Direct observations of airflow separation over ocean surface waves

Domain: earth_science
Published: 2025-07-01
Editorial outcome: minor_revision

Abstract
A large portion of the kinetic energy found within the ocean originates from the growth of ocean surface waves under the action of wind. However our understanding of wind wave dynamical coupling mechanisms remains incomplete. Competing theories exist but direct observational evidence is lacking, due to the technical challenges involved in measuring wind and wave dynamics in the vicinity of the highly energetic wavy ocean surface. Here, direct observations of airflow dynamics in the first millimeters to meters above ocean surface waves are shown. These were achieved using laser imaging techniques on the Floating Instrument Platform FLIP in the Pacific Ocean. The results show that two dynamical wind-wave coupling regimes coexist. Short (~1 m wavelength), strongly wind-forced waves travel more slowly than the wind and cause intermittent airflow separation events. On average, these slow waves are coupled with the airflow via a sheltering mechanism, while longer (~100 m), faster waves induce orbital motions in the airflow.

Introduction
The exchanges of momentum, energy, and mass between the atmosphere and the ocean, are strongly influenced by small scale physical processes very close to the ocean surface, within the first centimeters of the coupled oceanic and atmospheric wave boundary layers1. A significant portion of the kinetic energy within the ocean originates from atmospheric forcing, in particular through the generation and growth of ocean surface waves under the action of wind1,2. Wind wave growth results from a difference in airflow pressure between the leeward and windward sides of the wave3,4. Yet the mechanisms that trigger this pressure perturbation, remain the subject of debate1,5,6. Physical interpretations are largely based on one of two competing theories, "critical-layer theory"7, a linear shear-flow instability mechanism that takes place within the critical layer (thin region in the airflow, where the mean airflow speed matches that of the waves), and the "sheltering" mechanism, a turbulent process analogous to turbulent boundary modulations over low hills8, whereby slow, wind-forced waves create a sheltered zone (from the wind) on their lee-side9.

Field observations4,10,11 and high resolution laboratory measurements12 suggest that waves traveling faster than the wind very near the surface, but slower than the wind at ~10-m height, receive a significant amount of energy through the critical layer mechanism. However, recent laboratory measurements show frequent, highly turbulent airflow separation or "separated sheltering"13 events over strongly forced wind waves9; these are incompatible with linear critical-layer theory. On the other hand, longer waves that travel faster than the wind, are expected to cause sheltering effects on their windward side8 (though observational evidence is scarce), and very fast-running waves (swells) can return momentum back to the atmosphere in the form of wave-induced winds14–18.

When the wind forcing increases, wave steepening, breaking, and related turbulent processes are associated with an increase in air-sea exchanges of momentum and scalars1,19–23. In high to very high wind conditions, momentum and CO2 fluxes across the ocean surface eventually stop increasing24–28. Airflow separation past wave crests has been suggested as a possible reason for this flux saturation25,28,29. Yet direct, in situ observational evidence of airflow separation is lacking, due to difficulties in measuring airflow within centimeters of the wavy ocean surface.

We tackle these open questions on the structure of the airflow over the broad spectrum of ocean waves through the utilization of laser imaging techniques that capture airflow kinematics over ocean waves. Here we show in situ, instantaneous two-dimensional snapshots of airflow velocities in the first millimeters to meters above ocean surface waves, acquired over the Pacific Ocean, from the Floating Instrument Platform FLIP, a unique research platform designed for the study of air–sea interaction (Fig. 1). The data were collected in October 2017 over the ocean ~50 km offshore of Santa Monica, California, where the water depth is about 1000 m. A large field of view (0.69 m × 2 m), high resolution (up to 1 airflow velocity vector every 1.2 mm2), laser imaging system was developed and installed on the platform. It consisted of a vertical array of five cameras mounted on the first deck, that were focused on the airflow above waves that passed beneath the tip of the starboard boom (Fig. 1). A high-power, pulsed laser created a green light sheet down to the wavy surface, thereby illuminating the air-water interface, as well as fog micro-droplets that seeded the airflow. These flow seeding particles were injected into the airflow upwind of the imaging region. The system, operated at night, captured snapshots of the green laser-illuminated particles (Fig. 1, panel b), the motions of which were used to quantify the airflow kinematics within the first millimeters to meters above the wavy ocean surface, in a technique known as Particle Image Velocimetry (PIV).

We are able to directly observe and quantify turbulent, intermittent airflow separation events over short wind waves (with wavelengths ~1 m). These slow waves—with respect to the local, near surface wind speed—ride upon longer waves (~100 m) that travel faster than the wind. Using conditional averaging with respect to the along-wave position (wave phase), we demonstrate the coexistence of two different dynamical wind-wave coupling mechanisms: the slow wind waves are coupled with the airflow via a sheltering mechanism, while the fast waves induce orbital motions in the airflow.

Results
Airflow separation events
Instantaneous, two-dimensional snapshots of the velocity field within the first 50 cm of airflow above ocean surface waves, reveal the turbulent structure of the airflow as it is dynamically coupled with the waves (Fig. 2).

