{"id":"09970345-5950-4ebd-9864-c0c0ab1a2ed5","arxiv_id":"2608.01542","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Concave wall shape amplifies jet screech by up to 23 dB, and helical tones lock to a guided jet mode while axisymmetric tones follow the loop-length criterion.","lead":"Simulations of supersonic jets hitting curved, bowl-shaped walls show that a narrower indentation can boost the jet's screech tone by up to 23 decibels compared with a flat wall. The study also shows that spinning (helical) tones are set by waves trapped inside the jet, while symmetric tones follow the classic feedback-loop distance.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"23 dB curvature-amplification claim is confounded by standoff: Flat[L2.1] gains 20.4 dB over Flat[L2.6] from distance alone, so the headline overstates the curvature-specific effect.","rationale":"The reader's weakest_assumption focuses on q_d being identical across configurations, which affects only the source-transfer decomposition. The more load-bearing concern is the standoff confound in the headline 23 dB claim: the concave geometries change effective wall distance as well as curvature, and the paper's own Flat[L2.1] case demonstrates that standoff alone accounts for 20.4 dB of the 23 dB difference. The reader did note the Flat[L2.6] reference mixing standoff and shape in the limitations paragraph, but did not make it the central issue. Since the helical-mode locking and loading-direction results are independent of this confound, the appropriate verdict remains conditional, not rejection; however, the curvature-amplification claim needs a standoff-matched control before it can be stated as written.","tokens_in":38833,"tokens_out":7222,"duration_ms":78787,"concrete_test":"Run one additional flat-wall LES at the footprint-mean standoff of Concave[σ0.4], L_avg/D=2.43 (or lip-line ℓ_lip/D=2.31), using the same grid, solver, probe ring and spectral processing as the six existing cases, and compare SPL1 and St1 with Concave[σ0.4] (175.7 dB/St) and Flat[L2.6] (152.7 dB/St). If the flat-wall SPL1 at L/D=2.43 is within ~2-3 dB of 175.7, the 23 dB curvature claim collapses to a standoff effect; if it lies closer to 165 dB, a genuine curvature amplification of ~10 dB survives. A complementary case would set the Gaussian base so that L_avg of Concave[σ0.4] equals 2.58, matching Flat[L2.6] standoff.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline effect, up to 23 dB primary-tone amplification from concave indentation relative to Flat[L2.6], does not isolate wall curvature from nozzle-to-wall standoff. The concave family is defined by z/D = 2.08 + 0.5 exp(-(r/D)^2/(2σ^2)) (Eq. 2.1), so changing σ changes both indentation shape and the effective wall distance. For Concave[σ0.4], ℓ_lip/D=2.31 and L_avg/D=2.43 (Table 1), versus 2.58 for Flat[L2.6]. The paper's own Flat[L2.1] case shows the magnitude of the standoff effect: at L/D=2.08 its SPL1 is 173.1 dB/St, already 20.4 dB above Flat[L2.6] (152.7 dB/St) and only 2.6 dB below Concave[σ0.4] (175.7 dB/St) (Table 2). Thus most of the 23 dB difference is reproduced by moving a flat wall closer; it is not a measure of curvature. The §3.5 limitations admit that the Flat[L2.6] reference 'differs in mean standoff as well as in shape', and the budget's own source term gives Flat[L2.1] +10.4 dB over Flat[L2.6] purely from its shorter standoff. The abstract and conclusions nevertheless present the 23 dB as the curvature effect. Because no simulation holds standoff fixed while varying σ, the causal claim that wall curvature controls screech amplitude by up to 23 dB is quantitatively unsupported. This does not invalidate the helical-mode locking result, but it is central to the paper's novelty.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses compressible large-eddy simulations of an underexpanded round supersonic jet (Mj = 1.56, Re = 6e4) impinging on flat and Gaussian-concave walls, together with a vortex-sheet guided-jet-mode model and Powell's feedback-loop analysis. Six geometries are studied: two flat plates at L/D = 2.08 and 2.58, and four Gaussian indentations of fixed depth with spread sigma = 0.4, 0.8, 1.6, 4.0. The central claims are that (i) narrowing the indentation amplifies the primary screech tone by up to 23 dB relative to the flat wall at L/D = 2.6, with the amplification attributed to a Powell-Tam source-transfer budget; (ii) helical screech tones lock to the lower-limit frequency of the H1 guided jet mode, independent of wall geometry, while axisymmetric tones follow Powell's loop-length criterion; and (iii) the azimuthal symmetry of the screech mode selects whether the unsteady wall loading appears in the axial force or in the transverse force and bending moment.","tokens_in":39315,"tokens_out":4486,"duration_ms":53977,"significance":"If