Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations, standard strategies involve a smoothing of the fluid dynamics, either through time averaging or spatial filtering. These strategies raise formal issues in general relativity, where the split between space and time is observer dependent. To make progress, we develop a new covariant framework for filtering/averaging based on the fibration of spacetime associated with fluid elements and the use of Fermi coordinates to facilitate a meaningful local analysis. We derive the resolved equations of motion, demonstrating how “effective” dissipative terms arise because of the coarse-graining, and paying particular attention to the thermodynamical interpretation of the resolved quantities. Finally, as the smoothing of the fluid dynamics inevitably leads to a closure problem, we propose a new closure scheme inspired by recent progress in the modeling of dissipative relativistic fluids, and crucially, demonstrate the linear stability of the proposed model.

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相对论大涡模拟的协变方法：纤维化图片

湍流模型需要大量尺度的分辨率，从大涡流到与耗散直接相关的小尺度特征。由于所需的分辨率不在大规模数值模拟范围内，因此标准策略涉及通过时间平均或空间过滤来平滑流体动力学。这些策略在广义相对论中提出了形式问题，其中空间和时间之间的分裂取决于观察者。为了取得进展，我们基于与流体元素相关的时空纤维化和费米坐标的使用，开发了一个用于过滤/平均的新协变框架，以促进有意义的局部分析。我们推导出已解析的运动方程，展示了“有效”耗散项是如何由于粗粒度而产生的，并特别注意解析量的热力学解释。最后，由于流体动力学的平滑不可避免地导致闭合问题，我们提出了一种新的闭合方案，其灵感来自耗散相对论流体建模的最新进展，并且至关重要的是，证明了所提出模型的线性稳定性。