arXiv 0908.40082009-08astro-ph.SRnlin.CDphysics.flu-dyn

湍流热对流中的混沌平均风和太阳活动的长期相关

Chaotic mean wind in turbulent thermal convection and long-term correlations in solar activity

A. Bershadskii

备注：: extended version

摘要：

结果表明，湍流热对流中平均风速的关联函数（瑞利数$Ra \sim 10^{11}$）在很长的相关时间内呈指数衰减，而相应的最大李雅普诺夫指数肯定为正。这些结果与重建的相图一起表明在所研究的平均风中存在混沌分量。电报近似也被用来研究混沌和随机分量的平均风波动的相对贡献和这些组件之间的平衡进行了研究。由于太阳活动是建立在热对流过程的基础上的，因此可以推断，观测到的太阳活动长期相关性可以是平均风混沌特性的一个印记。特别是，日黑子数的关联函数呈现指数衰减，关联时间很长，对应的最大李雅普诺夫指数肯定为正，混沌和随机分量的相对贡献也遵循与对流平均风相同的模式。

英文摘要：

It is shown that correlation function of the mean wind velocity in a turbulent thermal convection (Rayleigh number $Ra \sim 10^{11}$) exhibits exponential decay with a very long correlation time, while corresponding largest Lyapunov exponent is certainly positive. These results together with the reconstructed phase portrait indicate presence of a chaotic component in the examined mean wind. Telegraph approximation is also used to study relative contribution of the chaotic and stochastic components to the mean wind fluctuations and an equilibrium between these components has been studied. Since solar activity is based on the thermal convection processes, it is reasoned that the observed solar activity long-term correlations can be an imprint of the mean wind chaotic properties. In particular, correlation function of the daily sunspots number exhibits exponential decay with a very long correlation time and corresponding largest Lyapunov exponent is certainly positive, also relative contribution of the chaotic and stochastic components follows the same pattern as for the convection mean wind.

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