Pith. sign in

REVIEW 5 major objections 4 minor 69 references

Intermittent turbulent gusts lift eagles

T0 review · 5 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Golden eagles gain lift from violent turbulent gusts

desk verdict Careful statistics show a real upward asymmetry in eagles' extreme accelerations, but the gust-harvesting claim outruns what an accelerometer alone can prove. read the letter →

arxiv 2412.00231 v2 pith:NMOS44FF submitted 2024-11-29 physics.bio-ph physics.flu-dyn

Dipendra Gupta , David Brandes , Michael J Lanzone , Tricia Miller , Gregory P Bewley This is my paper · ORCID
classification physics.bio-phphysics.flu-dyn
keywords eagleflightturbulentgustsgustharvestingintermittencynonlinearaerodynamicssoaringaccelerometryliftamplification
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that soaring golden eagles do not simply endure turbulence; they extract upward momentum from short, intense gust bursts. Accelerometer data from wild eagles show vertical accelerations up to 25 standard deviations from the mean, more than three times gravity, with upward bursts more frequent and stronger than downward ones. Such asymmetry is impossible under linear gust-response models, so the authors introduce a nonlinear correction in which strong gusts produce extra lift. They argue this constitutes the first quantitative evidence of turbulent gust harvesting by wildlife, meaning turbulence is an energy source rather than only a disturbance for animals and potentially for small aircraft.

What carries the argument

The central machinery is a conditional-averaging statistic from turbulence research: average the acceleration traces around local extrema of the acceleration difference $\delta a_z(t,\tau)$ to reconstruct the signature of a vortex encounter. The load-bearing identity is the nonlinear gust-amplification model $a_z = (w_z/\tau_b)(1 + k w_z \tau_b/\ell)$, with $k>0$, which ties the asymmetry between upward and downward excursions to a predicted crossover in the flatness $F_{\delta a_z}$ at $\tau_c \approx 0.3$ s. The flatness, defined as the normalized fourth moment of a distribution, measures tail breadth and is the key observable that separates turbulence-like scaling from the eagle-specific intermittency.

What would settle it

An experiment that would settle it: mount the same accelerometer package on a rigid glider or a taxidermied bird in a wind tunnel with intermittent gusts; if the upward bias disappears, the eagle's active body movements are the cause rather than the gust.

Watch

Extended reading notes

Core claim

On timescales below about 2 s, the vertical acceleration differences of soaring golden eagles are far more intermittent than turbulence itself and are biased upward. Conditional averages of extreme events (|H| ≥ 5 standard deviations) show that the eagles are pushed up more strongly than down, breaking the symmetry found in turbulent wind statistics at small scales. The authors model this with a single-parameter nonlinear law, $a_z = (w_z/\tau_b)(1 + k w_z \tau_b/\ell)$, with $k \approx 0.6 \pm 0.1 > 0$ indicating gust amplification rather than stall or mitigation. The model predicts a crossover near $\tau_c \approx 0.3$ s between turbulence-like intermittency (flatness $\sim \tau^{-0.2}$) and a steeper $\tau^{-1}$ rise, matching the data. The conclusion is a ratcheting mechanism: eagles repeatedly convert strong upward gust impulses into lift, and about 20% of soaring flight time is spent in gusts strong enough to trigger nonlinear aerodynamic changes.

Load-bearing premise

The load-bearing premise is that the extreme vertical accelerations recorded during gliding are caused by atmospheric wind gusts rather than by the eagles' own wing adjustments, partial flaps, or sensor motion.

