发表机构
Laboratoire de Physique des Plasmas, CNRS, Ecole Polytechnique, Sorbonne Université, Université Paris-Saclay, Observatoire de Paris（等离子体物理实验室，法国国家科学研究中心，巴黎综合理工学院，索邦大学，巴黎萨克雷大学，巴黎天文台）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过仿射变换将单个三元组的方程组合成三元组三重态的演化方程，发现其存在精确解，包括幂律解和用广义Jacobi椭圆函数表示的时间依赖解，为无粘Navier-Stokes方程提供了新的精确非线性解。
AI 中文摘要
考虑三维Navier-Stokes湍流的螺旋分解中的三元组，三个连续且形状和类别相同的三元组，其中参考波数分别作为最小、中间和最大的波数，构成一个有趣的对象，称为三元组三重态，它允许追踪由于给定形状和类别的三元组在波数空间中的局部传递。研究表明，三元组三重态的演化方程可以从单个三元组的三个腿的方程获得，这些方程通过涉及缩放、旋转和反射的仿射变换组合在一起。已知的对应于能量和螺旋度恒定通量的幂律解表现为三元组三重态链的精确解，对三元组相位有特殊影响。更有趣的是，在孤立的三元组三重态上存在一个精确的、依赖于时间的解，该解可以用似乎是Jacobi椭圆函数的直接推广来表达。这些解构成了无粘极限下Navier-Stokes方程的新颖精确非线性解。
英文摘要
Considering triads in helical decomposition of three dimensional Navier-Stokes turbulence, three consecutive triads of the same shape and class, where the reference wave-number appears as the smallest, the middle and the largest wave-numbers respectively, constitutes an interesting object called the triad triplet that allows tracing the local transfer in wave-number space due to a given shape and class of triads. It is shown that, evolution equations for the triad triplet can be obtained from the equations of the three legs of a single triad that are put together via affine transformations involving scaling, rotation and reflection. Known power law solutions corresponding to constant flux of energy and helicity appear as exact solutions of a chain of triad triplets, with particular implications for the triadic phases. More interestingly, an exact, time dependent solution is available on an isolated triad triplet, that can be expressed using what appears to be straightforward generalization of Jacobi elliptic functions. These solutions, constitute novel exact nonlinear solutions of the inviscid limit of the Navier-Stokes equations.
