标题： 可压缩湍流：级串及其局部性 显示英文标题

标题： Compressible Turbulence: The Cascade and its Locality

摘要： 我们证明，在可压缩湍流中，动能的尺度间转换主要由局部相互作用主导。特别是，我们的结果排除了在高雷诺数湍流中动能从大尺度直接转移到耗散尺度（如激波）的直接转移，这与通常的观点不同。 我们对结构函数尺度的假设较为微弱，并且得到了有力的经验支持。 在压力膨胀共谱有一个更强的假设下，我们表明平均动能和内能预算在超过一个过渡的“转换”范围后在统计上解耦。 我们的分析证实了随后存在一个惯性范围，在这个范围内，平均次网格动能通量变得恒定，不依赖于尺度。 在这个惯性范围内，尽管平均动能不是一个不变量，它仍然能够局部地、保守地级串。 显示英文摘要

摘要： We prove that inter-scale transfer of kinetic energy in compressible turbulence is dominated by local interactions. In particular, our results preclude direct transfer of kinetic energy from large-scales directly to dissipation scales, such as into shocks, in high Reynolds number turbulence as is commonly believed. Our assumptions on the scaling of structure functions are weak and enjoy compelling empirical support. Under a stronger assumption on pressure dilatation co-spectrum, we show that mean kinetic and internal energy budgets statistically decouple beyond a transitional "conversion" range. Our analysis establishes the existence of an ensuing inertial range over which mean SGS kinetic energy flux becomes constant, independent of scale. Over this inertial range, mean kinetic energy cascades locally and in a conservative fashion, despite not being an invariant.