Weak nonlinearity for strong nonnormality

Yves-Marie Ducimetière, Edouard Boujo, François Gallaire

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The candidate solution correctly derives the WNNh amplitude equation and identifies the two quadratic feedbacks (mean-flow distortion and the triad with the second harmonic). Its projection step onto the optimal left singular vector and the scaling a = sqrt(ε0) A, F = φ ε0^{3/2} reproduce equation (14) of the paper. For steady states, it writes the quadratic relation between Y and the nonlinear gain G (algebraically equivalent to the paper’s cubic in Y), but it labels this step as yielding a cubic and omits that the paper sets γ = 1 in the main-text cubic. A minor normalization slip appears in the second-harmonic problem: it uses (2 i ω0 I − L) u2,2 = −2 C(uo,uo) instead of the paper’s −C(uo,uo).

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

A solid and careful synthesis that extends weakly nonlinear amplitude modeling to nonnormal systems using resolvent/propagator ideas. The core derivations and scalings are correct and the validation compelling. Minor clarifications (normalization, when \gamma is set to 1, and explicit linkage between the cubic-in-Y and quadratic-in-Y forms) would improve accessibility and avoid confusion for readers implementing the method.