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DNS configuration and turbulence-regime identification are insufficiently documented (Sec. 2.1), preventing reproducibility and making it hard to assess whether the simulated flow corresponds to a well-developed inverse-cascade regime (and how general the conclusions are). Key missing items include: domain size/geometry and boundary conditions; numerical method (e.g., pseudo-spectral vs finite difference, de-aliasing); grid resolution; time integrator and time step; forcing definition (stochastic vs deterministic, correlation time, amplitude, injection rate, forcing wavenumber band); and large-scale energy control (e.g., linear friction/hypoviscosity) and whether a condensate forms. Also missing are standard diagnostics confirming the intended regime (energy spectrum slopes, fluxes, stationarity).
Recommendation: Substantially expand Sec. 2.1 (or add an appendix) to specify: (i) domain, BCs, and nondimensionalization; (ii) discretization, de-aliasing, resolution, and timestepper; (iii) forcing form and statistics including injection rates; (iv) any large-scale friction/hypoviscosity and how condensate/box-scale growth is controlled; and (v) regime diagnostics (time-averaged spectra and energy/enstrophy fluxes) demonstrating the inverse cascade and statistical stationarity. This will also help interpret why the accessible time window ($t\leq 600$) is/was not long relative to large-eddy times.
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The central interpretation (“superdiffusion is transient; $H(t)$ is slowly relaxing toward $0.5$”) is not yet statistically secured given the limited late-time range and lack of uncertainty quantification (Sec. 2.3, Sec. 3.1, Sec. 4). With $t\leq 600$ and a sliding window ($\Delta t=100$), the late-time estimate $H\approx 0.56$ could still be compatible with: (i) an eventual plateau at weak superdiffusion ($H>0.5$), (ii) continued decay to $0.5$, or (iii) biases from windowing/finite-length effects and limited independent samples.
Recommendation: In Sec. 3.1 (and echoed in Sec. 4), add robustness/uncertainty quantification for MSD and $H(t)$: (i) bootstrap or block-bootstrap confidence bands over tracers and over time origins $t_0$; (ii) sensitivity of $H(t)$ to window width (e.g., $\Delta t=50/100/200$) and the fitting range in Eq. (3); (iii) compensated plots such as $MSD(\tau)/\tau$ (diffusive compensation) and $MSD(\tau)/\tau^{2H_{\rm fit}}$ over the final decade to visualize convergence; and (iv) a simple model comparison on the late-time segment (constant plateau vs slowly decaying $H(t)$) with uncertainties. If longer runs or multiple realizations are available, extend the time range or ensemble; otherwise, soften Sec. 4 wording to “consistent with a slow approach toward normal diffusion over accessible times.”
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Okubo--Weiss (OW) conditioning may be unreliable as implemented due to sparse Eulerian sampling (15 snapshots) and potentially ambiguous partitioning using only ${\rm sign}(Q)$ (Sec. 2.2, Sec. 3.2). With $\sim 40$ time-unit snapshot spacing (if uniform over $600$), linear interpolation of $Q(x,t)$ may miss rapid evolution near hyperbolic regions and vortex boundaries; misclassification typically homogenizes conditional statistics, which could mask true subpopulation differences relevant to “highways.”
Recommendation: In Sec. 2.2, report snapshot spacing and compare it to relevant time scales (forcing-scale turnover, typical vortex orbital/trapping times, Lagrangian velocity correlation time). Where possible, recompute OW at higher cadence for a subset of the run and quantify classification stability (fraction of particles changing class; changes in residence-time PDFs; changes in conditional MSD/$H(t)$). Also test more robust OW criteria: apply a threshold $|Q|>Q_0$ (e.g., $Q_0$ based on $Q_{\rm rms}$ or local strain/vorticity scales) to exclude ambiguous $Q\approx 0$ regions, and/or use normalized OW. Document how $Q$ is computed (velocity recovery, differentiation, filtering) and how $Q$ is interpolated to particle positions (Sec. 2.2).
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The chosen diagnostic for “highways”---classifying particles by total fraction of time spent in strain ($>70\%$ vs $<30\%$)---may not detect intermittent flight-dominated transport (Sec. 2.2, Sec. 3.2). A particle could spend little time in strain yet acquire most of its net displacement during rare, fast strain-guided segments; conversely, long residence in strain does not guarantee large net displacement if motion frequently turns/cancels.
