Bandak Dmytro, Mailybaev Alexei A, Eyink Gregory L, Goldenfeld Nigel
Department of Physics, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801, USA.
Instituto de Matemática Pura e Aplicada - IMPA, Rio de Janeiro 22460-320, Brazil.
Phys Rev Lett. 2024 Mar 8;132(10):104002. doi: 10.1103/PhysRevLett.132.104002.
How predictable are turbulent flows? Here, we use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the nonuniqueness of the solutions to the Euler equation that is conjectured to occur in Navier-Stokes turbulence at high Reynolds numbers, leads to universal statistics at finite times, not just at infinite time as for standard chaos. These universal statistics are predictable, even though individual flow realizations are not. Any small-scale noise vanishing slowly enough with increasing Reynolds number can trigger spontaneous stochasticity, and here we show that thermal noise alone, in the absence of any larger disturbances, would suffice. If confirmed for Navier-Stokes turbulence, our findings would imply that intrinsic stochasticity of turbulent fluid motions at all scales can be triggered even by unavoidable molecular noise, with implications for modeling in engineering, climate, astrophysics, and cosmology.
湍流的可预测性如何？在此，我们使用理论估计和壳模型模拟来论证，欧拉自发随机性是欧拉方程解的非唯一性的一种表现，据推测在高雷诺数下的纳维 - 斯托克斯湍流中会出现，它在有限时间而非像标准混沌那样仅在无限时间导致通用统计量。这些通用统计量是可预测的，尽管单个流动实现不可预测。任何随着雷诺数增加而足够缓慢消失的小尺度噪声都能触发自发随机性，并且我们在此表明仅热噪声在没有任何更大扰动的情况下就足够了。如果对于纳维 - 斯托克斯湍流得到证实，我们的发现将意味着即使是不可避免的分子噪声也能触发所有尺度湍流流体运动的内在随机性，这对工程、气候、天体物理学和宇宙学中的建模具有重要意义。
