Mode-to-mode energy transfers in convective patterns

Pramana

Bhaskar Kamble²  Krishna Kumar¹  Mahendra K Verma1² 

[1] Department of Physics, Indian Institute of Technology Kharagapur, Kharagpur 721 302, India$$;Department of Physics, Indian Institute of Technology Kanpur, Kanpur 208 016, India$$

关键词: Convection;    patterns.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We investigate the energy transfer between various Fourier modes in a low-dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical equations for thermal convection in Boussinesq fluids. Numerical and analytical studies of this model show that convective rolls appear as the Rayleigh number 𝑅 is raised above its critical value 𝑅c. Further increase of Rayleigh number generates rolls in the perpendicular directions as well, and we obtain a dynamic asymmetric square pattern. This pattern is due to Hopf bifurcation. There are two sets of limit cycles corresponding to the two competing asymmetric square patterns. When the Rayleigh number is increased further, the limit cycles become unstable simultaneously, and chaotic motion sets in. The onset of chaos is via intermittent route. The trajectories wander for quite a long time almost periodically before jumping irregularly to one of the two ghost limit cycles.

【 授权许可】

Unknown