dorsal/arxiv
View SchemaConvective instabilities in two superposed horizontal liquid layers heated laterally
| Authors | S. Madruga, C. Perez-Garcia, G. Lebon |
|---|---|
| Categories | |
| ArXiv ID | physics/0308081 |
| URL | https://arxiv.org/abs/physics/0308081 |
| DOI | 10.1103/PhysRevE.68.041607 |
Abstract
This work is devoted to the theoretical study of the stability of two superposed horizontal liquid layers bounded by two solid planes and subjected to a horizontal temperature gradient. The liquids are supposed to be immiscible with a nondeformable interface. The forces acting on the system are buoyancy and interfacial tension. Four different flow patterns and temperature profiles are found for the basic state. A linear perturbative analysis with respect to two and three dimensional perturbations reveals the existence of three kind of patterns. Depending on the relative height of both liquids several situations are predicted: either wave propagation from cold to the hot regions, or waves propagating in the opposite direction or still stationary longitudinal rolls. The behavior of three different pairs of liquids which have been used in experiments on bilayers under vertical gradient by other authors have been examined. The instability mechanisms are discussed and a qualitative interpretation of the different behaviors exhibited by the system is provided. In some configurations it is possible to find a codimension-two point created by the interaction of two Hopf modes with different frequencies and wavenumbers. These results suggest to consider two liquid layers as an interesting prototype for the study of propagation and interaction of waves in the context of the B\'enard-Marangoni problem.
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"abstract": "This work is devoted to the theoretical study of the stability of two\nsuperposed horizontal liquid layers bounded by two solid planes and subjected\nto a horizontal temperature gradient.\n The liquids are supposed to be immiscible with a nondeformable interface.\n The forces acting on the system are buoyancy and interfacial tension. Four\ndifferent flow patterns and temperature profiles are found for the basic state.\nA linear perturbative analysis with respect to two and three dimensional\nperturbations reveals the existence of three kind of patterns. Depending on the\nrelative height of both liquids several situations are predicted: either wave\npropagation from cold to the hot regions, or waves propagating in the opposite\ndirection or still stationary longitudinal rolls. The behavior of three\ndifferent pairs of liquids which have been used in experiments on bilayers\nunder vertical gradient by other authors have been examined. The instability\nmechanisms are discussed and a qualitative interpretation of the different\nbehaviors exhibited by the system is provided. In some configurations it is\npossible to find a codimension-two point created by the interaction of two Hopf\nmodes with different frequencies and wavenumbers. These results suggest to\nconsider two liquid layers as an interesting prototype for the study of\npropagation and interaction of waves in the context of the B\\\u0027enard-Marangoni\nproblem.",
"arxiv_id": "physics/0308081",
"authors": [
"S. Madruga",
"C. Perez-Garcia",
"G. Lebon"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1103/PhysRevE.68.041607",
"title": "Convective instabilities in two superposed horizontal liquid layers heated laterally",
"url": "https://arxiv.org/abs/physics/0308081"
},
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