{"id":"c6ac1110-4417-4a9a-a110-8fe183a02b37","arxiv_id":"2505.22737","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A localized water blob of turbulence expands with a sharp, non-diffusive front and decays in two power-law stages that match a Kolmogorov-Barenblatt nonlinear diffusion model.","lead":"This paper lets a blob of turbulent water decay in a tank and films it for 17 minutes with a camera that slows down as the flow slows down. It finds the blob spreads with a sharp front and follows a nonlinear energy-balance equation, rather than ordinary diffusion, while decaying in two power-law stages.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The fixed closure of Eq. 4 fails after wall contact: reproducing the delayed decay onset requires reducing c0 from 1.2 to 0.001, so the full-range claim is not established.","rationale":"The central claim is broader than the free-expansion phase: Eq. 4 with order-unity dimensionless constants is offered as the spatiotemporal description of the blob from localized expansion through wall-filling decay. The paper has genuinely independent support for the expansion phase—the front propagation exponent is measured without fitting c0, the predicted relation r∼t^β with β≈2(1+γ)/7 is tested, and the CDS method is benchmarked against an analytic limit. The weakest load-bearing point is the late-time use of the same closure: the authors themselves must change c0 by a factor of 1200 at wall contact to match the crossover. Since c0 is a Kolmogorov-similarity closure constant whose value should not depend on boundary filling, this is not a cosmetic correction but evidence that Eq. 4 with fixed coefficients does not describe the full regime. The reader's conditional verdict remains appropriate: the expansion claim is well supported, the full decay claim is not, and public data/code would help but are secondary to the physical closure issue. My recommended check directly targets whether the fixed-closure model can be saved by boundary conditions, which would settle whether the ad hoc c0 reduction is necessary.","tokens_in":47261,"tokens_out":6103,"duration_ms":76231,"concrete_test":"Run a CDS boundary-condition sweep for the large blob, keeping c0=1.2 and ε0=0.88, with the experimentally measured ℓ(t), and vary the partial-absorption coefficient pabs from 0 to 1, including the reported 15% value. If any pabs reproduces the observed crossover time near t−t0≈80 s without lowering c0, the fixed-closure model can be retained; if no boundary condition removes the need for the 1200-fold reduction of c0, then Eq. 4 with fixed coefficients is contradicted in the wall-filling phase.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. 4 is presented as a fixed-closure model with dimensionless coefficients c0≈1.2 and ε0≈0.88 obtained from data. The paper's own CDS comparisons show that this fixed closure fails in the wall-filling phase: the blue curve in main Fig. 2c, computed with (c0, ε0)=(1.2, 0.88) and the measured ℓ(t), enters the q∼(t−t0)^−2 regime much earlier than the experiment. The cure is to lower c0 to 0.001 (main Fig. 2c; SI §V.E and Fig. 20), a change of three orders of magnitude in the transport coefficient, with no mechanism derived from the model; the SI attributes the discrepancy to persistent eddy structures that are 'beyond the scope of our mean-field model'. Because the transport term in Eq. 4 is proportional to c0, and c0 is assumed fixed by Kolmogorov similarity, this is not a routine parameter adjustment but a regime dependence of the central closure. The expansion-phase evidence (front exponent ~0.38, self-similar collapse, CDS benchmark) is largely independent of this issue and remains credible; however, the broader claim that Eq. 4 accounts for the detailed spatiotemporal decay, including the late-time crossover, is not supported by the fixed-coefficient model as stated.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports an experimental study of an isolated turbulent blob created by eight converging vortex rings in a water tank, with ensemble-averaged PIV measurements over several decades of time using a logarithmic sampling scheme. The central claim is that the spatiotemporal evolution of the blob is governed by the nonlinear diffusion equation Eq. (4), ∂t q = (2/3)c0 l ∇^2 q^{3/2} - ε0 q^{3/2}/l, with spatially uniform, measured integral length scale l(t). The authors present evidence for a sharp turbulent-quiescent front that propagates non-diffusively with self-similar collapse exponent ~0.38 (predicted 0.389), report agreement between the measured expansion rate Rdot and Eq. (4) with fitted