Voigt正则化湍流中的动力学减速、瓶颈及多标度行为
Dynamical slowdown, bottlenecks, and multiscaling in Voigt-regularised turbulence
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中文总结 AI 辅助
该研究采用Voigt正则化SABRA模型与NSV方程DNS，发现湍流存在三个谱区，揭示瓶颈形成与尺度相关减速及初始热化有关，证实小α下Voigt模型是NS方程的优秀近似。
中文摘要 AI 辅助
我们采用Voigt正则化SABRA模型及对应Voigt-Navier-Stokes（NSV）方程的直接数值模拟（DNS），研究湍流中瓶颈的形成机制。Voigt正则化引入了与尺度相关的非线性相互作用减速，且不增强耗散，为研究非线性输运与热行为的相互作用提供了自然场景。我们发现三种不同的谱区：$k<k_I$的惯性区、$k_I<k<k_{II}$对应部分热化的类中间平衡区，以及$k>k_{II}$的高波数热区，其中Voigt项主导守恒不变量。向高波数区的转变发生在$k_{II}\backsim 1/\alpha$处，而$k_I$标志着热化行为的起始。等时和多时统计结果显示，间歇性随尺度减小而逐渐被抑制，呈现高斯性，同时从湍流区的动力学多标度向平衡区的简单标度转变。壳模型在宽尺度范围内解析出这三个区，而对应NSV方程的DNS再现了相同的定性趋势，包括瓶颈形成、级联完成延迟、间歇性降低及小尺度下的高斯性倾向。我们发现瓶颈形成可能与尺度相关的动力学减速和初始热化相关，而非纯耗散起源。我们提供了有力证据：在正则化参数$\alpha$远小于耗散长度尺度的区域，Voigt模型再现了与Navier-Stokes（NS）方程相同的惯性区湍流及湍流统计特性，这表明小$\alpha$下Voigt模型是NS方程的优秀实用近似。
英文摘要
We investigate bottleneck formation in turbulence using the Voigt-regularised SABRA model and DNS of the corresponding Voigt-Navier-Stokes (NSV) equations. The Voigt regularisation introduces a scale-dependent slowdown of nonlinear interactions without enhancing dissipation, providing a natural setting to study the interplay between nonlinear transfer and thermalised behaviour. We find three distinct spectral regimes: an inertial range at $k<k_I$, an intermediate equilibrium-like range associated with partial thermalisation for $k_I<k<k_{II}$, and a high-$k$ thermal regime for $k>k_{II}$, where the Voigt contribution dominates the conserved invariant. The crossover to the high-$k$ regime occurs at $k_{II}\sim 1/α$, while $k_I$ marks the onset of thermalised behaviour. Equal and multi-time statistics reveal a progressive suppression of intermittency and a tendency towards Gaussianity at small scales, together with a transition from dynamic multiscaling in the turbulent regime to simple scaling in the equilibrium ranges. The shell model resolves these three regimes over a broad range of scales, while DNS of the corresponding NSV equations reproduces the same qualitative trends, including bottleneck formation, delayed cascade completion, reduced intermittency, and a tendency towards Gaussianity at small scales. We find that bottleneck formation might be associated with scale-dependent dynamical slowdown and incipient thermalisation, rather than being purely dissipative in origin. We provide strong evidence that, in the regime where the regularization parameter $α$ is much smaller than the dissipation length scale, the Voigt model reproduces the same inertial-range turbulent regime and turbulence statistics as the Navier-Stokes (NS) equations. This provides evidence that the Voigt model constitutes an excellent practical approximation to the NS equations for small $α$.
