Turbulence modeling over riblets via domain transformation

The paper and the candidate solution use the same perturbative decomposition in the riblet height α, the same block-harmonic/operator structure for Aθ and Xθ, and the same decomposition of the steady Lyapunov equation into smaller Sylvester/Lyapunov problems. The paper states and implements the Toeplitz/diagonal structure and α-ordered Lyapunov hierarchy and mean-flow corrections, while the model solution gives a more formal operator-level sketch (with standard assumptions) and makes explicit the symmetry-driven O(α) vs O(α^2) selection rule and a conditional monotonicity statement. Where the paper provides empirical/analytic evidence (e.g., KH-window growth with riblet size), the model adds clear hypotheses to draw a monotonicity conclusion. No substantive contradictions were found; both are consistent and largely the same proof strategy for the core structural results.