Department of Physics, Indian Institute of Technology, Kanpur 208 016, India.
Chaos. 2011 Jun;21(2):023118. doi: 10.1063/1.3591793.
We present a detailed bifurcation scenario of zero-Prandtl number Rayleigh-Bénard convection using direct numerical simulations (DNS) and a 27-mode low-dimensional model containing the most energetic modes of DNS. The bifurcation analysis reveals a rich variety of convective flow patterns and chaotic solutions, some of which are common to that of the 13-mode model of Pal et al. [EPL 87, 54003 (2009)]. We also observed a set of periodic and chaotic wavy rolls in DNS and in the model similar to those observed in experiments and numerical simulations. The time period of the wavy rolls is closely related to the eigenvalues of the stability matrix of the Hopf bifurcation points at the onset of convection. This time period is in good agreement with the experimental results for low-Prandtl number fluids. The chaotic attractor of the wavy roll solutions is born through a quasiperiodic and phase-locking route to chaos.
我们使用直接数值模拟（DNS）和包含最具活力模式的 27 模式低维模型，呈现了零普朗特数瑞利-贝纳对流的详细分岔情景。分岔分析揭示了丰富多样的对流流动模式和混沌解，其中一些与 Pal 等人的 13 模式模型的解相同。[EPL 87, 54003 (2009)]。我们还在 DNS 和模型中观察到了一组类似于实验和数值模拟中观察到的周期性和混沌波状滚流。波状滚流的时间周期与对流起始时 Hopf 分岔点的稳定矩阵特征值密切相关。这个时间周期与低普朗特数流体的实验结果非常吻合。波状滚流解的混沌吸引子是通过准周期和锁相到混沌的途径产生的。