the claims hold, the paper provides a useful demonstration that wall curvature can control both screech amplitude and the direction of unsteady surface loading, and it offers a clean separation between helical and axisymmetric frequency-selection mechanisms. The helical result is especially strong: the H1 lower-limit prediction is computed from an external vortex-sheet benchmark with no fitted constants, and it is supported by both the measured frequencies and the radial eigenfunctions across all four helical cases. The loading-selection rule in Eq. (4.1) is elegant and directly verified by the spectral content of Fz and the bending moment. However, the headline 23 dB curvature-amplification claim is quantitatively confounded by standoff, and the axisymmetric Powell claim is based on only two cases, one of which is poorly predicted. The paper deserves publication only after these load-bearing issues are addressed.","major_comments":[{"comment":"The headline claim of 'up to 23 dB' amplification from concave indentation is not a clean measure of curvature because the concave family also changes the nozzle-to-wall standoff. Concave[σ0.4] has ℓlip/D = 2.31 and Lavg/D = 2.43, versus L/D = 2.58 for Flat[L2.6]. The paper's own Flat[L2.1] case shows the size of the standoff effect: at L/D = 2.08 its SPL1 is 173.1 dB/St, only 2.6 dB below Concave[σ0.4] (175.7 dB/St), while Flat[L2.6] is 152.7 dB/St. The §3.5 limitations admit that the Flat[L2.6] reference 'differs in mean standoff as well as in shape', and the budget's own source term assigns +10.4 dB to Flat[L2.1] purely from standoff. No simulation holds standoff fixed while varying σ, so the 23 dB value in the abstract and conclusions overstates the curvature-specific effect. This should be either reworded to acknowledge the standoff contribution explicitly, or supported by matched-s","section":"§3.2, Table 2, Eq. (2.1), Conclusions (i)"},{"comment":"The source-transfer budget is not a quantitative attribution for most of the configurations. The transfer term ΔTu is a residual by construction, and the source term ΔSPL^PT_src uses the total rms Mach-disk displacement. For the four helical cases, the axial Mach-disk displacement retains only 5–10% of its rms in a band around the primary tone, and the axial motion is not the tonal source for a helical mode, as the paper itself states in the Limitations. Since four of the six cases are helical, the claimed 62%/38% and 40%/60% splits in Fig. 8(c) rest on a source estimate that is not the relevant tonal source for half the configurations. The direct upstream-wave measurements of §5.2 support a real increase in the returning wave, but they do not quantify the source/transfer split. The conclusions should be reworded to present this as a first-order, two-channel observation rather than a mea","section":"§3.5, Eqs. (3.2)–(3.3), Fig. 8(c)"},{"comment":"The claim that 'axisymmetric frequencies follow Powell's loop-length criterion' is weakly supported. For Flat[L2.1] the Powell prediction is within 2%, but for Concave[σ0.4] it overpredicts the tone by 17.9% using ℓlip and by 12.2% using Lavg. Matching the measured tone would require uc ≈ 0.46–0.50uj, well below the measured 0.599uj, and the paper notes that this case's convection velocity is the least reliable. With only two axisymmetric cases, one degraded by more than 12%, the contrast with the helical H1-lower-limit agreement (3–9% across four cases) is not strong enough to support a distinct 'loop-length selection' mechanism as a firm conclusion. The axisymmetric result should be presented as tentative, or additional axisymmetric cases at other standoffs should be added.","section":"§5.4, Table 3, Fig. 18(b)"}],"minor_comments":[{"comment":"Typos: 'Distructive interference' should be 'Destructive interference'.","section":"Figure 7 caption"},{"comment":"The mode labels 'A' and 'C' are used without an explicit definition of 'C' at first appearance; state that 'C' denotes the helical (m = ±1) family, for example after Eq. (3.1) or in the Table 2 caption.","section":"§3.4, Table 2"},{"comment":"The Wagner (1971) entry in the reference list appears to have a mismatched title; please verify that it corresponds to the cited impinging-jet study.","section":"References"},{"comment":"The vertical offset of the spectra by +30 dB makes the comparison across curves possible, but the y-axis label is unclear; specify which curve is offset and by how much in the caption.","section":"§3.2, Fig. 3(a)"}],"recommendation":"major_revision","confidential_remarks":"The helical H1 lower-limit locking result is the strongest and most original contribution; it is supported by an external benchmark and should survive revision. The 23 dB curvature-amplification claim, by contrast, is currently overstated because of the standoff confound, and