Physics – Fluid Dynamics
Scientific paper
2010-05-30
Physics
Fluid Dynamics
16 pages, 13 figures
Scientific paper
We investigate the origin of various convective patterns using bifurcation diagrams that are constructed using direct numerical simulations. We perform two-dimensional pseudospectral simulations for a Prandtl number 6.8 fluid that is confined in a box with aspect ratio $\Gamma = 2\sqrt{2}$. Steady convective rolls are born from the conduction state through a pitchfork bifurcation at $r=1$, where $r$ is the reduced Rayleigh number. These fixed points bifurcate successively to time-periodic and quasiperiodic rolls through Hopf and Neimark-Sacker bifurcations at $r \simeq 80$ and $r \simeq 500 $ respectively. The system becomes chaotic at $r \simeq 750$ through a quasiperiodic route to chaos. The size of the chaotic attractor increases at $r \simeq 840$ through an "attractor-merging crisis" which also results in travelling chaotic rolls. We also observe coexistence of stable fixed points and a chaotic attractor for $ 846 \le r \le 849$ as a result of a subcritical Hopf bifurcation. Subsequently the chaotic attractor disappears through a "boundary crisis" and only stable fixed points remain. Later these fixed points become periodic and chaotic through another set of bifurcations which ultimately leads to turbulence.
Kumar Krishna
Paul Supriyo
Reddy Sandeep K.
Verma Mahendra K.
Wahi Pankaj
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