coefficients c0=1.2 and ε0=0.88, and reproduce the late-time q~(t-t0)^-2 decay when l is constant. They also acknowledge that the fixed-closure simulation enters the q~(t-t0)^-2 regime earlier than the experiment and that reducing c0 to 0.001 is needed to delay the crossover, attributing the discrepancy to persistent eddy structures beyond the mean-field model.","tokens_in":47557,"tokens_out":5080,"duration_ms":60897,"significance":"The expansion-phase evidence, if taken alone, is a substantial contribution: the authors provide a controlled, boundary-free experimental configuration for studying turbulent-non-turbulent front propagation, and the sharp-front prediction, the non-diffusive propagation scaling, and the absence of Gaussian spreading are parameter-free qualitative consequences of the nonlinear transport term in Eq. (4). The log-movie acquisition method is a practical and broadly applicable technique for power-law decaying flows, and the cross-validation virtual-origin method is a useful analysis tool. The comparison across three different forcing methods in the same chamber, and the demonstration that a constant l gives q~(t-t0)^-2, strengthen the empirical part of the paper. However, the quantitative validation of Eq. (4) as a fixed-coefficient model is incomplete, because c0 and ε0 are fitted to data that are also used for validation, and because the crossover to the t^-2 regime is reproduced only after a three-order-of-magnitude change in c0 that is not derived from the model.","major_comments":[{"comment":"The paper's broad claim that Eq. (4) accounts for the detailed spatiotemporal decay is not supported by the fixed-coefficient model as stated. The blue CDS curve in Fig. 2c, computed with (c0, ε0)=(1.2, 0.88) and the measured l(t), enters the q~(t-t0)^-2 regime much earlier than the experiment. The cure, reducing c0 to 0.001, changes the transport coefficient by three orders of magnitude, and SI §V.E explicitly attributes the need to persistent eddy structures that are 'beyond the scope' of the mean-field model. Since the transport term in Eq. (4) is proportional to c0 and c0 is presented as a fixed dimensionless constant from Kolmogorov similarity, this is a regime dependence of the central closure rather than a routine parameter adjustment. The expansion-phase conclusions (Fig. 5) are largely independent of this issue, but the abstract and conclusion should be revised to state that Eq. (4) applies to the free-expansion phase and that the wall-filling crossover is captured only with an empirically modified c0, or an additional closure for the persistent inhomogeneity should be provided.","section":"Main text, Fig. 2c; SI §V.E"},{"comment":"The validation of the dissipation relation is partially circular. The value ε0=0.88±0.10 is estimated from the asymptotic decay by solving dq/dt=-ε0 q^{3/2}/l_sat assuming q~(t-t0)^-2, and the same relation is then presented as 'agreement' in Fig. 4a. To establish Eq. (1) independently, ε0 should be estimated from a direct measurement such as the structure-function or strain-rate methods described in SI §IV.C.4, without using the decay curve itself, or the circularity should be explicitly acknowledged and its influence on the reported uncertainty quantified.","section":"Eq. (1) and Fig. 4a-b"},{"comment":"The model treats l(t) as a spatially uniform, exogeneous input and assumes the closures κq=c0 l sqrt(q) and ε=ε0 q^{3/2}/l hold for the ensemble-averaged 3D energy field down to Re_lambda~10 and across the wall-filling phase. The paper's own Fig. 2c shows the fixed closure fails in exactly the wall-filling regime, and SI §V.A reports persistent eddy structures that are not captured by the mean-field radial description. A clear statement of the regime of validity of Eq. (4) (free expansion, ensemble-averaged fields, and a lower Reynolds-number bound) is needed before the model can be claimed as a general framework for decaying turbulence.","section":"Eq. (4) and Table III"},{"comment":"The comparison between the fast-transport and slow-transport simulations is confounded by the use of different initial conditions and initial times. The main-text Fig. 2c caption states that the fast simulation uses the ensemble-averaged profile at t=0.4 s and the slow one uses t=2 s, while SI Table III lists t=0.5 s for the slow case. This discrepancy should be resolved, and the two simulations should be initialized from the same time and the same field, or the dependence of the crossover on the initial condition should be shown, so that the delayed crossover can be attributed specifically to the change in c0.","section":"Fig. 2c