Editorial extensions

If this is right

  • If the ratcheting mechanism is correct, turbulence must be treated as an energy input in the flight energetics of soaring birds, not merely as a dissipative disturbance.
  • The measured 20% of soaring time spent in strong gusts implies that unsteady, nonlinear aerodynamics is the norm in boundary-layer soaring flight, not a rare edge case.
  • The predicted crossover near 0.3 s provides a target for when gust exploitation outweighs linear response, a scale directly relevant to the design of small aircraft and drones.
  • The same conditional-averaging and flatness analysis could be applied to accelerometer data from other volant species to detect gust harvesting wherever it occurs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the ratcheting picture holds, the energy gained from gusts could partially offset the metabolic cost of flapping and gliding, a net energy budget that the paper does not attempt to calculate.
  • An extension of the model suggests that smaller birds with shorter wing chords should show an earlier crossover and stronger short-scale intermittency, a testable prediction across species.
  • The coefficient k could be estimated per individual from the flatness data; if k varies with wind conditions or body condition, it would point toward active control rather than purely passive aerodynamics.
  • A direct experimental test would be to expose a fixed-wing glider or a non-flapping model in a wind tunnel to intermittent gusts and check whether the upward bias appears without active wing motion; if it does, the effect is passive aerodynamic amplification.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 4 minor

Summary. The paper analyzes 40 Hz accelerometer data from six golden eagles and six bald eagles in free flight. It reports that vertical acceleration differences in soaring golden eagles have heavy-tailed distributions, with excursions up to 25 standard deviations, that the conditional averages around extreme events resemble turbulent vortex passages, and that extreme upward acceleration events break the up/down symmetry of the underlying wind statistics. The authors propose a nonlinear response model az = (wz/τb)(1 + k wz τb/ℓ), estimate k ≈ 0.6 from the up/down asymmetry of extreme events, and claim the model predicts a crossover timescale τc ≈ 0.3 s near which acceleration flatness rises as τ^{-1}, consistent with observed small-scale intermittency. They interpret the results as a 'ratcheting mechanism' and 'the first quantitative evidence in favor of turbulent gust harvesting by wildlife.'

Significance. The statistical work is careful: the flapping classification uses cross-correlation with template flaps, the golden-eagle versus bald-eagle comparison separates flapping-related intermittency from turbulence-like intermittency, and sensitivity checks on thresholds are reported. If the extreme accelerations are indeed caused by atmospheric gusts, the observed upward asymmetry and small-scale intermittency enhancement would be a novel and physically interesting example of nonlinear interaction between a flying animal and boundary-layer turbulence, with implications for the design of small aerial vehicles and for interpreting bio-logging data. However, the paper's headline conclusion—gust harvesting—requires an energy budget and a direct attribution of accelerations to wind, neither of which is provided; the currently available evidence supports a more modest claim about nonlinear, asymmetric acceleration statistics during soaring.

