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Asymptotically exact formulation of superfluid turbulence with discrete topological defects at all continuum scales

Demosthenes Kivotides

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Phys. Rev. Fluids 11, 054602 – Published 7 May, 2026

DOI: https://doi.org/10.1103/xp9w-f6ks

Abstract

We present an asymptotically exact continuum formulation of finite-temperature superfluid turbulence that consistently couples quantized vortex filaments to the turbulent normal fluid across all continuum scales. The key ingredient is the explicit linear-response theory (LRT) Stokes microhydrodynamic response generated by the line-supported mutual-friction and Iordanskii forces acting on the normal fluid. This response yields hydrodynamic-interaction (HI)-resolved vortex dynamics in which the filament-sampled normal-fluid velocity includes the full disturbance flow. Analytical solutions for canonical configurations (parallel and antiparallel line pairs and a vortex ring) show that microhydrodynamic coupling renormalizes defect motion and can permit stalling and reversal phenomena excluded in freely draining defect dynamics. To bridge the prohibitive separation between microhydrodynamic and turbulent scales in practical calculations, we couple a filtered Navier-Stokes description of the normal component to a concurrent low-Reynolds-number (LRT/Stokes) microflow solver. In the filtered normal-fluid equations the LRT microflow enters in two distinct, explicit ways: (i) it generates a deterministic residual (subfilter) stress from the subcutoff microflows, and (ii) it supplies hydrodynamically consistent mutual-friction and Iordanskii forcing via the HI-resolved defect reaction forces. The resulting hydrodynamic-scale system resolves inertial turbulence down to the physical cutoff set by viscous damping and two-fluid coupling. The formulation is boundary-condition agnostic—periodic, unbounded, and wall-bounded geometries enter only through the Stokes mobility returned by the solver—and is asymptotically exact in the scale-separated limit as a consequence of the overdamped Stokes/LRT response, which relaxes rapidly compared with the smallest resolved turbulent timescales. We indicate a detailed algorithmic procedure implementing the new formulation.

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Phys. Rev. Fluids 11, 054602– Published 7 May, 2026
  • Received 2 February 2026
  • Accepted 13 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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