Recommendation: Augment Sec. 3.2 with event-/segment-based diagnostics closer to the “highway” mechanism: (i) condition instantaneous or short-lag displacement/velocity statistics on being in strain at the current time ($Q>0$, or $|Q|>Q_0$) rather than global occupancy; (ii) decompose MSD growth into contributions from strain vs vortex segments (e.g., via conditioned velocity autocorrelation integrals); (iii) define “flights” between trapping events (or via turning-angle/curvature criteria) and report flight-length and flight-duration distributions and their contribution to MSD; and (iv) test robustness to thresholds/quantile splits (not only $70/30$). This can either strengthen the negative result (“no highway contribution”) or reveal a more subtle mechanism missed by occupancy-based grouping.
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Phase-randomized surrogate construction and interpretation contain conceptual and methodological ambiguities (Sec. 2.4, Sec. 3.3, Sec. 4). As written, the surrogate is described as destroying “all temporal ordering and correlations” and preserving the “exact same velocity PDF,” which is generally incorrect for standard phase randomization. Moreover, if phases are randomized independently per component/particle, cross-component correlations ($u$--$v$), rotational structure, and geometric constraints of 2D incompressible dynamics are destroyed; large MSD differences could therefore reflect loss of kinematic constraints rather than (or in addition to) “restorative temporal correlations.” The reported near-ballistic surrogate scaling across the full duration also needs reconciliation with what statistics are actually preserved (PSD implies preservation of the autocorrelation function under stationarity/Wiener--Khinchin).
Recommendation: Rewrite Sec. 2.4 and the related claims in Sec. 3.3--4 to state precisely which statistics are preserved (Fourier amplitudes/PSD; under stationarity this preserves second-order autocorrelation) and which are destroyed (phase coherence/higher-order temporal structure, intermittency, and potentially cross-component/cross-particle structure). Provide implementation details: detrending/windowing, treatment of finite-length periodicity, whether phases are randomized per component and whether $u$--$v$ cross-spectra are preserved, and how surrogate trajectories are integrated. In Sec. 3.3, plot original vs surrogate Lagrangian velocity autocorrelation $R_v(\tau)$ (and ideally cross-correlation between components) to support the mechanistic interpretation. If the intent is a “memoryless” null, additionally include a time-shuffled surrogate that preserves the one-point velocity PDF but breaks temporal dependence, and compare outcomes. Temper conclusions to attribute differences to specific destroyed structures (e.g., coherent turning/vortex-induced phase relations) rather than “removal of all correlations.”
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The evidence used to rule out L\'evy-flight and CTRW mechanisms is currently under-specified and lacks uncertainty estimates (Sec. 2.3, Sec. 3.4). Hill-estimator tail exponents $\beta$ and trapping-time analyses depend strongly on threshold/fit-range choices and on dependence in the data; without methodological transparency and confidence intervals, the negative conclusion (“rules out L\'evy/CTRW”) is not fully supported.
Recommendation: Expand Sec. 2.3 and Sec. 3.4 to document: (i) the precise tail convention (PDF vs CCDF) and moment criteria under that convention; (ii) how the Hill threshold (number of upper order statistics) is chosen (Hill plots, stability ranges), with confidence intervals (bootstrap/block-bootstrap); (iii) sample sizes and dependence handling; and (iv) vortex-core and trapping-event definitions ($Q$ threshold(s), additional $|\omega|$ criteria, connectivity/size filters, and entry/exit detection). Include empirical CCDFs for increments and trapping times with alternative tail-model comparisons (e.g., power law vs stretched exponential) and revise the wording to “no compelling evidence for L\'evy/CTRW in this dataset” unless the strengthened analysis justifies a stronger exclusion.
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Key figures supporting the main claims appear incomplete and/or lack essential uncertainty/robustness information (notably Fig. 1 as referenced in Sec. 3.1--3.2). The caption indicates an MSD and an $H(t)$ panel, but the $H(t)$ panel is reported as missing/not visible; curves are compared without confidence bands; and surrogate results are shown without variability across surrogate realizations, making the strength of the contrast hard to gauge.
Recommendation: Ensure Fig. 1 includes both panels with clear (a)/(b) labels matching the caption. Add uncertainty bands for MSD and $H(t)$ (bootstrap over tracers/time origins), and show multiple surrogate realizations (median plus 5--95% envelope, or thin-line overlays). On the $H(t)$ panel, mark the late-time averaging window used for quoted values (e.g., $H\approx 0.56$) and report that value with a CI. These changes directly support the manuscript’s primary inferences.