## Abstract

Energy stability theory has been formulated for two-dimensional buoyancy–thermocapillary convection in a layer with a free surface. The theory yields a critical Rayleigh number R_{E} for which R < R_{E} is a sufficient condition for stability of the layer. R_{E} emerges from the variational formulation as an eigenvalue of a nonlinear system of Euler–Lagrange equations. For the case of small capillary number (large mean surface tension) explicit values are obtained for R_{E}. The analogous linear-theory results for this case are obtained in terms of a critical Rayleigh number R_{L}. These are compared. It is found that the existence of the deformable interface can lead to a stabilization relative to the case of a planar interface. This result is explained in physical terms. The energy theory is then generalized to include general flow problems having three-dimensional disturbances, non-Newtonian bulk fluids and general interfacial mechanics such as surface viscosity and elasticity.

Original language | English (US) |
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Pages (from-to) | 527-553 |

Number of pages | 27 |

Journal | Journal of fluid Mechanics |

Volume | 98 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1980 |

## ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics