### Abstract

In this paper we use classical linear stability theory to analyse the onset of thermocapillary-driven Marangoni convection in a semi-infinitely deep layer of quiescent fluid. We use a combination of analytical and numerical techniques to obtain for the first time a detailed description of the marginal stability curves for the onset of oscillatory convection. We perform a comprehensive asymptotic analysis of the marginal curves in the limits of both long-wave and short-wave perturbations and present the results of numerical calculations which illustrate the effect of varying the problem parameters on the marginal curves and hence on the critical Marangoni number, frequency of oscillation and wavenumber for the onset of convection.

Original language | English |
---|---|

Pages (from-to) | 546-558 |

Number of pages | 13 |

Journal | Zeitschrift fur Angewandte Mathematik und Physik |

Volume | 50 |

Issue number | 4 |

Publication status | Published - Jul 1999 |

### Fingerprint

### Keywords

- Marangoni
- Oscillatory convection
- Stability
- Thermocapillary

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Zeitschrift fur Angewandte Mathematik und Physik*,

*50*(4), 546-558.

**The onset of oscillatory Marangoni convection in a semi-infinitely deep layer of fluid.** / Hashim, Ishak; Wilson, S. K.

Research output: Contribution to journal › Article

*Zeitschrift fur Angewandte Mathematik und Physik*, vol. 50, no. 4, pp. 546-558.

}

TY - JOUR

T1 - The onset of oscillatory Marangoni convection in a semi-infinitely deep layer of fluid

AU - Hashim, Ishak

AU - Wilson, S. K.

PY - 1999/7

Y1 - 1999/7

N2 - In this paper we use classical linear stability theory to analyse the onset of thermocapillary-driven Marangoni convection in a semi-infinitely deep layer of quiescent fluid. We use a combination of analytical and numerical techniques to obtain for the first time a detailed description of the marginal stability curves for the onset of oscillatory convection. We perform a comprehensive asymptotic analysis of the marginal curves in the limits of both long-wave and short-wave perturbations and present the results of numerical calculations which illustrate the effect of varying the problem parameters on the marginal curves and hence on the critical Marangoni number, frequency of oscillation and wavenumber for the onset of convection.

AB - In this paper we use classical linear stability theory to analyse the onset of thermocapillary-driven Marangoni convection in a semi-infinitely deep layer of quiescent fluid. We use a combination of analytical and numerical techniques to obtain for the first time a detailed description of the marginal stability curves for the onset of oscillatory convection. We perform a comprehensive asymptotic analysis of the marginal curves in the limits of both long-wave and short-wave perturbations and present the results of numerical calculations which illustrate the effect of varying the problem parameters on the marginal curves and hence on the critical Marangoni number, frequency of oscillation and wavenumber for the onset of convection.

KW - Marangoni

KW - Oscillatory convection

KW - Stability

KW - Thermocapillary

UR - http://www.scopus.com/inward/record.url?scp=0033245870&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033245870&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033245870

VL - 50

SP - 546

EP - 558

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 4

ER -