major comments (5)
  1. [Vortical structure of the eagles' acceleration / Discussion and conclusions] The attribution of extreme accelerations to external gusts is not established. The measurements are body-fixed accelerations; there is no independent, co-located wind measurement, and the flight-behavior classification separates only flapping from non-flapping, leaving partial flaps, wing tucks, tail adjustments, and harness/sensor dynamics inside the gliding class. The paper itself acknowledges an oscillation 'whose origin is unknown to us' that 'could be related to the way the sensors were attached ... or to wing adjustments,' and in the Discussion assumes 'that all extreme events observed in the interval 0.2 s < τ < 2 s are due to interactions with gusts, which is what the statistics suggest.' That sentence is circular for the causal question: the statistics are statistics of the eagles' measured accelerations and cannot by themselves identify the aerodynamic cause. Because the gust-harvesting claim depends on this assumption, the manuscript needs either a direct test (e.g., temporal or spatial correlation with independently measured atmospheric turbulence, or a kinematic control using the lateral and longitudinal channels to detect wing adjustments) or a substantial reframing of the conclusions as conditional on the gust assumption.
  2. [Nonlinear model of the eagles' response to gusts] The nonlinear coefficient k is estimated from the asymmetry of the very extreme events (the relation a+z/a−z ≈ −1 + k(τb^2/ℓ)(a+z − a−z)), and the same k is then used to derive the flatness enhancement Fδaz ≈ (1 + 4kσwzτb/ℓ)Fδwz and the crossover timescale τc = 1/(4V kσwzτb). Consequently, the agreement of the predicted crossover near 0.3 s with the observed crossover near 0.4 s is an internal consistency check, not an independent prediction of the model. The abstract's phrase 'predicts the scale at which symmetry breaks' is thus overstated. To make the claim non-circular, the authors would need to estimate k from one subset of events (or from a different observable) and then test the flatness and crossover prediction on independent data.
  3. [Nonlinear model of the eagles' response to gusts] The model and the flatness comparison are constructed asymmetrically: the text states that the nonlinearity is not physical for large negative wz, so the flatness Fδaz is calculated only for positive excursions in wz, while the turbulent wind flatness Fδwz is computed from both signs. The derived scaling Fδaz ∼ (1 + 4kσwzτb/ℓ)Fδwz therefore depends on this sign restriction and on the assumptions of local isotropy and ⟨δwΣw⟩ = 0. These restrictions should be stated as part of the model definition, and the comparison should be justified or the metric defined consistently; otherwise the predicted 'stronger intermittency than turbulence' may be an artifact of the asymmetric truncation.
  4. [Discussion and conclusions] The claim of gust harvesting requires an energy budget. A ratcheting mechanism that increases the mean mechanical energy of the eagle must show that the work done by the fluctuating wind on the bird is positive on average after accounting for induced drag, the cost of the bird's control responses, and the vertical component of the flight path. The paper states only that the eagles experienced upward accelerations and that these are 'in the eagles' interest to stay aloft'; it does not show that the eagles extract net energy from the gusts. The phrase 'first quantitative evidence in favor of turbulent gust harvesting' is therefore not supported by the presented analysis. At minimum, the manuscript should identify the energy (or power) balance needed and state why the observed asymmetry implies net positive energy gain, or soften the conclusion to 'consistent with' rather than 'evidence in favor of.'
  5. [Discussion and conclusions] The estimate that about 20% of flight time was spent in extreme events with gust ratio GR > 0.3 uses the linear relation |δaz| = |δwz|/τb to convert acceleration tails to wind velocity tails, but this is the same regime for which the paper argues linearity breaks down. Because the nonlinear model amplifies upward accelerations, the mapping from δaz to δwz is not one-to-one, and the 20% figure is model-dependent. The authors should provide the estimate under the linear model and under the nonlinear model, or explicitly label the number as a linear-model estimate whose uncertainty includes the nonlinearity.
minor comments (4)
  1. [Materials and Methods, Classification of flight behaviors] In the flap detection description, 'we labeled the time corresponding to the peak of mean flap as T = 0' should be 't = 0' to avoid confusion with the averaging time T in the flap period notation.
  2. [Materials and Methods, Conditional Averaging] In the sentence 'we selected δ(t) within ±5T', the symbol δ(t) should be written as δaz(t, τ) (or δa(t, τ)) to be consistent with the definitions used elsewhere in the paper.
  3. [Fig. 2 caption] The caption states that the findings hold for any τ between 0.2 and 4 s, but the figure displays only τ = 0.2 s and τ = 2 s; the caption should either show the additional timescales or qualify the statement as applying to the tested range.
  4. [Data availability] Because the central claims are driven by rare tail events (N ≈ 10^3 for H = ±5), the data availability statement should clarify how an independent researcher can obtain the full dataset and the analysis scripts, since the current 'available upon request with permission' policy limits verification of the extreme-event statistics.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the single fitted coefficient k is estimated from the observed up/down asymmetry of extreme acceleration events, while the flatness enhancement and crossover timescale are distinct empirical statistics, so the model comparison is a consistency check rather than a reduction to its inputs.

full rationale

The only fitted parameter in the derivation is the nonlinear coefficient k, estimated from the asymmetry of extreme acceleration excursions (Section "Nonlinear model of the eagles' response to gusts"). The flatness enhancement and the crossover timescale are then computed from that k and compared with independently measured statistics in Fig. 3. Since the flatness is an unconditional fourth-order moment and the crossover location is a derived scale, neither is identical by construction to the conditional asymmetry used to infer k; the comparison is a genuine, if in-sample, consistency test. The crossover prediction also depends on sigma_wz, which is not quoted directly, but that is a transparency weakness rather than a circular step. The Discussion's sentence "Assuming that all extreme events observed in the interval 0.2 s < tau < 2 s are due to interactions with gusts, which is what the statistics suggest" is an openly stated causal identification assumption about wing adjustments, body tucks, or harness motion; it is a correctness and attribution risk, not a derivation that reduces to its own inputs. The cited linear relation from Laurent et al. (ref. 5) is prior independent published work by the same group, and it supplies the linear baseline and tau_b without incorporating the present paper's nonlinear target result. No equation in the paper is shown to equal its own input by construction, and no fitted parameter is renamed as a prediction. Thus no circularity meeting the quoted-evidence bar is present.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim depends on a quadratic response model whose coefficient k is fitted from the same extreme-event data, on an unstated value of σwz for the crossover prediction, and on the assumption that all gliding extreme accelerations are gusts rather than wing adjustments or sensor artifacts. The linear model and τb, V are inherited from prior work by the same group. No new physical entities are postulated.

