2010.03330
Pattern formation in clouds via Turing instabilities
Juliane Rosemeier, Peter Spichtinger
correctmedium confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves (i) the trivial equilibrium cannot exhibit a diffusion-driven (Turing) instability when the underlying ODE fixed point is asymptotically stable, and (ii) a concrete cloud microphysics scheme (γ=1, βc=βr=2, B=0) admits a stable ODE equilibrium that can be destabilized by diffusion for suitable D1,D2. The candidate solution reproduces both results with essentially the same linearization, Jacobian, stability, and Turing-criterion calculations, even adding a constructive diffusion-coefficient choice. Small editorial inconsistencies in the paper about a12 at the trivial equilibrium do not affect correctness.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper adapts classical Turing analysis to a compact cloud microphysics model and obtains clear analytical conditions, including a negative result at the trivial equilibrium and a positive example with βc=βr=2. The derivations are standard but careful, and simulations support the claims. A small inconsistency about a12 at the trivial equilibrium and the lack of an explicit constructive diffusion choice are minor and easily fixable.