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Momentum-scalar coupled turbulence with anomalous momentum and scalar diffusions. Part 2: With short-range external force and implementation in electrokinetic turbulence

Year: 2026
Type: preprint
Abstract: We extend the generalized anomalous diffusion framework established in Part 1 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, $k_{\mathrm{MD}}$ and $k_{\mathrm{SD}}$, 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 $k_{\mathrm{MD}}$ and $k_{\mathrm{SD}}$ are governed by the scale-dependent anomalous Schmidt number $\mathrm{Sc}_Z$. We identify two new spectral subranges that emerge exclusively in this short-range forcing regime: (i) the convective-forcing-viscous subrange ($k_{\mathrm{MU}}\ll k\ll k_{\mathrm{CFVD}}$) for either $\mathrm{Sc}_Z\gg1$ or $\mathrm{Sc}_Z\ll1$ with $γ>α$, where the scalar field drives viscous flow through electric body force; and (ii) the diffusive-forcing-convective subrange ($k_{\mathrm{MU}}\ll k\ll k_{\mathrm{DFCD}}$) for $\mathrm{Sc}_Z\ll1$ and $γ\leα$, where the scalar structure dominated by diffusion determines electric body force, which in turn causes momentum convection. 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.
DOI: 10.48550/arxiv.2608.23947
Author: Zhao, Wei
Language: English
Open Access status: green
OpenAlex ID: W7204265553
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