Oscillatory Instability and High-Frequency Wave Modes in a Marangoni-Bénard Layer with Deformable Free Surface
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A. Ye. Rednikov
Abstract
A linear analysis of oscillatory thermocapillary instability associated with deformation of the free surface in a finite-depth horizontal liquid layer heated from above is carried out. First, we numerically solve the problem and determine the conditions of marginal stability. Then, assuming that Galileo and Marangoni numbers are large enough while the capillary number is small enough, which corresponds to the time scales of transverse and longitudinal oscillations related to the free surface being much smaller than the characteristic viscous and thermal time scales, we construct an asymptotic solution of the problem. Two high-frequency overstable modes—transverse (capillary-gravity waves) and longitudinal—are identified and analyzed. Mode-mixing occurring at their possible resonance is also studied.
Copyright (c)2000 by Walter de Gruyter GmbH & Co. KG
Articles in the same Issue
- Guest Editorial
- On the Role of Porosity in the Stokes Flow Around a Solid Particle
- Permanent Excitation of Standing Gravity Surface Waves by the Resonant Coalescence of Non-Coalescent Cold and Hot Pure Liquid
- Molecular Description of the Surface Tension of Curved Interfaces
- The Effect of Surfactants on Marangoni Convection in the Isobutanol/Water System
- Generalized Separation of Variables in Nonlinear Heat and Mass Transfer Equations
- Chaos and Hyperchaos in a Model of the Belousov-Zhabotinsky Reaction in a Batch Reactor
- Anomalous Damping of Capillary Waves With Surfactant Solutions
- A New Discrete Model for the Non-Isothermic Dynamics of the Exothermic CO-Oxidation on Palladium Supported Catalyst
- Foam Microgeometry
- Instabilities By Local Heating Below an Interface
- Oscillatory Instability and High-Frequency Wave Modes in a Marangoni-Bénard Layer with Deformable Free Surface
Articles in the same Issue
- Guest Editorial
- On the Role of Porosity in the Stokes Flow Around a Solid Particle
- Permanent Excitation of Standing Gravity Surface Waves by the Resonant Coalescence of Non-Coalescent Cold and Hot Pure Liquid
- Molecular Description of the Surface Tension of Curved Interfaces
- The Effect of Surfactants on Marangoni Convection in the Isobutanol/Water System
- Generalized Separation of Variables in Nonlinear Heat and Mass Transfer Equations
- Chaos and Hyperchaos in a Model of the Belousov-Zhabotinsky Reaction in a Batch Reactor
- Anomalous Damping of Capillary Waves With Surfactant Solutions
- A New Discrete Model for the Non-Isothermic Dynamics of the Exothermic CO-Oxidation on Palladium Supported Catalyst
- Foam Microgeometry
- Instabilities By Local Heating Below an Interface
- Oscillatory Instability and High-Frequency Wave Modes in a Marangoni-Bénard Layer with Deformable Free Surface