the Powell-Tam budget is partly circular for the helical cases. The paper is likely publishable after the claims are reworded to match the actual evidence and, if feasible, after adding a matched-standoff flat case to isolate curvature. I would not reject, but the central quantitative claim needs work before acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick read of arXiv:2608.01542. The strongest genuinely new result is the helical-tone locking: all four helical cases, flat and concave, sit within 3–9% of the H1 guided-jet-mode lower limit from the vortex-sheet model, and the radial eigenfunctions match the J1 structure. That's an independent benchmark with no fitted constants, and it's convincing. The loading selection rule (m=0 controls axial force, m=±1 controls transverse force and moment) is clean and useful, and the wall-pressure modal decomposition is well executed. The LES is carefully validated against Gojon & Bogey, and the paper is unusually honest about the limits of its source-transfer budget.\n\nThe soft spot is the 23 dB headline. The concave family does not hold standoff fixed: as sigma decreases, the wall moves closer. Flat[L2.1] at L/D=2.08 already reaches 173.1 dB/St, 20.4 dB above Flat[L2.6]. Concave[sigma0.4] is 175.7 dB/St, only 2.6 dB higher. So most of the claimed curvature amplification is actually a standoff effect. The paper acknowledges in §3.5 that the reference differs in mean standoff, but the abstract and conclusions still present 23 dB as curvature-induced. That overstates the evidence. The monotonic trend across the concave family is real, but it conflates geometry and distance. A fixed-standoff series, or at least an L_avg-matched flat case, is needed before you can claim curvature controls amplitude by 20+ dB.\n\nThe Powell–Tam budget is a secondary worry. The transfer term is a residual by construction, so the abstract's 'more efficient return of the upstream feedback wave' is an interpretation, not a measurement. The direct upstream-wave measurements do show the upstream field amplifying, but the source/transfer split should be labelled conditional. The axisymmetric Powell prediction uses a hand-assigned integer N; that's standard, but it's a free parameter, so that agreement is weaker evidence than the H1 locking.\n\nAll that said, this is a serious piece of work. The H1 locking and the loading rules are new and likely to hold up. It deserves a proper referee. My recommendation: send to review, but require the authors to either add a fixed-standoff control (or an L_avg-matched flat case) or explicitly reframe the 23 dB claim as a combined standoff-plus-curvature effect. Also soften the source-transfer attribution. I'd bring it to the reading group and would cite the helical-mode result.","headline":"The helical-mode locking to the H1 guided-jet-mode lower limit is the solid, citable result; the 23 dB curvature-amplification claim is overstated because standoff is not controlled — Flat[L2.1] already gains 20.4 dB purely from distance.","tokens_in":39765,"tokens_out":3513,"would_cite":true,"duration_ms":42628,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["47.40.Ki","43.28.Ra"],"model":"deepseek-v4-flash","headline":"A concave wall facing a supersonic jet can amplify the primary screech tone by up to 23 dB compared with a flat wall, because the curved surface focuses the returning feedback wave back toward the nozzle lip.","keywords":["aeroacoustics","screech tones","supersonic impinging jets","guided jet modes","wall curvature effects","large-eddy simulation","surface loading"],"falsifier":"Keep the jet at Mj=1.56 and sweep the flat-wall standoff L/D between about 2.0 and 3.0 in the same computational setup: the helical-tone claim predicts the tone stays pinned near St≈0.325 (the H1 lower limit is set by the jet profile alone), while the axisymmetric tone steps along the Powell ladder; if the helical tone instead moves with L/D, the dispersive-selection claim fails. Separately, computing q_d directly from the shear-layer wavepacket growth for each of the six geometries would settle the source-transfer split: a variation of more than about 1 dB across cases would misattribute the","tokens_in":38758,"feed_emoji":"🔊","tokens_out":15438,"duration_ms":127563,"temperature":0.7,"pith_summary":"The paper argues that a concave wall facing an underexpanded supersonic jet is not a passive receiver: the indentation acts as an acoustic mirror and resonator that focuses the feedback wave back toward the nozzle, amplifying the primary screech tone by up to 23 dB relative to a flat wall at comparable standoff. It further claims helical and axisymmetric tones are chosen by different physics — helical tones lock to the lower-frequency edge of the H1 guided jet mode set by the jet's own shear-layer profile, while axisymmetric