AI 中文总结
该研究将广义反常扩散框架扩展至短程外力 regime，以电动湍流为例推导相关波数关系，识别出两个新谱子区间，构建相图明确参数对级联拓扑的影响。
AI 中文摘要
我们将第1部分建立的广义反常扩散框架扩展至短程外力 regime（β > 2/3），此时多尺度力主导（MFD）子区间插入惯性子区间之后，直接与耗散区间竞争。以β=1的电动（EK）湍流为典型示例，我们推导了四级级联过程（惯性、常量Π_u、常量Π_s及可变通量）所有四个子区间内的速度与标量耗散波数k_MD和k_SD的关系。通过结合Golestanian预测的电解质反常扩散 regime，我们构建了综合相图，展示了k_MD与k_SD的相对大小如何由尺度依赖的反常施密特数Sc_Z控制。我们识别出仅在该短程外力 regime 中出现的两个新谱子区间：（i）当Sc_Z ≫ 1时，速度谱的对流-粘性子区间（k_MD ≪ k ≪ k_SD），其中标量场驱动粘性流，产生E_u ~ k^(-(3/2 + ξ_s/2))并带有拉伸指数截止；（ii）当Sc_Z ≪ 1且γ ≤ α时，标量谱的扩散-外力子区间（k_SD ≪ k ≪ k_MD），其中标量耗散区间决定电外力，导致E_s ~ k^(ξ_u - 2α)。这些结果为反常扩散下的EK湍流提供了完整的分析图谱，揭示了电场强度、离子扩散率等外部参数如何决定级联拓扑。
英文摘要
We extend the generalized anomalous diffusion framework established in Part I to the short-range forcing regime ($β> 2/3$), where the multiscale-force dominated (MFD) subrange is intercalated after the inertial subrange, competing directly with the dissipation ranges. Focusing on electrokinetic (EK) turbulence as the prototypical example with $β=1$, we derive the relations for the velocity and scalar dissipation wavenumbers, $k_{MD}$ and $k_{SD}$, across all four subranges of the Quad-cascade process (inertial, constant-$Π_u$, constant-$Π_s$, and variable flux). By incorporating Golestanian's predicted anomalous diffusion regimes for electrolytes, we construct comprehensive phase diagrams showing how the relative magnitudes of $k_{MD}$ and $k_{SD}$ are governed by the scale-dependent anomalous Schmidt number $Sc_Z$. We identify two new spectral subranges that emerge exclusively in this short-range forcing regime: (i) the convective-viscous subrange ($k_{MD} \ll k \ll k_{SD}$) of velocity spectrum for $Sc_Z \gg 1$, where the scalar field drives a viscous flow yielding $E_u \sim k^{-\left(\frac{3}{2} + \frac{ξ_s}{2}\right)}$ with a stretched-exponential cutoff; and (ii) the diffusive-forcing subrange ($k_{SD} \ll k \ll k_{MD}$) of scalar spectrum for $Sc_Z \ll 1$ and $γ\leq α$, where the scalar dissipation range determines the electric forcing, leading to $E_s \sim k^{ξ_u - 2α}$. These results provide a complete analytical map of EK turbulence under anomalous diffusion, revealing how external parameters such as electric field strength and ionic diffusivity determine the cascade topology.
