论文标题
Navier-Stokes湍流的限制可逆系统：Gallavotti等价猜想的证据
Constrained Reversible system for Navier-Stokes Turbulence: evidence for Gallavotti's equivalence conjecture
论文作者
论文摘要
在加拉沃蒂的猜想之后，提议除NS方程本身以外的替代方程式等效地描述了Navier-Stokes流体的固定状态。我们根据限制的Navier-Stokes方程来提出一个模型系统对称，以保持肠胃不变。通过高分辨率的数值实验证明，可逆模型演变为固定态，该状态非常准确地重现了与不同雷诺数在不同雷诺数下直接数值模拟提取的湍流物理学相关的所有统计观察结果。如大型模拟中所用的那样，使用可逆模型来模仿湍流动力学对于navier-stokes方程的粗粒版本至关重要。此外，可逆模型在数学上看起来更简单，因为腹部的每个雷诺都是恒定的。最后，简要讨论了对统计力学背景的理论上的兴趣。
Following the Gallavotti's conjecture, Stationary states of Navier-Stokes fluids are proposed to be described equivalently by alternative equations besides the NS equation itself. We propose a model system symmetric under time-reversal based on the Navier-Stokes equations constrained to keep the Enstrophy constant. It is demonstrated through high-resolved numerical experiments that the reversible model evolves to a stationary state which reproduces quite accurately all statistical observables relevant for the physics of turbulence extracted by direct numerical simulations at different Reynolds numbers. The possibility of using reversible models to mimic turbulence dynamics is of practical importance for coarse-grained version of Navier-Stokes equations, as used in Large-eddy simulations. Furthermore, the reversible model appears mathematically simpler, since enstrophy is bounded to be constant for every Reynolds. Finally, the theoretically interest in the context of statistical mechanics is briefly discussed.
