Combined Effects of a Magnetic Field and a Helical Force on the Onset of a Rotating Rayleigh-Bénard Convection With Free-Free Boundaries

G Pomalégni,Jean Bio Chabi Orou

doi:10.5539/apr.v6n6p87

Abstract

We investigate the combined effects of rotation, magnetic field and helical force on the onset of stationary and oscillatory convection in a horizontal electrically conducting fluid layer heated from below with free-free boundary conditions. For this investigation the linear stability analysis studied in detail by Chandrasekhar (1961) is used. We obtain the condition for the formation of a single large-scale structure. In (Pomalegni et al., 2014) it was shown the existence of a critical value of the intensity of the helical force for which the apparition of two cells at marginal stability for the oscillatory convection is obtained. Then, we have shown here how the increasing of parameter Ta influences this critical value of the helical force intensity.

Highlights

The rotating Rayleigh-Bénard convection (Busse & Heikes, 1980; Cox & Mattews, 2000) and the Rayleigh-Bénard convection in the presence of a magnetic field possess control parameters which are the Taylor number characteristic of the rotation and the Chandrasekhar number characteristic of magnetic field
We have shown from figures 1, 2 and 3 the respective influence of the parameters S, Q and Ta on the onset of the stationary convection
The combined effects of the magnetic field, rotation and the helical force on the onset of stationary and oscillatory convections in a horizontal electrically conducting fluid layer heated from below with free-free boundary conditions are examined by the application of the linear stability analysis

Summary

Introduction

The rotating Rayleigh-Bénard convection (Busse & Heikes, 1980; Cox & Mattews, 2000) and the Rayleigh-Bénard convection in the presence of a magnetic field possess control parameters which are the Taylor number characteristic of the rotation and the Chandrasekhar number characteristic of magnetic field. The generating properties of small-scale helical turbulence were first discovered in magnetohydrodynamic (Steenbeck et al, 1966) According to (Essoun & Chabi Orou, 2010), for the free-free boundary conditions, it was found that in the presence of rotation, the helical force has the no- monotonic effects on the onset of convection for all values of Taylor number but decreases the corresponding critical wave number for any value of Taylor number. Pomalégni et al (2014) has shown that the helical force has the no- monotonic effects on both the onset of stationary and oscillatory convection in the presence of a magnetic field with free-free boundaries. We use in this work, the classical linear stability analysis to examine the combined effects of the magnetic field, the rotation and the helical force on the onset of stationary and oscillatory convections with free-free boundaries. Vol 6, No 6; 2014 increasing of the parameter Ta influences the critical value of the intensity of helical force for which we have the apparition of two cells at marginal stability for the oscillatory convection

Mathematical Formulation of the Problem

Linear Stability Analysis

Results and Discussion

Conclusion