free parameters (4)
  • k (nonlinear response coefficient) = 0.6 ± 0.1
    Estimated from the asymmetry between upward and downward peak accelerations during extreme events (GR > 1). Used in the nonlinear model, flatness formula, and crossover prediction.
  • σwz (RMS vertical wind velocity) = implied ~0.14 m/s, unstated
    The crossover prediction τc = 1/(4 V k σwz τb) ≈ 0.3 s requires σwz ≈ 0.14 m/s given V = 10 m/s, τb = 1 s, k = 0.6, but the paper does not state this value or its source.
  • τb (eagle response timescale) = ≈ 1 s (from prior work)
    Inherited from Laurent et al. 2021; used in linear model az = wz/τb and in the nonlinear model. Not fitted in this paper but is an assumed input.
  • V (flight speed) = ≈ 10 m/s
    Assumed typical flight speed used to convert timescales to length scales via ℓ = τ V and to estimate gust ratios and the crossover timescale.
assumptions (6)
  • domain assumption Taylor's frozen-flow hypothesis (ℓ = τ V) applies to eagle trajectories and wind statistics
    Used throughout to convert temporal increments to spatial scales; requires approximately straight flight and flight speed large relative to wind fluctuations. Location: 'How we related turbulence, gusts and eagle accelerations' and ref. 54.
  • domain assumption Linear relation az = wz/τb holds at leading order for typical fluctuations
    Inherited from Laurent et al. 2021; used to compute variances and to convert accelerations to gust ratios. Location: 'For straight and level flight...'.
  • domain assumption Small-scale turbulence is locally isotropic and velocity sums and differences are uncorrelated
    Used in deriving moment formulas for flatness and k. Location: 'Theory' section, relying on refs. 49 and 69.
  • ad hoc to paper The nonlinear model is physical only for positive wz, so flatness is calculated only for positive excursions
    This restriction avoids unphysical negative-lift behavior of the quadratic model and shapes the model's prediction. Location: 'The latter is necessary since the nonlinearity is not physical for large negative fluctuations in wz...'.
  • domain assumption All extreme events in gliding flight are due to wind gusts rather than to eagle behavior or sensor artifacts
    Explicitly assumed in Discussion: 'Assuming that all extreme events observed... are due to interactions with gusts...' and undercut by the acknowledged oscillation of unknown origin possibly from wing adjustments or sensor mounting.
  • domain assumption Wind tunnel turbulence at Rλ ≈ 700 is representative of atmospheric turbulence for the relevant scale comparisons
    Used to provide Fδwz and δwz statistics for comparison with eagles in Figs. 2 and 3. Location: Materials and Methods, Wind Tunnel Turbulence data.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Intermittent turbulent gusts lift eagles." pith.science (2026). https://pith.science/paper/NMOS44FF

@misc{pith2026241200231,
  author       = {Pith},
  title        = {Pith review of: Intermittent turbulent gusts lift eagles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NMOS44FF}},
  note         = {Machine review of arXiv:2412.00231}
}
read the original abstract

