Momentum-scalar coupled turbulence with anomalous momentum and scalar diffusions. Part 2: With short-range external force and implementation in electrokinetic turbulence
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, kMD and kSD, across all four subranges of the Quad-cascade process (inertial, constant-Πu, constant-Πs, and variable flux). By incorporating Golestanian's predicted anomalous diffusion regimes for electrolytes, we construct comprehensive phase diagrams showing how the relative magnitudes of kMD and kSD are governed by the scale-dependent anomalous Schmidt number ScZ. We identify two new spectral subranges that emerge exclusively in this short-range forcing regime: (i) the convective-forcing-viscous subrange (kMU≪ k≪ kCFVD) for either ScZ≫1 or ScZ≪1 with γ>α, where the scalar field drives viscous flow through electric body force; and (ii) the diffusive-forcing-convective subrange (kMU≪ k≪ kDFCD) for ScZ≪1 and γ≤α, 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.
Versions
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BibTeX
@misc{zhao2026momentumscalar,
title = {{Momentum-scalar coupled turbulence with anomalous momentum and scalar diffusions. Part 2: With short-range external force and implementation in electrokinetic turbulence}},
author = {Wei Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.23947},
eprint = {2608.23947},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.23947},
}
RIS
TY - UNPB
TI - Momentum-scalar coupled turbulence with anomalous momentum and scalar diffusions. Part 2: With short-range external force and implementation in electrokinetic turbulence
AU - Wei Zhao
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2608.23947
UR - https://arxiv.org/abs/2608.23947
AB - 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_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-forcing-viscous subrange (k_MU≪ k≪ k_CFVD) for either Sc_Z≫1 or Sc_Z≪1 with γ>α, where the scalar field drives viscous flow through electric body force; and (ii) the diffusive-forcing-convective subrange (k_MU≪ k≪ k_DFCD) for Sc_Z≪1 and γ≤α, 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.
ER -