and SI Table III"}],"minor_comments":[{"comment":"The virtual-origin fitting method is described briefly in the main text; please specify the number of cross-validation folds, the procedure for selecting the fitting window [ta,tb], and how the reported r^2 values account for the number of data points, since the exponential spacing of the logarithmic sampling makes the effective sample size window-dependent.","section":"SI §IV.C.3"},{"comment":"The statement that the energy spectra collapse onto a universal DNS profile should clarify whether the collapse is obtained by rescaling with the measured dissipation rate from -d<q>_x,n/dt or with a fitted dissipation rate, because the spectral and structure-function methods in SI yield different ε values at late times.","section":"Main text, Fig. 4d and SI §IV.C.4"},{"comment":"The factor 2/3 appears in Eq. (4) but is not present in the SI radial equation (17); please clarify whether c0 in the SI is redefined or whether the factor arises from the identity ∇^2 q^{3/2} = (3/2) q^{1/2} ∇^2 q + (3/4) q^{-1/2} |∇q|^2, and state the convention consistently throughout.","section":"Main text, Eq. (3) and SI §II.B"},{"comment":"The error map in Fig. 5c shows a linear valley of near-minimal error, meaning that c0 and ε0 are not independently determined by the Rdot measurement. The paper should state explicitly that the quoted c0=1.2 relies on the independently chosen ε0=0.88, and that the Rdot data alone would allow a range of (c0, ε0) combinations.","section":"Main text, Fig. 5b-c and SI §V.B"}],"recommendation":"major_revision","confidential_remarks":"The expansion-phase data are valuable and likely to be of broad interest, but the manuscript currently overclaims the scope of Eq. (4). The required revision is not merely editorial: the authors need either to narrow the abstract/conclusion to the free-expansion regime or to provide a principled mechanism for the c0 reduction after wall contact, with independent support. I would also encourage the authors to archive the reconstruction code and the processed data, since the 'available upon reasonable request' statement weakens the reproducibility of a paper whose central evidence is numerical and experimental. If the claims are appropriately narrowed, the paper could become a strong contribution to the turbulence-decay literature."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: the paper earns its keep on the expansion phase. The vortex-ring blob, ensemble-averaged PIV, and log-movie acquisition give a clean, boundary-free view of a localized turbulent patch spreading into quiescent fluid. The measured front is sharp, the radial profiles collapse with r/t^0.38 against a predicted 0.389, and the growth of the integral scale is measured directly rather than assumed. That last piece is a real step beyond Barenblatt and Chen-Goldenfeld: l(t) is not proportional to blob size, so the old closure is falsified and Eq. 4 with time-dependent l is the right framework for comparison. The CDS split-step integrator is carefully benchmarked, and comparing ensemble-averaged fields with simulation is the right methodology. The double-grid control, with l constant and q~t^-2 throughout, is a nice consistency check.\n\nWhere I part company with the abstract is the claim that Eq. 4 accounts for the full decay, including the crossover to t^-2. The stress-test note is right, and the paper itself admits it: with (c0, ε0)=(1.2, 0.88), the CDS enters the t^-2 regime far too early. The fix is to drop c0 to 0.001, three orders of magnitude, with no mechanism, because wall interactions and persistent eddies are described as 'beyond the scope of our mean-field model.' That is not a fixed-closure success; it is a fitted regime switch. Also, ε0 is estimated from the very same late-time q~t^-2 decay the model is said to reproduce, and c0 comes from fitting Rdot over the expansion interval that is then used for validation. None of this destroys the expansion-phase result—that part is largely parameter-free—but it should be presented as partial validation, not full accounting.\n\nTwo smaller complaints: the 2D spectral integral scale is standing in for the 3D eddy field, and the paper does not make data or code available, only 'upon reasonable request.' For a paper selling a direct measurement, that is a meaningful gap.