On the onset of multi-wave patterns in laterally heated floating zones for slightly supercritical conditions

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

This analysis follows and integrates the line of inquiry started in past author’s works (Phys. Fluids, 15(3): 776-789, 2003, and Phys. Fluids 16(2): 331-343, 2004) about the typical instabilities of Marangoni flow and associated hierarchy of bifurcations in laterally heated floating zones with various shapes and aspect ratios. The main motivation for re-examining this kind of problems, which so much attention have attracted over the last twenty years, is the recent discovery (Kudo, Ueno and Kawamura, (2014), in Japanese, DOI: 10.1299/transjsme.2014tep0095) of a chaotic state in region of the space of parameters where on the basis of existing theories and earlier results for the classical liquid-bridge problem with organic fluids, the flow should be relatively regular in time and with a simple structure in space. Axisymmetric computations are used to obtain the steady basic state, and then the Navier Stokes equations are solved in their complete, three-dimensional, time-dependent and non-linear formulation to investigate the evolution of azimuthal disturbances. It is shown that the “apparent” doubling or quadrupling of the azimuthal wavenumber in the equatorial plane, previously reported for the case of floating zones of liquid metals, is replaced for high-Prandtl-number liquids by the complex interaction of disturbances with distinct spatial and temporal scales. These disturbances become critical at relatively comparable values of the Marangoni number. The unexpected multiplicity of waveforms and competition of spatial modes is explained according to the increased complexity of the considered system in terms of flow topology and structure with respect to the classical half-zone configuration.
LanguageEnglish
Article number124105
Number of pages22
JournalPhysics of Fluids
Volume28
Issue number12
DOIs
Publication statusPublished - 19 Dec 2016

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floating
disturbances
Fluids
fluids
liquid bridges
Prandtl number
Liquids
liquid metals
Liquid metals
Navier-Stokes equation
Navier Stokes equations
hierarchies
aspect ratio
Aspect ratio
waveforms
topology
Topology
formulations
liquids
configurations

Keywords

  • Marangoni flow
  • lateral heating
  • instability
  • bifurcation
  • fluid dynamics
  • chaos
  • liquid bridge
  • flow topology

Cite this

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abstract = "This analysis follows and integrates the line of inquiry started in past author’s works (Phys. Fluids, 15(3): 776-789, 2003, and Phys. Fluids 16(2): 331-343, 2004) about the typical instabilities of Marangoni flow and associated hierarchy of bifurcations in laterally heated floating zones with various shapes and aspect ratios. The main motivation for re-examining this kind of problems, which so much attention have attracted over the last twenty years, is the recent discovery (Kudo, Ueno and Kawamura, (2014), in Japanese, DOI: 10.1299/transjsme.2014tep0095) of a chaotic state in region of the space of parameters where on the basis of existing theories and earlier results for the classical liquid-bridge problem with organic fluids, the flow should be relatively regular in time and with a simple structure in space. Axisymmetric computations are used to obtain the steady basic state, and then the Navier Stokes equations are solved in their complete, three-dimensional, time-dependent and non-linear formulation to investigate the evolution of azimuthal disturbances. It is shown that the “apparent” doubling or quadrupling of the azimuthal wavenumber in the equatorial plane, previously reported for the case of floating zones of liquid metals, is replaced for high-Prandtl-number liquids by the complex interaction of disturbances with distinct spatial and temporal scales. These disturbances become critical at relatively comparable values of the Marangoni number. The unexpected multiplicity of waveforms and competition of spatial modes is explained according to the increased complexity of the considered system in terms of flow topology and structure with respect to the classical half-zone configuration.",
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On the onset of multi-wave patterns in laterally heated floating zones for slightly supercritical conditions. / Lappa, Marcello.

In: Physics of Fluids, Vol. 28, No. 12, 124105, 19.12.2016.

Research output: Contribution to journalArticle

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