Amplitude equations for Rayleigh-Benard convective rolls far from threshold

An extension of the amplitude method is proposed. An iterative algorithm is developed to build an amplitude equation model that is shown to provide precise quantitative results even far from the linear instability threshold. The method is applied to the study of stationary Rayleigh-Benard thermoconvective rolls in the nonlinear regime. In particular, the generation of second and third spatial harmonics is analyzed. Comparison with experimental results and direct numerical calculations is also made and a very good agreement is found.Peer reviewe

Analyse de stabilité linéaire d'un ferrofluide saturant un milieu poreux en rotation

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Coupling between Rayleigh-Benard and rotation for a ferrofluid in a normal strong magnetic field

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Linear coupling between the Rayleigh-Benard instability and rotation for a ferrofluid in a normal strong magnetic field

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Rayleigh-Marangoni-Benard instability of a Ferrofluid Layer, in a Vertical Magnetic Field

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Steady flows of a laterally heated ferrofluid layer: Influence on inclined strong magnetic field and gravity level

A horizontal ferrofluid layer is submitted to a lateral heating and to a strong oblique magnetic field. The problem, combining the momentum and heat balance equations with the Maxwell equations, introduces two Rayleigh numbers, Ra the gravitational one and Ram the magnetic one, to represent the buoyancy and the Kelvin forces, which induce motion, versus the momentum viscous diffusion and heat diffusion. Whatever the inclination of the magnetic field, the steady solution of the problem is presented as a power series of a small parameter eps_H measuring the ratio of variation of the magnetization across the layer divided by the magnitude of the external imposed field. For cases of physical relevance, comparisons between analytical and numerical studies have lead to a major statement: in the strong field region eps_H<<1 the zero order solution is the product of the Birikh solution that corresponds to the usual Newtonian fluid submitted to a lateral gradient, multiplied by a modulating factor accounting for inclination and both Rayleigh numbers. Physically, this simplified solution is valid for microgravity conditions where the magnetic field competes enough with microgravity effects to invert the laminar flow and thus suppress the motion for two specific values of the inclination angle.info:eu-repo/semantics/publishe

Coupled capillary and gravity-driven instability in a liquid film overlying a porous layer.

In this work, we study the problem of onset of thermal convection in a fluid layer overlying a porous layer, the whole system being heated from below. We use Brinkman's model to describe the porous medium and determine the corresponding linear stability equations. The eigenvalue problem is solved by means of a modified Galerkin method. The behavior of the critical wave number and temperature gradient is discussed in terms of the various parameters of the system. We also emphasize the influence of the boundary conditions at the upper surface of the fluid layer; in particular, we examine the role of a free surface whose surface tension is temperature dependent (Marangoni effect). Comparison with earlier works is also made.Journal ArticleSCOPUS: ar.jSCOPUS: ar.jSCOPUS: ar.jinfo:eu-repo/semantics/publishe