\n\nRecommendation: send it to referees. The expansion-phase dataset and the l(t) measurement are worth publishing on their own; a serious referee can push the authors to separate what Eq. 4 actually explains from what it is forced to fit.","headline":"This is a serious experimental paper whose expansion-phase result—a directly measured sharp front with 0.38 collapse exponent and a measured l(t) that kills the instantaneous-eddy-adaptation assumption—is new and convincing; the late-time modeling claim is not.","tokens_in":48099,"tokens_out":2060,"would_cite":true,"duration_ms":25415,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["47.27.-i","47.27.Gs"],"model":"deepseek-v4-flash","headline":"An isolated turbulent blob in still water spreads and decays by a single nonlinear diffusion equation, with a sharp front advancing as (t-t0)^0.38 and a universal (t-t0)^-2 decay once the integral length scale saturates.","keywords":["turbulent decay","nonlinear diffusion","turbulent-non-turbulent interface","integral length scale","vortex ring collider","log-movie PIV","Kolmogorov-Barenblatt equation","porous medium equation"],"falsifier":"Follow the same isolated blob in a domain large enough that the eddies never feel the walls — a much larger tank, or a direct numerical simulation box with an identical initial blob — and check two predictions at once: the front profile should stay compact, $q \\propto [1-(r/h)^2]^2_+$ with no exponential tail and $h \\sim (t-t_0)^{0.38}$, and the decay exponent should change only when the measured $\\ell(t)$ changes. An exponential front tail, or a decay-rate change uncorrelated with $\\ell(t)$, would refute both the $m = 3/2$ nonlinearity and the claim that $\\ell$ controls the decay exponent.","tokens_in":47050,"feed_emoji":"🌊","tokens_out":18122,"duration_ms":178241,"temperature":0.7,"pith_summary":"This paper claims that an isolated blob of turbulence, once the forcing stops, spreads and decays according to a single nonlinear diffusion equation — the Kolmogorov-Barenblatt equation — rather than by ordinary diffusion plus a separately fitted decay law. The evidence comes from a new experimental platform: eight colliding vortex rings create a localized turbulent blob in the center of a water tank, and a logarithmically timed camera follows its relaxation for 17 minutes while the energy falls by a factor of $10^5$. The equation predicts a sharp, finite-speed front between turbulent and quiescent fluid, and the measured front advances as $(t-t_0)^{0.38}$, matching the predicted $0.389$; energy decays as $(t-t_0)^{-1.3}$ while the integral length scale grows, then as $(t-t_0)^{-2}$ once that scale saturates. If the claim holds, the scattered decay exponents reported across decades of experiments fall into place: the decay rate at any moment is set by the integral length scale, and both the spreading and the dying of turbulence come from the same Kolmogorov closures that govern the energy cascade.","feed_headline":"One equation predicts how a turbulent blob spreads and dies","feed_subtitle":"A sharp front advances as t^0.38 while energy decays; once eddies stop growing, decay locks onto t^-2.","key_machinery":"The carrying object is the Kolmogorov-Barenblatt turbulent energy balance equation, $$\\partial_t q = \\tfrac{2}{3} c_0 \\ell(t) \\$nabla^{2}$ $q^{{3/2}}$ - \\varepsilon_0 \\frac{$q^{{3/2}}$}{\\ell(t)},$$ a porous-medium-type nonlinear diffusion equation for the turbulence energy density $q$. The superlinear transport term $\\nabla^2 q^{3/2}$ (exponent $m = 3/2 > 1$) does the central work: unlike linear diffusion it yields compactly supported self-similar fronts with profile $q \\propto [1-(r/h)^2]^2_+$ and a sharp cutoff at $r = h(t)$, so the turbulent-non-turbulent boundary propagates at finite speed instead of sending a Gaussian precursor. The measured integral length scale $\\ell(t)$ enters both transport and dissipation, making it the single control parameter of the decay rate: constant $\\ell$ forces $q \\sim t^{-2}$, while a growing $\\ell$ slows the decay. Supporting machinery includes the log-movie PIV acquisition (frame spacing grows so tracer displacement stays measurable while velocities drop by three orders of magnitude), the virtual-origin cross-validated power-law fit, and the Cell Dynamical System split-step solver that integrates the stiff, front-bearing equation from experimental initial conditions.","core_discovery":"On the paper's own terms, an ensemble-averaged, isolated decaying turbulent blob obeys $$\\partial_t q = \\tfrac{2}{3} c_0 \\ell(t) \\$nabla^{2}$ $q^{{3/2}}$ - \\varepsilon_0 \\frac{$q^{{3/2}}$}{\\ell(t)},$$ with transport closure $\\kappa_q = c_0 \\ell \\sqrt{q}$ and dissipation $\\varepsilon = \\varepsilon_0 q^{3/2}/\\ell$ taken from Kolmogorov's similarity hypotheses, the integral length scale $\\ell(t)$ measured from the three-dimensional energy spectrum, and $O(1)$ coefficients $c_0 \\approx 1.2$, $\\varepsilon_0 \\approx 0.88$. The front measurement uses a smaller, more localized blob so propagation can be followed before walls are reached; the decay laws use a larger blob with initial $Re_\\lambda = 203$. Three consequences are then verified: the turbulent-quiescent boundary is a sharp front with a compact profile that propagates non-diffusively as $r \\sim (t-t_0)^{0.38}$ (predicted $0.389$); during free expansion the spatially averaged energy decays as $(t-t_0)^{-1.3}$ while $\\ell(t) \\sim t^{0.16}$ is still growing; and once $\\ell$ saturates at roughly a quarter of the chamber width, decay becomes the universal $(t-t_0)^{-2}$, reproduced from the start in a control experiment with a double oscillating grid whose $\\ell$ is constant. Throughout the 17 minutes, rescaling the energy spectra by the measured dissipation collapses them onto the universal dissipation-range profile down to $Re_\\lambda \\approx 10$, so the cascade's fingerprint survives into the final decay.","pith_inferences":["The paper's own need to cut $c_0$ from $1.2$ to $0.001$ after wall contact points to what a next model should add: a second field for the chamber-filling circulation that wall interaction feeds, which would let the crossover time be predicted rather than fitted.","If the sharp-front solution is as strong an attractor as the initial-condition tests suggest, the same equation should describe natural turbulent patches — island wakes, convective thermals, ash clouds — where the front's finite speed sets how fast a patch can contaminate surrounding quiescent fluid; field measurements of $q(r,t)$ and $\\ell(t)$ would suffice to test it.","The log-movie acquisition idea transfers to any power-law-dominated dynamics — gravity currents, phase separation, critical-point relaxation — as a way to span many decades of time in one recording with constant tracer displacement; applying it to a different self-similar system would be a direct check of its generality.","A clean test of the $\\ell$-governance claim: in a much larger chamber the $(t-t_0)^{-1.3}$ regime should persist longer and the crossover should occur exactly when $\\ell$ saturates; a decay-exponent change while $\\ell$ is still measurably growing would falsify it."],"forward_implications":["Decay-exponent scatter across grid, pipe, and spin-down experiments is explained as differences in how the integral length scale grows in each apparatus, with constant $\\ell$ always yielding $t^{-2}$.","Because the front is sharp and propagates at finite speed with no Gaussian precursor, an aircraft or probe crossing into a turbulent patch would encounter it abruptly; the model gives that invasion speed from local $q$ and $\\ell$.","Turbulent statistics remain on the universal dissipation-range spectrum down to $Re_\\lambda \\approx 10$, so flow that looks still to the eye can still be fully turbulent, and naked-eye quiescence is not a valid stopping criterion for decay experiments.","The same $O(1)$ coefficients ($c_0 \\approx 1.2$, $\\varepsilon_0 \\approx 0.88$) reproduce both the instantaneous front speed and the long-time decay curve, so the model is quantitative rather than merely scaling-consistent.","Only the ensemble-averaged field obeys the mean-field equation; single realizations spread in a branched, non-uniform manner, so the equation's predictions are statistical statements about many realizations."],"supporting_citations":[{"why":"Kolmogorov's 1942 mean-field kinetic equations for turbulence; the source of the transport and dissipation closures $\\kappa_q = c_0 \\ell \\sqrt{q}$ and $\\varepsilon = \\varepsilon_0 q^{3/2}/\\ell$ that define the model.","marker":"[43]"},{"why":"Barenblatt's self-similar analysis of a turbulent burst from an instantaneous point source; the origin of the sharp-front, intermediate-asymptotics framework tested here.","marker":"[44]"},{"why":"Renormalization-group theory for turbulent burst propagation; the source of the predicted anomalous scaling exponent (0.389) the measured front is compared with.","marker":"[46]"},{"why":"Establishment of the vortex-ring collider that creates an isolated turbulent blob; the experimental platform supplying all datasets and initial conditions.","marker":"[47]"},{"why":"Demonstration of the $t^{-2}$ vorticity decay law in constant-length-scale homogeneous turbulence; the baseline the late-time universal decay must match.","marker":"[12]"},{"why":"Oscillating-grid source of nearly isotropic turbulence; the grid geometry and protocol for the constant-$\\ell$ control experiment are chosen from it.","marker":"[28]"},{"why":"Public DNS database