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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >An investigation into the maximum entropy production principle in chaotic Rayleigh-Bénard convection
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An investigation into the maximum entropy production principle in chaotic Rayleigh-Bénard convection

机译：混沌瑞利-贝纳德对流中最大熵产生原理的研究

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摘要

The hypothesis is made that the temperature and velocity fields in Rayleigh-Bénard convection can be expressed as a superposition of the active modes with time-dependent amplitudes, even in the chaotic regime. The maximum entropy production principle is interpreted as a variational principle in which the amplitudes of the modes are the variational degrees of freedom. For a given Rayleigh number, the maximum heat flow for any set of amplitudes is sought, subject only to the constraints that the energy equation be obeyed and the fluid be incompressible. The additional hypothesis is made that all temporal correlations between modes are zero, so that only the mean-squared amplitudes are optimising variables. The resulting maximal Nusselt number is close to experimental determinations. The Nusselt number would appear to be simply related to the number of active modes, in particular the number of distinct vertical modes. It is significant that reasonable results are obtained for the optimised Nusselt number in that the dynamics (the Navier-Stokes equation) is not used as a constraint. This suggests grounds for optimism that the maximum entropy production principle, interpreted in this variational manner, can provide a reasonable guide to the dynamic steady states of non-equilibrium systems whose detailed dynamics are unknown.
机译：假设是，即使在混沌状态下，Rayleigh-Bénard对流中的温度场和速度场也可以表示为具有随时间变化幅度的活动模式的叠加。最大熵产生原理被解释为变分原理，其中模的振幅是变化的自由度。对于给定的瑞利数，仅在遵守能量方程且流体不可压缩的约束下，寻求任何振幅集的最大热流。另外的假设是，模式之间的所有时间相关性均为零，因此只有均方振幅才是优化变量。最终的最大努塞尔数接近于实验确定。努塞尔数似乎仅与活动模式的数量有关，特别是与不同垂直模式的数量有关。重要的是，由于动力学（Navier-Stokes方程）没有用作约束，因此对于优化的Nusselt数可以获得合理的结果。这暗示了乐观的理由，即以这种变化的方式解释的最大熵产生原理可以为详细动力学未知的非平衡系统的动态稳态提供合理的指导。

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