Turbulence grounds aircraft and combating it in flight requires energy, yet volant wildlife fly effortlessly even on windy days. The nature of the interactions between soaring birds and transient turbulent gusts is not clear, especially when compared with our understanding of flight in larger and steadier airflows during thermal or dynamic soaring. We show that soaring golden eagles (Aquila chrysaetos) experienced short upward accelerations indicative of preferential engagement with strong and intermittent turbulent updrafts. The vertical accelerations reflect changes in lift that were as large as 25 standard deviations from the mean, or more than three times the acceleration of gravity, and so large as not to be consistent with gust mitigation or avoidance. These extreme events occurred in short bursts that mimic movement with turbulent vortices. The burst statistics and their symmetries approach those of turbulence toward longer timescales. On the shortest timescales, the bursts break the symmetry of small-scale turbulence in favor of upward accelerations that are more intermittent than turbulence. We introduce a simple nonlinear model that predicts the scale at which symmetry breaks and the stronger intermittency on the smaller scales. These findings suggest a ratcheting mechanism on turbulent gusts and constitute the first quantitative evidence in favor of turbulent gust harvesting by wildlife. An implication is that turbulence is so strong and pervasive as to make unsteady and nonlinear aerodynamics an intrinsic and beneficial aspect of both flapping and soaring flight in the atmospheric boundary layer - one that we need to incorporate in our understanding of the energetics of flight.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

69 extracted references · 69 canonical work pages

  1. [1]

    Population limitation in birds (Acad

    Newton, I. Population limitation in birds (Acad. Press, 1998)

    work page 1998

  2. [2]

    Rapid advance of spring arrival dates in long-distance migratory birds

    Jonz´ en, N.et al. Rapid advance of spring arrival dates in long-distance migratory birds. Science 312, 1959–1961 (2006)

    work page 2006

  3. [3]

    & Yamaguchi, N

    Nourani, E. & Yamaguchi, N. M. The effects of atmospheric currents on the migratory behavior of soaring birds: a review. Ornithol. Sci. 16, 5–15 (2017)

    work page 2017

  4. [4]

    & Bodenschatz, E

    Hejazi, B., Antigny, H., Huellstrunk, S. & Bodenschatz, E. Honeybee flight dynam- ics and pair separation in windy conditions near the hive entrance. New J. Phys. 10 25, 093046 (2023)

    work page 2023

  5. [5]

    Laurent, K. M. et al. Turbulence explains the accelerations of an eagle in natural flight. Proc. Nat. Acad. Sci. USA 118, e2102588118 (2021)

    work page 2021

  6. [6]

    Lempidakis, E. et al. Estimating fine-scale changes in turbulence using the movements of a flapping flier. J. R. Soc. Interface 19, 20220577 (2022)

    work page 2022

  7. [7]

    & Peinke, J

    Boettcher, F., Renner, C., Waldl, H.-P. & Peinke, J. On the statistics of wind gusts. Bound.-Layer Meteorol. 108, 163–173 (2003)

    work page 2003

  8. [8]

    Lanzone, M. J. et al. Flight responses by a migratory soaring raptor to changing meteorological conditions. Biol. Lett. 8, 710–713 (2012)

    work page 2012

Show all 69 references
  1. [9]

    Duerr, A. E. et al. Testing an emerging paradigm in migration ecology shows surprising differences in efficiency between flight modes. PLoS One 7, e35548 (2012)

    2012

  2. [10]

    Bohrer, G. et al. Estimating updraft velocity components over large spatial scales: contrasting migration strategies of golden eagles and turkey vultures. Ecol. Lett. 15, 96–103 (2012)

    2012

  3. [11]

    Batchelor, G. K. & Townsend, A. A. The nature of turbulent motion at large wave-numbers. Proc. R. Soc. Lond. A. 199, 238–255 (1949)

    1949

  4. [12]

    & Peinke, J

    B¨ ottcher, F., Barth, S. & Peinke, J. Small and large scale fluctuations in atmospheric wind speeds. Stoch. Environ. Res. Risk Assess. 21, 299–308 (2007)

    2007

  5. [13]

    Sreenivasan, K. R. & Antonia, R. The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435–472 (1997)

    1997

  6. [14]

    & Clothier, R

    Mohamed, A., Massey, K., Watkins, S. & Clothier, R. The attitude control of fixed-wing mavs in turbulent environments. Prog. Aerosp. Sci. 66, 37–48 (2014)