of forced isotropic turbulence; provides the universal rescaled spectrum that the decaying experimental spectra collapse onto down to $Re_\\lambda \\approx 10$.","marker":"[55]"},{"why":"Introduction of the Cell Dynamical System split-step method used to solve the governing equation from experimental initial conditions.","marker":"[62]"}],"fun_headline_variants":["Turbulent blob's spread and decay predicted by one equation","Sharp front and t^-2 decay emerge from blob turbulence","Cascade fingerprint survives to final decay of turbulent blob","Blob of turbulence expands and dies by nonlinear diffusion","One nonlinear diffusion equation governs turbulent blob's fate"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the measured two-dimensional integral length scale $\\ell(t)$ faithfully represents the three-dimensional eddy field and that the two Kolmogorov closures — transport $\\kappa_q = c_0 \\ell \\sqrt{q}$ and dissipation $\\varepsilon = \\varepsilon_0 q^{3/2}/\\ell$ — hold at every instant, down to $Re_\\lambda \\approx 10$ and across the moment the blob touches the tank walls; the paper itself drops $c_0$ from $1.2$ to $0.001$ after wall contact to reproduce the observed crossover, conceding that the closure fails in exactly that regime.","fun_headline_variants_meta":{"raw":{"variants":["Turbulent blob's spread and decay predicted by one equation","Sharp front and t^-2 decay emerge from blob turbulence","Cascade fingerprint survives to final decay of turbulent blob","Blob of turbulence expands and dies by nonlinear diffusion","One nonlinear diffusion equation governs turbulent blob's fate"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000343,"raw_usage":{"total_tokens":1991,"prompt_tokens":1155,"completion_tokens":836,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":771,"completion_tokens_details":{"reasoning_tokens":758}},"tokens_in":771,"tokens_out":836,"duration_ms":9000,"temperature":1.0,"reasoning_tokens":758,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T13:01:55.193732+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Follow the same isolated blob in a domain large enough that the eddies never feel the walls — a much larger tank, or a direct numerical simulation box with an identical initial blob — and check two predictions at once: the front profile should stay compact, $q \\propto [1-(r/h)^2]^2_+$ with no exponential tail and $h \\sim (t-t_0)^{0.38}$, and the decay exponent should change only when the measured $\\ell(t)$ changes. An exponential front tail, or a decay-rate change uncorrelated with $\\ell(t)$, would refute both the $m = 3/2$ nonlinearity and the claim that $\\ell$ controls the decay exponent.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Kolmogorov's 1942 mean-field kinetic equations for turbulence; the source of the transport and dissipation closures $\\kappa_q = c_0 \\ell \\sqrt{q}$ and $\\varepsilon = \\varepsilon_0 q^{3/2}/\\ell$ that define the model."},{"cited_title":"Goldenfeld, O","cited_arxiv_id":null,"evidence_quote":"Barenblatt's self-similar analysis of a turbulent burst from an instantaneous point source; the origin of the sharp-front, intermediate-asymptotics framework tested here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Renormalization-group theory for turbulent burst propagation; the source of the predicted anomalous scaling exponent (0.389) the measured front is compared with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishment of the vortex-ring collider that creates an isolated turbulent blob; the experimental platform supplying all datasets and initial conditions."},{"cited_title":"Using the logarithmic triggering scheme described in §IV A 4, these subregions are [ta,tm] and [tm,tb], where tm =√ta·tb","cited_arxiv_id":null,"evidence_quote":"Demonstration of the $t^{-2}$ vorticity decay law in constant-length-scale homogeneous turbulence; the baseline the late-time universal decay must match."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Oscillating-grid source of nearly isotropic turbulence; the grid geometry and protocol for the constant-$\\ell$ control experiment are chosen from it."},{"cited_title":"Goldenfeld, P","cited_arxiv_id":null,"evidence_quote":"Public DNS database of forced isotropic turbulence; provides the universal rescaled spectrum that the decaying experimental spectra collapse onto down to $Re_\\lambda \\approx 10$."},{"cited_title":"Raffel, C","cited_arxiv_id":null,"evidence_quote":"Introduction of the Cell Dynamical System split-step method used to solve the governing equation from experimental initial conditions."}],"review_version":1}