发表机构
State Key Laboratory of Photon-Technology in Western China Energy, International Scientific and Technological Cooperation Base of Photoelectric Technology and Functional Materials and Application, Laboratory of Optoelectronic Technology of Shaanxi Province, Institute of Photonics and Photon-technology, Northwest University（西北大学光子与光子技术研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出动量-标量耦合湍流的理论模型，推导相关谱与特征波数的解析表达式，定义反常施密特数，统一经典标度，为理解复杂湍流系统的非费克输运提供基础。
AI 中文摘要
本文提出了一种动量-标量耦合湍流的理论模型，其中两个场均经历反常扩散，分别由阶数为γ/4和α/4的分数双调和算子描述。针对长程外力湍流或无外力湍流，我们推导了动能谱E_u(k)、标量谱E_s(k)，以及特征波数k_K = (ε_u^(1/3)/c_u)^(1/(γ - 2/3))（柯尔莫哥洛夫尺度的倒数）和k_S = (ε_u^(1/3)/c_s)^(1/(α - 2/3))（标量耗散尺度的倒数）的解析表达式，这些量分别为γ、α、湍流动能耗散率ε_u、动量扩散率c_u和标量扩散率c_s的函数。定义了反常施密特数Sc_Z = k_0^(γ - α) * (c_u/c_s)，其控制级联拓扑，描述了最小波数k_0下标量与动量的扩散时间之比。研究表明，超扩散（γ<2或α<2）会违反直觉地增大k_K和k_S，拓宽惯性范围。该理论在γ=α=2时统一了经典柯尔莫哥洛夫-奥布霍夫-科辛-巴彻勒标度作为特殊情况，为理解复杂湍流系统中的非费克输运提供了基础。
英文摘要
We present a theoretical model for momentum--scalar coupled turbulence in which both fields undergo anomalous diffusion, described by fractional biharmonic operators of orders $γ/4$ and $α/4$, respectively. Focusing on the long-range external forcing or unforced turbulence, we derive analytical expressions for the kinetic energy spectrum $E_u(k)$, the scalar spectrum $E_s(k)$, and the characteristic wavenumbers $k_K = \left( \frac{ε_u^{1/3}}{c_u} \right)^{1/(γ- 2/3)}$ (reciprocal of Kolmogorov scale) and $k_S = \left( \frac{ε_u^{1/3}}{c_s} \right)^{1/(α- 2/3)}$ (reciprocal of scalar dissipation scale) as functions of $γ$, $α$, turbulent dissipation rate $ε_u$, diffusivities of momentum ($c_u$) and scalar ($c_s$), respectively. An anomalous Schmidt number $Sc_Z = k_0^{γ- α} \frac{c_u}{c_s}$ is defined to governs the cascade topology. It describes the ratio of diffusion times of scalar and momentum on the minimum wavenumber $k_0$. Superdiffusion ($γ<2$ or $α<2$) is shown to counter-intuitively enlarge $k_K$ and $k_S$, broadening the inertial range. The theory unifies the classical Kolmogorov--Obukhov--Corrsin--Batchelor scalings as special cases when $γ=α=2$, and provides a foundation for understanding non-Fickian transport in complex turbulent systems.
Journal refTransport Phenomena (2026)
