos and phenomena of intermittency. In some intervals of the elasticity number, the interference among states corresponding to different branches produces strange attractors for which we estimate the correlation dimension by means of the algorithm originally proposed by Grassberger and Procaccia.",
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author = "Marcello Lappa and Hermes Ferialdi",
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Multiple solutions, oscillons and strange attractors in thermoviscoelastic marangoni convection. / Lappa, Marcello; Ferialdi, Hermes.

In: Physics of Fluids, Vol. 30, No. 10, 104104, 19.10.2018.

Research output: Contribution to journalArticle

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AB - Through numerical solution of the governing time-dependent and non-linear Navier-Stokes equations cast in the framework of the Oldroyd-B model, the supercritical states of thermal Marangoni-Bénard convection in a viscoelastic fluid are investigated for increasing values of the relaxation time while keeping fixed other parameters (the total viscosity of the fluid, the Prandtl number and the intensity of the driving force, Ma=300). A kaleidoscope of patterns is obtained revealing the coexistence of different branches of steady and oscillatory states in the space of parameters in the form of multiple solutions. In particular, two main families of well-defined attractors are identified, i.e. multicellular steady states and oscillatory solutions. While the former are similar for appearance and dynamics to those typically produced by thermogravitational hydrodynamic disturbances in layers of liquid metals, the latter display waveforms ranging from pervasive standing waves to different types of spatially localised oscillatory structures (oscillons). On the one hand, these localised phenomena contribute to increase the multiplicity of solutions and, on the other hand, give rise to interesting events, including transition to chaos and phenomena of intermittency. In some intervals of the elasticity number, the interference among states corresponding to different branches produces strange attractors for which we estimate the correlation dimension by means of the algorithm originally proposed by Grassberger and Procaccia.

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