2402.18000
EXACT SOLUTIONS FOR NONLINEAR TRAPPED LEE WAVES IN THE β-PLANE APPROXIMATION
Lili Fan, Ruonan Liu, Heyang Li
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem 3.1 constructs an exact Gerstner-like Lagrangian solution to the full β-plane system with nontraditional Coriolis terms and thermodynamics, verifies mass conservation and the first law, and derives the dispersion relation kc^2 + f̂ c = f̂ c0 + g. The candidate solution reproduces the same mapping, pressure–density ansatz, dispersion relation, and verification steps. Differences are superficial (e.g., presenting Px,Pz after imposing the dispersion relation and using Φ′=F explicitly), not mathematical. No substantive contradiction was found.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper provides a clean and self-contained construction of an exact, three-dimensional Gerstner-like solution for trapped lee waves in the full β-plane setting with thermodynamics. The proof is correct and well motivated. A few notational clarifications (pressure potential as a primitive of the density function, explicit statement of the positivity condition f̂ c0+g>0, and the label domain) would aid readability. The contribution is specialized yet valuable: it extends the exact-solution toolkit for nonlinear atmospheric waves beyond earlier f-plane and upward-propagating constructions.