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摘要翻译：
最近建立的一个数学等价--弱扰动惠更斯锋（例如，弱湍流中的火焰或轻微非均匀介质中的几何光学波锋）与白噪声驱动的Burgers湍流的无粘极限--激发了对特定类型的时间内白强迫的Burgers湍流性质的理论和数值估计。利用Burgers湍流与定向聚合物统计力学之间已有的数学关系，利用复本方法，得到了对应于定向聚合物基态结合能和惠更斯前沿加速比的Burgers能量密度的系统上界。这一结果补充了先前对Burgers湍流和定向聚合物的研究，这些研究集中在普遍的标度性质上，而不是依赖于强迫的参数。结果表明，在一定湍流强度下，理想湍流火焰的燃烧速度不随雷诺数的增加而发散，这一结论甚至适用于强湍流情况。用拉格朗日有限元方法对一维无粘Burgers方程的数值模拟表明，对于不同的强迫谱（对应于不同的二维随机介质），理论上界在15%左右。这些计算结果为复本方法提供了一个新的定量检验。前加速比的非普适性（谱依赖性）对燃烧模型有直接的重要性。
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英文标题：
《Fronts in randomly advected and heterogeneous media and nonuniversality
of Burgers turbulence: Theory and numerics》
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作者：
Jackson R. Mayo and Alan R. Kerstein (Sandia National Laboratories)
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最新提交年份：
2008
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：Chaotic Dynamics 混沌动力学
分类描述：Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统，混沌，量子混沌，拓扑动力学，循环展开，湍流，传播
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英文摘要：
A recently established mathematical equivalence--between weakly perturbed Huygens fronts (e.g., flames in weak turbulence or geometrical-optics wave fronts in slightly nonuniform media) and the inviscid limit of white-noise-driven Burgers turbulence--motivates theoretical and numerical estimates of Burgers-turbulence properties for specific types of white-in-time forcing. Existing mathematical relations between Burgers turbulence and the statistical mechanics of directed polymers, allowing use of the replica method, are exploited to obtain systematic upper bounds on the Burgers energy density, corresponding to the ground-state binding energy of the directed polymer and the speedup of the Huygens front. The results are complementary to previous studies of both Burgers turbulence and directed polymers, which have focused on universal scaling properties instead of forcing-dependent parameters. The upper-bound formula can be heuristically understood in terms of renormalization of a different kind from that previously used in combustion models, and also shows that the burning velocity of an idealized turbulent flame does not diverge with increasing Reynolds number at fixed turbulence intensity, a conclusion that applies even to strong turbulence. Numerical simulations of the one-dimensional inviscid Burgers equation using a Lagrangian finite-element method confirm that the theoretical upper bounds are sharp within about 15% for various forcing spectra (corresponding to various two-dimensional random media). These computations provide a new quantitative test of the replica method. The inferred nonuniversality (spectrum dependence) of the front speedup is of direct importance for combustion modeling.
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PDF链接：
https://arxiv.org/pdf/712.2668
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