    2014

  7. [15]

    R., Cetiner, O

    Jones, A. R., Cetiner, O. & Smith, M. J. Physics and modeling of large flow disturbances: Discrete gust encounters for modern air vehicles. Annu. Rev. Fluid Mech. 54, 469–493 (2022)

    2022

  8. [16]

    Pennycuick, C. J. Field observations of thermals and thermal streets, and the theory of cross-country soaring flight. J. Avian Biol. 33–43 (1998)

    1998

  9. [17]

    Reddy, G., Celani, A., Sejnowski, T. J. & Vergassola, M. Learning to soar in turbulent environments. Proc. Nat. Acad. Sci. USA 113, E4877–E4884 (2016)

    2016

  10. [18]

    & Vicsek, T

    ´Akos, Z., Nagy, M., Leven, S. & Vicsek, T. Thermal soaring flight of birds and unmanned aerial vehicles. Bioinspir. Biomim. 5, 045003 (2010)

    2010

  11. [19]

    Flight strategies of migrating hawks (Univ

    Kerlinger, P. Flight strategies of migrating hawks (Univ. Chicago Press, 1989). 11

    1989

  12. [20]

    The soaring of birds

    Rayleigh, L. The soaring of birds. Nature 27, 534–535 (1883)

  13. [21]

    Richardson, P. L. Upwind dynamic soaring of albatrosses and uavs. Prog. Oceanogr. 130, 146–156 (2015)

    2015

  14. [22]

    & Kroo, I

    Patel, C., Lee, H.-T. & Kroo, I. Extracting energy from atmospheric turbulence with flight tests. Techn. Soaring 33, 100–108 (2009)

    2009

  15. [23]

    M., Bildstein, K

    Mallon, J. M., Bildstein, K. L. & Katzner, T. E. In-flight turbulence benefits soaring birds. Auk 133, 79–85 (2016)

    2016

  16. [24]

    Bollt, S. A. & Bewley, G. P. How to extract energy from turbulence in flight by fast tracking. J. Fluid Mech. 921, A18 (2021)

    2021

  17. [25]

    & Rycroft, C

    He, D., Reddy, G. & Rycroft, C. H. Energy-positive soaring using transient turbulent fluctuations. arXiv preprint arXiv:2304.05983 (2023)

    2023 arXiv

  18. [26]

    Reddy, G., Wong-Ng, J., Celani, A., Sejnowski, T. J. & Vergassola, M. Glider soaring via reinforcement learning in the field. Nature 562, 236–239 (2018)

    2018

  19. [27]

    A., Eyink, G

    Bandak, D., Mailybaev, A. A., Eyink, G. L. & Goldenfeld, N. Spontaneous stochas- ticity amplifies even thermal noise to the largest scales of turbulence in a few eddy turnover times. Phys. Rev. Lett. 132, 104002 (2024)

    2024

  20. [28]

    V., Thomas, A

    Reynolds, K. V., Thomas, A. L. & Taylor, G. K. Wing tucks are a response to atmospheric turbulence in the soaring flight of the steppe eagle aquila nipalensis. J. R. Soc. Interface 11, 20140645 (2014)

    2014

  21. [29]

    Lempidakis, E. et al. Turbulence causes kinematic and behavioural adjustments in a flapping flier. J. R. Soc. Interface 21, 20230591 (2024)

    2024

  22. [30]

    Langley, S. P. The internal work of the wind Vol. 27 (Smithsonian institution, 1893)

  23. [31]

    & Gustavsson, K

    Biferale, L., Bonaccorso, F., Buzzicotti, M., Clark Di Leoni, P. & Gustavsson, K. Zermelo’s problem: optimal point-to-point navigation in 2d turbulent flows using reinforcement learning. Chaos 29 (2019)

    2019

  24. [32]

    & Dabiri, J

    Gunnarson, P., Mandralis, I., Novati, G., Koumoutsakos, P. & Dabiri, J. O. Learning efficient navigation in vortical flow fields.Nat. Commun. 12, 7143 (2021)

    2021

  25. [33]