tones follow Powell's loop-length criterion. If both claims hold, wall curvature becomes a practical control for tone amplitude and, through a mode-selection rule, for the direction of the unsteady surface load: axial pounding for axisymmetric screech, a rotating in-plane bending moment for helical screech. The stakes are concrete because surface shape appears in vertical take-off and landing over contoured ground, jet-blast deflectors, and cold-spray deposition, where tonal loading drives fatigue.","feed_headline":"Curved wall boosts supersonic jet screech 23 dB","feed_subtitle":"Curvature refocuses the returning sound wave and steers where the unsteady load hits the surface","key_machinery":"Four coupled pieces. (1) The Gaussian indentation $z/D=2.08+0.5\\exp(-(r/D)^2/2\\sigma^2)$ reduces wall shape to one parameter $\\sigma$ interpolating between the two flat-wall limits. (2) The Powell-Tam source-transfer budget $\\Delta\\mathrm{SPL}_{\\mathrm{lip}}=\\Delta\\mathrm{SPL}^{\\mathrm{PT}}_{\\mathrm{src}}+\\Delta T_u$ (Eq. 3.2) partitions curvature-induced amplification: the source term scales with rms Mach-disk displacement times tone Strouhal (Eq. 3.3), and the transfer term $\\Delta T_u$ is the residual that measures the efficiency of the upstream return to the lip. (3) The vortex-sheet guided-jet-mode dispersion relation (Tam & Hu 1989; Tam & Ahuja 1990), whose H1 lower limit — where the m","core_discovery":"A concave impingement wall actively shapes the screech resonance. Narrowing the indentation spread $\\sigma$ from 4.0 to 0.4 raises the primary-tone level by about 23 dB above the Flat[L2.6] reference, to $\\approx$176 dB/St. A Powell-Tam budget splits this gain between a stronger Mach-disk tonal source (62% at $\\sigma$0.4) and a more efficient upstream return of the feedback wave to the nozzle (38%); direct measurement shows the returning wave strengthens by up to 27 dB, carried mainly inside the jet column. All four helical cases pick tones within St=0.336–0.357, just 3–9% above the H1 guided-jet-mode lower limit, with matching J1 eigenfunctions — evidence a guided jet mode closes the helica","pith_inferences":["My inference: because the H1 lower limit depends only on the jet's shear-layer profile and operating condition, the paper's claim implies the helical tone frequency should stay nearly fixed as the nozzle-to-wall distance is swept at constant Mj — a test the six-case matrix does not isolate, since standoff and mode type co-vary there.","My inference: the Hartmann-whistle analogy the authors invoke suggests indentation depth (fixed at 0.5D here) is the natural second control; varying depth at fixed σ should move the tone through cavity-mode staging, possibly recovering the screech suppression reported for convex cylindrical walls in earlier experiments.","My inference: the axisymmetric tone's failure to match any A_n branch may reflect the underexpanded shock structure rather than a true non-GJM mechanism; a shock-free (ideally expanded) jet at the same loop length should land on a guided branch if the guided-mode picture extends.","My inference: for applications (VTOL over contoured terrain, jet-blast deflectors, cold-spray deposition), the practical reading is that terrain shape can be treated as a control input: a narrow pocket both amplifies the tone and decides whether fatigue loading pulses along the axis or rotates in-plane."],"forward_implications":["If the wall-curvature result is correct, a narrow concave indentation is an effective amplifier rather than a suppressor of impingement tones: up to 23 dB of extra tonal level at L/D≈2.6, strongest when the indentation stays within about two jet diameters of the axis (r99/D ≲ 2.4).","Helical screech frequency is governed by the jet's shear-layer profile, not the wall: all four helical cases sit within St=0.336–0.357, within 3–9% of the H1 lower limit, so wall geometry can change helical tone amplitude but not its frequency.","The screech mode is the fatigue-load switch: axisymmetric screech concentrates tonal energy in the axial force (up to 43% of the mean net load in rms at σ0.4), while helical screech hides the tone from the axial force and puts it in a precessing in-plane bending moment, largest at intermediate indentation spread.","The concave wall focuses the returning wave through both the jet column and the ambient, and the channel that benefits depends on how far the indentation extends past the column — 78% of the σ0.4 indentation area sits within r/D=0.7, and the column channel gains 15.8 dB more than the ambient there."],"supporting_citations":[{"why":"Supplies the feedback-loop model — downstream-convected instability waves plus upstream acoustic return — and the loop-length criterion used for the axisymmetric tones.","marker":"Powell (1953)"},{"why":"Supplies the vortex-sheet