THE ROLE OF CHAOTIC ORBITS IN THE DETERMINATION OF POWER SPECTRA OF PASSIVE SCALARS

THE ROLE OF CHAOTIC ORBITS IN THE DETERMINATION OF POWER SPECTRA OF PASSIVE SCALARS
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混沌轨道在无源标量功率谱测定中的作用

DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
E. Garcia‐Lopez
E. Garcia‐Lopez
中科院分区：
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文献类型：
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作者：
T. Antonsen;Z. Fan;E. Ott;E. Garcia‐Lopez

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本文将被动标量受混沌流体对流作用的功率谱性质与有限时间李雅普诺夫指数的分布联系起来。考虑的属性包括早期的时间演变的功率谱，后期的标量方差的指数衰减，和波数依赖的功率谱中存在的源标量方差。理论预测进行了测试，通过比较完整的数值解的相关偏微分方程的模型系统，其中包括扩散，并涉及集成沿着流体轨道的解决方案。该模型系统示出的结果与完整的问题的数值解密切一致。这表明，可能的普遍效用的模型方程的范围广泛的问题，涉及被动标量对流。
This paper relates properties of the power spectrum of a passive scalar convected by a chaotic fluid flow to the distribution of finite time Lyapunov exponents. The properties considered include the early time evolution of the power spectrum, the late time exponential decay of the scalar variance, and the wave number dependence of the power spectrum in the presence of a source of scalar variance. Theoretical predictions are tested by comparing full numerical solutions of the relevant partial differential equation to solutions of a model system which includes diffusion and involves integrations along the fluid orbits only. The model system is shown to give results in close agreement with the numerical solutions of the full problem. This suggests the possible general utility of the model equations for a broad range of problems involving passive scalar convection.