论文标题
二维不可压缩的高雷诺数Navier-Stokes湍流的长期命运：理论与仿真之间的定量比较
Long time fate of two-dimensional incompressible high Reynolds number Navier-Stokes turbulence: A quantitative comparison between theory and simulation
论文作者
论文摘要
预测二维不可压缩的高雷诺数的长时间或迟到的状态，缓慢腐烂的湍流一直是长期存在的问题之一。使用``点涡旋''作为``Inviscid''的构建模块，不尊重不可压缩性，仅保存总能量的统计机械模型和零总循环导致了众所周知的SINH-POISSON关系，涡流和流函数之间的关系。另一方面，``无粘性斑块''涡流的统计力学通过保存零和非零涡度的区域来尊重不可压缩性，预测了一种广义的放松状态，与直接数值模拟（DNS）相比，这种宽松状态从未系统地进行系统。在这项研究中，从非零初始涡度的高度填充区域开始，我们证明了使用高分辨率，高雷诺数DNS，即较晚的时间状态与斑块涡流模型的预测一致。随着总循环的减少或稀释，我们表明我们的DNS的较晚时间是系统地，明确地导致涡度和流功能之间的Sinh-Poisson关系。我们认为，我们的定量发现解决了二维湍流中长期存在的问题之一。
Predicting the long time or late time states of two-dimensional incompressible, high Reynolds number, slowly decaying turbulence has been one of the long-standing problems. Using ``point vortices'' as ``inviscid'' building blocks, which do not respect incompressibility, statistical mechanical models conserving only total energy and zero total circulation result in the well-known sinh-Poisson relation between vorticity and stream function. On the other hand, statistical mechanics of ``inviscid patch'' vortices, which respects incompressibility by conserving regions of zero and nonzero vorticity, predicts a generalized relaxed state, which has never been systematically compared with direct numerical simulations (DNS). In this study, starting from highly packed regions of nonzero initial vorticity, we demonstrate using high resolution, high Reynolds number DNS that the late time states agree with predictions from patch vortex models. As total circulation is reduced or diluted, we show that late time states of our DNS systematically and unambiguously lead to the sinh-Poisson relationship between vorticity and stream function. We believe that our quantitative findings solve one of the long-standing problems in two-dimensional turbulence.
