Steady and oscillatory side-band instabilities in Marangoni convection with deformable interface

A. A. Golovin*, A. A. Nepomnyashchy, L. M. Pismen, H. Riecke

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

The stability of Marangoni roll convection in a liquid-gas system with deformable interface is studied in the case when there is a nonlinear interaction between two modes of Marangoni instability: long-scale surface deformations and short-scale convection. Within the framework of a model derived in [1], it is shown that the nonlinear interaction between the two modes substantially changes the width of the band of stable wave numbers of the short-scale convection pattern as well as the type of the instability limiting the band. Depending on the parameters of the system, the instability can be either long- or short-wave, either monotonic or oscillatory. The stability boundaries strongly differ from the standard ones and sometimes exclude the band center. The long-wave limit of the side-band instability is studied in detail within the framework of the phase approximation. It is shown that the monotonic instability is always subcritical, while the long-wave oscillatory instability can be supercritical, leading to the formation of either travelling or standing waves modulating the pattern wavelength and the surface deformation.

Original languageEnglish (US)
Pages (from-to)131-147
Number of pages17
JournalPhysica D: Nonlinear Phenomena
Volume106
Issue number1-2
DOIs
StatePublished - 1997

Keywords

  • Marangoni convection
  • Modulational waves
  • Side-band instability

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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