随机平流和非均匀介质中的锋面和Burgers turbulence的非普适性：理论和数值
Fronts in randomly advected and heterogeneous media and nonuniversality of Burgers turbulence: Theory and numerics
摘要：
最近建立的数学等价性--弱扰动惠更斯波前（例如，火焰在弱湍流或几何光学波前在稍微不均匀的介质）和白噪声驱动的Burgers湍流的无粘极限-激励理论和数值估计的Burgers湍流特性的特定类型的白时间强迫。Burgers湍流和定向聚合物的统计力学之间的现有数学关系，允许使用的副本方法，利用获得系统的上界的Burgers能量密度，对应于基态的定向聚合物的结合能和惠更斯前的加速。这些结果是对以前Burgers湍流和定向聚合物研究的补充，这些研究集中在通用的标度特性，而不是强迫依赖的参数。上限公式可以根据与以前燃烧模型中使用的不同类型的重整化来启发式地理解，并且还表明，在固定的湍流强度下，理想化湍流火焰的燃烧速度不会随着雷诺数的增加而发散，这一结论甚至适用于强湍流。数值模拟的一维无粘Burgers方程使用拉格朗日有限元方法证实，理论上的上限是尖锐的各种强迫谱（对应于各种二维随机介质）约15%。这些计算提供了一个新的定量测试的副本方法。推断的非普适性（频谱依赖）的前端加速是燃烧建模的直接重要性。
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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