Reduced Subgrid Scale Terms in Three-Dimensional Turbulence

Rik Hoekstra, Wouter Edeling

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:57 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

Part (A) of the model mirrors the paper’s tau-orthogonal derivation and is correct. Parts (B)–(C) introduce a linear-Gaussian Markov framework and consistency/KS-distance guarantees that the paper neither assumes nor needs; more critically, (B) incorrectly treats the augmented regressor state as evolving linearly in closed form, ignoring the nonlinear LES solver that generates q^{*}. Hence the stationary Gaussian/unique Lyapunov solution and ensuing KS claims do not follow for the coupled LES–TO–LRS system.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The work convincingly reframes SGS closure around scale-aware QoIs with a simple stochastic residual model, demonstrating robust empirical performance. The projection/orthogonality framework is sound. However, theoretical properties of the coupled LES–TO–LRS dynamics (stability, stationarity) are not analyzed; claims must remain empirical. Explicitly stating projector properties, non-degeneracy of calibration factors, and clarifying the nonlinear role of q* would improve rigor.