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, 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 cause 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.