扩展Duchon-Robert框架以处理压缩流体中的异常耗散
Extending the Duchon-Robert framework for anomalous dissipation to compressible fluid flows
AI总结：
本文扩展Duchon-Robert框架以研究压缩流体中的异常耗散，通过分析激波前沿和比较两种理论，揭示了压缩性效应的对应关系。
摘要：
异常耗散是指当雷诺数趋于无穷大时，平均动能耗散仍保持有限的现象，发生在速度场足够空间粗糙的流动中。可压缩湍流进一步引入了额外的异常耗散机制，本文对此进行了研究。为此，将Duchon-Robert框架（DR）从不可压缩扩展到可压缩纳维-斯托克斯流情况。我们得到了三个积分耗散项，两个异常和一个粘性项，它们分别来自压力-膨胀和密度变化，与不可压缩情况不同。随后，详细分析了完全可压缩的一维流动，其中包含传播和相互交叉的激波波。在这些流动中，DR揭示了在激波前沿处存在局部异常耗散的最大值。此外，DR与Aluie（AL）提出的可压缩湍流粗粒 cascade 理论进行了比较，识别并比较了两种框架的相关耗散通量项。比较表明，DR中与压缩性效应相关的每个贡献都有其在AL中的对应项。最后，使用了一种分段线性的激波型速度分布，该分布近似了模拟中两个激波波的交叉，用于分析DR的异常耗散项，并分析这些项对局部Hölder指数的依赖性。本工作是向比较压缩湍流中相干流动结构及其相关异常耗散迈出的第一步。
英文摘要：
Anomalous dissipation, the persistence of a finite mean kinetic energy dissipation as the Reynolds number tends to infinity, occurs in flows with sufficiently spatially rough velocity fields. Compressible turbulence adds further anomalous dissipation mechanisms, which we investigate in this work. To this end, the Duchon-Robert framework (DR) for anomalous dissipation is extended from the incompressible to the compressible Navier-Stokes flow case. We obtain three integral dissipation terms, two anomalous and a viscous one, which arise from the pressure-dilatation and density variations, differently from the incompressible case. Subsequently, fully compressible one-dimensional flows with traveling and mutually crossing shock waves are analysed in detail. In such flows, DR reveals a local maximum of anomalous dissipation at the shock front. Furthermore, DR is compared with a coarse-grain cascade theory of compressible turbulence due to Aluie (AL) and the relevant dissipation flux terms of both frameworks are identified and compared with each other. The comparison shows that each contribution related to the compressibility effects in DR has its analogue in AL. Finally, a piecewise linear shock-type velocity profile, which approximates the crossing of two shock waves from the simulations, is used for an analytical analysis of the anomalous dissipation terms of DR to analyse the dependence of the terms on the local Hölder exponent. Our work is a first step towards a comparison of coherent flow structures in a compressible turbulent flow and related anomalous dissipation.
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