    A., Favier, B

    Monthiller, R., Loisy, A., Koehl, M. A., Favier, B. & Eloy, C. Surfing on turbulence: a strategy for planktonic navigation. Phys. Rev. Lett. 129, 064502 (2022)

    2022

  26. [34]

    & Xi, H.-D

    Xu, A., Wu, H.-L. & Xi, H.-D. Long-distance migration with minimal energy consumption in a thermal turbulent environment. Phys. Rev. Fluids 8, 023502 (2023). 12

    2023

  27. [35]

    Engel, S. B. Racing the wind: Water economy and energy expenditure in avian endurance flight. Ph.D. thesis, University of Groningen (2005)

    2005

  28. [36]

    A., Biebach, H., Daan, S

    Schmidt-Wellenburg, C. A., Biebach, H., Daan, S. & Visser, G. H. Energy expendi- ture and wing beat frequency in relation to body mass in free flying barn swallows (hirundo rustica). J. Comp. Physiol. B 177, 327–337 (2007)

    2007

  29. [37]

    Friman, S. I. et al. It pays to follow the leader: Metabolic cost of flight is lower for trailing birds in small groups. Proc. Nat. Acad. Sci. USA 121, e2319971121 (2024)

    2024

  30. [38]

    & Jones, A

    Mohamed, A., Marino, M., Watkins, S., Jaworski, J. & Jones, A. Gusts encountered by flying vehicles in proximity to buildings. Drones 7, 22 (2023)

    2023

  31. [39]

    EBOOK: Fundamentals of Aerodynamics (SI units) (McGraw hill, 2011)

    Anderson, J. EBOOK: Fundamentals of Aerodynamics (SI units) (McGraw hill, 2011)

    2011

  32. [40]

    R., Saritas, M

    Biler, H., Sedky, G., Jones, A. R., Saritas, M. & Cetiner, O. Experimental inves- tigation of transverse and vortex gust encounters at low reynolds numbers. AIAA J. 59, 786–799 (2021)

    2021

  33. [41]

    & Taira, K

    Fukami, K. & Taira, K. Grasping extreme aerodynamics on a low-dimensional manifold. Nat. Commun. 14, 6480 (2023)

    2023

  34. [42]

    Eldredge, J. D. & Jones, A. R. Leading-edge vortices: mechanics and modeling. Annu. Rev. Fluid Mech. 51, 75–104 (2019)

    2019

  35. [43]

    Turbulence modeling for gust loading

    Solari, G. Turbulence modeling for gust loading. J. Struct. Eng. 113, 1550–1569 (1987)

    1987

  36. [44]

    & Cheng, P.-W

    Bierbooms, W. & Cheng, P.-W. Stochastic gust model for design calculations of wind turbines. J. Wind Eng. Ind. Aerodyn. 90, 1237–1251 (2002)

    2002

  37. [45]

    Documentation of the linear statistical discrete gust method (Office of Aviation Research, Federal Aviation Administration, 2004)

    Jones, J. Documentation of the linear statistical discrete gust method (Office of Aviation Research, Federal Aviation Administration, 2004)

    2004

  38. [46]

    & Song, L.-L

    Liu, L., Hu, F., Cheng, X.-L. & Song, L.-L. Probability density functions of velocity increments in the atmospheric boundary layer. Bound.-Layer Meteorol. 134, 243–255 (2010)

    2010

  39. [47]

    & Kawashima, Y

    Mouri, H., Hori, A. & Kawashima, Y. Vortex tubes in velocity fields of laboratory isotropic turbulence: dependence on the reynolds number.Phys. Rev. E 67, 016305 (2003)

    2003

  40. [48]

    Burgers, J. M. A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 1, 171–199 (1948). 13

    1948

  41. [49]

    Kolmogorov, A. N. The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers. Proc. R. Soc. Lond. A 434, 9–13 (1991)

    1991

  42. [50]

    & Sreenivasan, K

    Kurien, S. & Sreenivasan, K. R. Anisotropic scaling contributions to high-order structure functions in high-reynolds-number turbulence. Phys. Rev. E 62, 2206 (2000)

    2000

  43. [51]