guided-jet-mode dispersion relation, eigenfunctions, and the lower-limit formulas (Eqs. A8–A9) that predict the helical tones.","marker":"Tam & Ahuja (1990)"},{"why":"Supplies the computational setup, grid design, and the Flat[L2.1] LES baseline used for validation, plus the empirical convection-velocity relation (Eq. 5.1).","marker":"Gojon & Bogey (2017)"},{"why":"Supplies the experimental reference configuration at Mj=1.56 and the PIV data used to validate the Flat[L2.1] flow field and Mach-disk unsteadiness.","marker":"Henderson et al. (2005)"},{"why":"Establishes that upstream-propagating waves close the loop as column-confined guided jet modes in ideally expanded impinging jets, the comparison point for the helical claim.","marker":"Bogey & Gojon (2017)"},{"why":"Demonstrates GJM closure of axisymmetric screech on an inclined plate up to Mj=1.56 and shows an external boundary can modulate the resonance; the closest prior evidence for lower-limit locking.","marker":"Li et al. (2023b)"},{"why":"Review that frames the internal-versus-external upstream-pathway debate and the azimuthal mode classification the paper draws on.","marker":"Edgington-Mitchell (2019)"},{"why":"Shows external boundary geometry controls azimuthal mode selection in impinging underexpanded jets, the precedent for the claim that the wall can select the loading mode.","marker":"Weightman et al. (2019)"}],"fun_headline_variants":["Curved impingement wall boosts jet screech by 23 dB","Concave wall focuses feedback, amplifying jet tone 23 dB","Supersonic jet screech increases 23 dB with wall curvature","Wall curvature controls screech amplitude: 23 dB rise","Jet impingement: curved walls yield 23 dB stronger tones"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The load-bearing premise is that the downstream shear-layer gain q_d is the same for all six geometries (Section 3.5), so that every curvature effect can be attributed to the Mach-disk source and the upstream return — a premise the paper's own Limitations paragraph hedges, noting that the transfer term is a residual rather than a measured ratio and that the Flat[L2.6] reference mixes standoff with shape.","fun_headline_variants_meta":{"raw":{"variants":["Curved impingement wall boosts jet screech by 23 dB","Concave wall focuses feedback, amplifying jet tone 23 dB","Supersonic jet screech increases 23 dB with wall curvature","Wall curvature controls screech amplitude: 23 dB rise","Jet impingement: curved walls yield 23 dB stronger tones"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000257,"raw_usage":{"total_tokens":1493,"prompt_tokens":898,"completion_tokens":595,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":642,"completion_tokens_details":{"reasoning_tokens":506}},"tokens_in":642,"tokens_out":595,"duration_ms":6684,"temperature":1.0,"reasoning_tokens":506,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T00:02:59.242400+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Keep the jet at Mj=1.56 and sweep the flat-wall standoff L/D between about 2.0 and 3.0 in the same computational setup: the helical-tone claim predicts the tone stays pinned near St≈0.325 (the H1 lower limit is set by the jet profile alone), while the axisymmetric tone steps along the Powell ladder; if the helical tone instead moves with L/D, the dispersive-selection claim fails. Separately, computing q_d directly from the shear-layer wavepacket growth for each of the six geometries would settle the source-transfer split: a variation of more than about 1 dB across cases would misattribute the","supporting_citations":[{"cited_title":"Proceedings of the Physical Society","cited_arxiv_id":null,"evidence_quote":"Supplies the feedback-loop model — downstream-convected instability waves plus upstream acoustic return — and the loop-length criterion used for the axisymmetric tones."},{"cited_title":"Journal of Fluid Mechanics 214 , 67--87","cited_arxiv_id":null,"evidence_quote":"Supplies the vortex-sheet guided-jet-mode dispersion relation, eigenfunctions, and the lower-limit formulas (Eqs. A8–A9) that predict the helical tones."},{"cited_title":"Journal of Fluid Mechanics 542 , 115--137","cited_arxiv_id":null,"evidence_quote":"Supplies the experimental reference configuration at Mj=1.56 and the PIV data used to validate the Flat[L2.1] flow field and Mach-disk unsteadiness."},{"cited_title":"International Journal of Aeroacoustics 18 (2-3), 118--188","cited_arxiv_id":null,"evidence_quote":"Review that frames the internal-versus-external upstream-pathway debate and the azimuthal mode classification the paper draws on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows external boundary geometry controls azimuthal mode selection in impinging underexpanded jets, the precedent for the claim that the wall can select the loading mode."}],"review_version":1}