发表机构
Universität Konstanz（康斯坦茨大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过完全分辨的DIA数值解，发现涨落-耗散关系仅在大尺度成立，惯性区衰减时间与直接数值模拟一致，展示了DIA在捕捉时域动力学方面的能力。
AI 中文摘要
Kraichnan的直接相互作用近似（DIA）为均匀湍流提供了一个经典的闭合框架，然而其跨所有尺度的定量预测仍未得到完全理解。我们在不添加额外建模假设的情况下，给出了受迫DIA方程的完全分辨数值解，从而能够在所有波数上对平稳谱性质和时域动力学进行一致的分析。主要关注点在于归一化速度相关函数与线性响应格林函数之间的涨落-耗散关系。该关系仅在大尺度上成立，在惯性区和耗散区则被系统性违反。这种违反的非高斯性质通过DIA的非马尔可夫方程编码其中，尽管DIA可以通过随机场泛函中的高斯平均场近似推导出来。在惯性区，特征衰减时间与直接数值模拟得到的结果定量一致，而在耗散区则出现偏差。这些结果凸显了DIA在预测谱标度方面存在局限性的同时，仍能捕捉时域动力学的能力。
英文摘要
Kraichnan's Direct Interaction Approximation (DIA) provides a classical closure framework for homogeneous turbulence, yet its quantitative predictions across all scales remain incompletely understood. We present a fully resolved numerical solution of the forced DIA equations without additional modelling assumptions, enabling a consistent analysis of stationary spectral properties and temporal dynamics across all wavenumbers. The main focus is on the fluctuation-dissipation relation between the normalised velocity correlation function and the Green function of linear response. This relation holds only at large scales and is systematically violated in the inertial and dissipation ranges. The non-Gaussian nature of this violation is encoded in the DIA through its non-Markovian equations, even though the DIA can be derived using a Gaussian mean-field approximation in the stochastic field functional. In the inertial range, characteristic decay times agree quantitatively with those obtained from direct numerical simulations, while deviations arise in the dissipation range. These results highlight the ability of the DIA to capture temporal dynamics despite its limitations in predicting spectral scaling.
Comments51 pages, 23 figures