    & Procaccia, I

    Biferale, L. & Procaccia, I. Anisotropy in turbulent flows and in turbulent transport. Phys. Rep. 414, 43–164 (2005)

    2005

  44. [52]

    Miller, T. A. et al. Implications for bird aircraft strike hazard by bald eagles. J. Wildl. Manag. 83, 879–892 (2019)

    2019

  45. [53]

    D., Miller, T

    Garstang, M., Greco, S., Emmitt, G. D., Miller, T. A. & Lanzone, M. An instru- mented golden eagle’s (aquila chrysaetos) long-distance flight behavior. Animals 12, 1470 (2022)

    2022

  46. [54]

    Taylor, G. I. The spectrum of turbulence. Proc. R. Soc. Lond. A 164, 476–490 (1938)

    1938

  47. [55]

    Dhruva, B. R. An experimental study of high Reynolds number turbulence in the atmosphere. Ph.D. thesis, Yale University (2000)

    2000

  48. [56]

    & Sreenivasan, K

    Dhruva, B., Tsuji, Y. & Sreenivasan, K. R. Transverse structure functions in high-reynolds-number turbulence. Phys. Rev. E 56, R4928 (1997)

    1997

  49. [57]

    & Heppner, F

    Pomeroy, H. & Heppner, F. Laboratory determination of startle reaction time of the starling (sturnus vulgaris). Anim. Behav. 25, 720–725 (1977)

    1977

  50. [58]

    Cheney, J. A. et al. Bird wings act as a suspension system that rejects gusts. Proc. R. Soc. B 287, 20201748 (2020)

    2020

  51. [59]

    Usherwood, J. R. et al. High aerodynamic lift from the tail reduces drag in gliding raptors. J. Exp. Biol. 223, jeb214809 (2020)

    2020

  52. [60]

    A., Wietstruk, M., Gosdin, L., Bellah, J

    Swiney, P. A., Wietstruk, M., Gosdin, L., Bellah, J. & Raghav, V. Preliminary investigation of the aerodynamic response of a red-tailed hawk to a vertical gust. AIAA Scitech 2020 Forum 2001 (2020)

    2020

  53. [61]

    Tucker, V. A. Gliding birds: reduction of induced drag by wing tip slots between the primary feathers. J. Exp. Biol. 180, 285–310 (1993)

    1993

  54. [62]

    Norberg, U. M. Vertebrate flight: mechanics, physiology, morphology, ecology and evolution Vol. 27 (Springer Science & Business Media, 2012)

    2012

  55. [63]

    Combes, S. A. & Dudley, R. Turbulence-driven instabilities limit insect flight performance. Proc. Natl. Acad. Sci. USA 106, 9105–9108 (2009). 14

    2009

  56. [64]

    L., Ross, A

    Shepard, E. L., Ross, A. N. & Portugal, S. J. Moving in a moving medium: new perspectives on flight (2016)

    2016

  57. [65]

    & Warhaft, Z

    Yoon, K. & Warhaft, Z. The evolution of grid-generated turbulence under conditions of stable thermal stratification. J. Fluid Mech. 215, 601–638 (1990)

    1990

  58. [66]

    & Bewley, G

    Gupta, D., Kumar, V., Larsson, J. & Bewley, G. On the experimental study of 3d turbulent shear layers. Bull. Am. Phys. Soc. (2023)

    2023

  59. [67]

    P., Shepard, E

    Wilson, R. P., Shepard, E. & Liebsch, N. Prying into the intimate details of animal lives: use of a daily diary on animals. Endang. Species Res. 4, 123–137 (2008)

    2008

  60. [68]

    & Guj, G

    Camussi, R. & Guj, G. Experimental analysis of intermittent coherent structures in the near field of a high re turbulent jet flow. Phys. Fluids. 11, 423–431 (1999)

    1999

  61. [69]

    Blum, D. B. et al. Signatures of non-universal large scales in conditional structure functions from various turbulent flows. New J. Phys. 13, 113020 (2011). 15 Materials and Methods Data acquisition Eagle Flight Acceleration data We observed six golden eagles (A. chrysaetos ) ...

    2011

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.