约束可逆Navier-Stokes方程组Turbulence：Gallavotti等价猜想的证据
Constrained Reversible system for Navier-Stokes Turbulence: evidence for Gallavotti's equivalence conjecture
摘要：
根据Gallavotti猜想，提出了用NS方程以外的替代方程来等价描述Navier-Stokes流体定态。我们提出了一个基于纳维-斯托克斯方程的时间反演下对称的模型系统，该模型系统被约束以保持拟能常数。它是通过高分辨率的数值实验表明，可逆的模型演变到一个稳定的状态，相当准确地再现所有的统计观测相关的湍流物理提取的直接数值模拟在不同的雷诺数。对于大涡模拟中使用的粗粒度版本的纳维-斯托克斯方程，使用可逆模型来模拟湍流动力学的可能性具有实际重要性。此外，可逆模型在数学上似乎更简单，因为拟能对于每个雷诺数都是恒定的。最后，简要讨论了统计力学的理论意义。
英文摘要：
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.
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