Abstract
The rotating Rayleigh-Benard convection in the presence of helical force is modeled by a four mode Lorenz model. This model is extended to study how this force affects the onset of Kuppers-Lortz (KL) instability. We observed that when S < 3ߨ , the critical Taylor number and the critical angle for the onset of KL instability decrease as helical force intensity S increases. This influence of helical force is similar to that obtained in rotating fluid layer under periodic modulation of the rotation rate (Bhattacharjee, 1990). In the range 3 S 14.9246, the system exhibits the reentrant behavior of rolls demonstrating the constructive and destructive role of rotation in the KL instability apparition. In this case, we observed that the application of this force allows the KL instability for small values of Taylor number. In addition, it has been found that there exists a threshold (14.9246) in the magnitude of the helical force that allows suppressing the KL instability in the system for any value of Taylor number.
Highlights
Rayleigh-Bénard convection in a plane layer heated from below and rotating about a vertical axis, has been the objects of special attention motivated by both astrophysical and geophysical applications and by the existence of additional instabilities occuring in this system
The rotating Rayleigh-Bénard convection in the presence of helical force is modeled by a four mode Lorenz model
We observed that when S < 3, the critical Taylor number and the critical angle for the onset of KL instability decrease as helical force intensity S increases
Summary
Rayleigh-Bénard convection in a plane layer heated from below and rotating about a vertical axis, has been the objects of special attention motivated by both astrophysical and geophysical applications and by the existence of additional instabilities occuring in this system. Küppers and Lortz (1969) reported that for an infinite Prandtl number in a rotating Rayleigh-Bénard system with free-free boundary conditions, at the onset of stationary convection, the roll solution was unstable to perturbations by rolls with different axes when the Taylor number (which measures the rotation rate) exceeds the critical value 2285 and the angle close to 58° These new sets of rolls are unstable This process continues resulting in complex dynamics. In (Levina et al, 2000), the authors have proposed the special force called helical force that has the structure of the alpha term, which provides excitation of large-scale instability within the framework of the model of the hydrodynamic alpha-effect in a convective system This force simulates the influence of small-scale helical turbulence which is generated in a rotating fluid with internal heat sources (Rutkevich, 1993).
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