Verma, Mahendra K ; Kumar, Krishna ; Kamble, Bhask Ar (2006) Mode-to-mode energy transfers in convective patterns Pramana - Journal of Physics, 67 (6). pp. 1129-1140. ISSN 0304-4289
Full text not available from this repository.
Official URL: https://doi.org/10.1007%2Fs12043-006-0028-7
Abstract
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 R c. 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.
Item Type: | Article |
---|---|
Source: | Copyright of this article belongs to Indian Academy of Sciences. |
Keywords: | Convection; Patterns. |
ID Code: | 119057 |
Deposited On: | 07 Jun 2021 11:24 |
Last Modified: | 07 Jun 2021 11:24 |
Repository Staff Only: item control page