AI 中文总结
本文扩展三叶结涡旋模拟至更晚时间，利用Rosenhead涡量剖面生成Kolmogorov谱和结构函数，实现无强迫初始状态下的充分发展湍流，并验证能量衰减与积分尺度增长遵循Loitsyanskii积分守恒。
AI 中文摘要
受Matsuzawa等人（2026）最近在水箱中碰撞多个涡环的实验观察的启发，本文将紧凑的三叶结涡旋模拟扩展到更晚的时间，并生成了一个持续的、遵循Kolmogorov标度的能量谱，以及充分发展湍流的其他统计特征，包括结构函数标度。这种时间扩展使用更大的(4π)³周期域，通过使用代数Rosenhead涡量剖面实现改进的紧凑性，由此产生与粘度ν无关的有限能量耗散，以及重连前ν^{1/4}依赖的高阶涡量矩的收敛。这些性质或许首次表明，衰减的Navier-Stokes模拟如何能从远离边界的无强迫初始状态生成充分发展的湍流，从而暗示如何利用更高Re值的进一步模拟进行实验比较。此外，能量衰减和积分尺度增长的指数，E(t)~(t+t₀)^{-10/7}和ℓ(t)~(t+t₀)^{2/7}，遵循基于Loitsyanskii积分守恒的预测。在一个相关问题上，只有在不考虑周期域尺度上的Fourier模式时，才能获得接近实验速率ℓ_X~(t+t₀)^{(0.16或1/7)}的积分尺度增长率ℓ。
英文摘要
Motivated by recent experimental observations by Matsuzawa et al. (2026) of colliding several vortex rings within a water tank, this paper extends a compact trefoil vortex simulation to later times and generates a persistent ==energy spectrum that obeys Kolmogorov scaling, together with other statistics characteristic of fully developed turbulence, including structure function scaling. This temporal extension uses a larger (4pi)3 periodic domain, with the improved compactness being achieved by the use of an algebraic Rosenhead vorticity profile, from which viscosity(nu)-independent finite energy dissipation is generated and pre-reconnection convergence of nu1/4-dependent higher-order vorticity moments. These properties suggest, perhaps for the first time, how decaying Navier-Stokes simulations can generate fully-developed turbulent flow from an unforced initial state that is far from boundaries, thereby suggesting how further simulations at higher values of Re could be harnessed for experimental comparisons. Moreover, the exponents for the energy decay and the integral scale growth, E(t)~(t+t0)-10/7 and and ell(t)~(t+t0)2/7, follow those based upon preservation of the Loitsyanskii integral. On a related question, an integral scale growth rate ell that is close to the experiment rate of ellX~(t+t0)(0.16or1/7)is only obtained if the Fourier modes at the scale of the periodic domain are not considered.
