Different Types of Convective Oscillations in Multilayer Systems
Ilya B. Simanovskii
Technion
Israel Institute of Technology
Abstract:
Convective phenomena in fluid systems with an interface have been a subject of an extensive investigation (for a review, see
1).
There are two basic physical phenomena that produce convective instability in systems with an interface: buoyancy and thermocapillary
effect. When heating is from below, the buoyancy instability generates the Rayleigh - Bénard convection
2, while the thermocapillary effect is the origin of the Marangoni - Bénard convection 3. The case where buoyancy and thermocapillary effect act simultaneously, is the most typical.
During the past few decades, a new scientific direction of investigation, convection in multilayer systems, was developed 4. Some new phenomena which arose as a result of the interaction between different interfaces, were discovered.
In the present work, the nonlinear regimes of convection in a multilayer system where the Marangoni convection is produced by the upper interface and hence developed in the top layer and in the middle layer, while the buoyancy convection is produced in the
bottom layer, are investigated. Two types of boundary conditions, the periodic boundary conditions on the lateral boundaries and rigid heat-insulated lateral walls, are considered.
In the case of periodic boundary conditions, it is shown that the joint action of buoyancy and thermocapillary effect, leads to the development of a specific type of nonlinear traveling wave. The thermocapillary convection in the top and middle layers coexists
with the buoyancy convection in the bottom layer. The maximum values of the stream function in all the layers are constant in time. The oscillatory flow keeps its periodicity even on a large distance from the linear stability boundary. The weakening of the thermocapillary effect leads to the development of the pulsating traveling wave in the system. For this flow, the maximum values of the stream function in all the layers are not constant in time and oscillate in a periodic way. The diagram of regimes on the plane 'the Grashof number - the Marangoni number' has been constructed.
For rigid heat-insulated lateral walls, various types of symmetric and asymmetric standing waves have been obtained. Transitions between the motions with different spatial structures have been investigated. It is found that for both, periodic boundary conditions and rigid heat-insulated lateral walls, the oscillatory motion is observed in a finite interval of the Grashof number values, between the stability regions of a quiescent state and stationary convection. The cavities with di®erent lengths have been considered.
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Department of Mathematics, Technion - Israel Institute of Technology, 32000 Haifa, Israel.
1. Simanovskii and Nepomnyashchy, Convective Instabilities in Systems with Interface, Gordon and Breach, London (1993).
2. Gershuni and Zhukhovitsky, Convective Stability of Incompressible Fluid, Keter, Jerusalem (1976).
3. Pearson, J. Fluid Mech., 4,489 (1958).
4. Nepomnyashchy, Simanovskii and Legros, I nterfacial Convection in Multilayer Systems, Springer, New York (2006).