The bulk of the airflow shown in Fig. 2a (horizontal velocity component) is traveling significantly faster (at ~4 m/s) than the wave, which is moving with a crest speed of ~1.4 m/s. This velocity difference, combined with the geometry of the wave (with a half wavelength λ/2 ~ 0.56 m and a crest-to-trough height of H ~ 9.4 cm), causes the local airflow boundary layer to detach from the surface just past the crest of the wave, creating an airflow separation (or separated sheltering) event, whereby a region of the airflow just downwind of the wave crest is spared from the full force of the wind. In fact, the sheltered region is characterized by a slight flow reversal (Fig. 2a, b). In panel b, vertical profiles of the horizontal velocity field at the crest and downwind of the crest illustrate the strong modulation of the airflow’s boundary layer by the wave.

Two-dimensional instantaneous vorticity fields (spanwise component, Fig. 2e–h) display typical boundary layer separation features30. The near-surface high vorticity layer (due to viscous shear, ref. 31), relatively thin upwind of the crest, thickens past the wave crest, and is ejected away from the surface. The flow reversal (or "recirculation", see for example ref. 30) is accompanied by a patch of negative vorticity (panel f). Downwind of the detached region, we observe a gradual regeneration of the surface vorticity layer. Such vorticity patterns, previously only observed in controlled laboratory studies, are characteristic of airflow separation events over slow (with respect to the wind speed above), strongly forced wind waves9,32.

We note that the airflow separation event takes place on a wave that is not very steep (H/λ ~ 0.1). This, combined with its wave age (c/u*, where c is the wave crest speed and u* the friction velocity) of 6.4, means that this wave is far from the "incipient breaking" limit suggested by Banner and Phillips33, and falls within the range of waves that have a 30% chance of experiencing airflow separation, following the classification of Buckley et al.9. Nonetheless, the airflow separation event persists for the duration of the imaging interval of the slow wind-wave displayed in Fig. 2 (0.27 s, with one velocity field every 1/15 of a second), but the rapid evolution of the velocity and vorticity fields demonstrates the highly variable and turbulent (or "intermittent", ref. 30) nature of the event.

These instantaneous observations of airflow velocities above such short, slow waves, indicate that the momentum and mechanical energy transfers from the atmosphere to these waves are dominated by sheltering dynamics. In fact, the observed sheltering event (Fig. 2a) is incompatible with a linear (critical layer) growth mechanism because the contour u = c, where u is the horizontal velocity and c the wave’s crest speed (black dashed lines in Fig. 2a), merely reflects the separated flow, rather than a small perturbation to the mean wind profile.

Instantaneous structure of the airflow over fast waves
The ocean surface is generally composed of a broad spectrum of waves of different scales and ages (e.g., 4, 16, 19). During this experiment, relatively long (λ ~ 70 m) and fast waves were observed, traveling at a peak phase speed of 10.4 m/s, with a wave age of c/u* = 33 (or c/U10 = 1.2, where U10 is the mean wind speed at a height of 10 m above the water surface), upon which smaller, slower locally generated wind waves such as the one displayed in Fig. 2 were superimposed. A reconstructed snapshot of the airflow velocities over a long, fast wave (Fig. 3) contrasts with the airflow kinematics over the short, slow wave from Fig. 2. Contrary to the slow wave case where the sheltered region is to the right of the crest (lee ward side with respect to the mean wind), the magnitude of the horizontal velocity (panel a) decreases here on the left side of the wave, which is traveling faster than the local, near-surface wind. In other words, a form of sheltering takes place on the windward face of the long, fast wave’s crest (also known as "negative asymmetry", 13). The vertical velocity field (panel b) indicates that the orbital motions of the wave draw (resp. push) the airflow downward (resp. upward) on the windward (resp. leeward) side of the crest. The vectors plotted in panel c represent the mean velocities across the sampled air column; they illustrate the forcing of the airflow by the fast wave’s orbital motions. This quasi-instantaneous observation of the modulation of the airflow by a single, fast wave over the open ocean, is in qualitative agreement with previous laboratory studies of instantaneous airflow kinematics over waves of similar age (see for example ref. 31, who conducted an experiment with a similar wave age, c/u* = 31.7).

Wave-induced motions
In order to quantify the average effect of the waves on the airflow, and better understand the airflow’s coupling with the slow waves versus the fast waves, the airflow velocity horizontal and vertical components (u, w, respectively) were binned and averaged according to their along-wave location, or phase φ (phase averaging). Subsequently subtracting the mean velocity profile from the phase average provides wave-coherent motions, or velocity perturbations induced by the waves:

~u(φ, z) = 〈ui(φ, z)〉 − u(z) (1)

where z is a measure of the vertical distance from the water surface, 〈u〉 and u represent the conditional (with respect to wave phase) and temporal averages, respectively (e.g., Sullivan et al.34, Hara and Sullivan35).

The mean wave-coherent velocities (~u, ~w) shown in Fig. 4 demonstrate the important differences between wind-wave coupling mechanisms for slow, locally generated wind-waves (with wavelengths λ < 1 m, Fig. 4a, b) versus those for fast waves (with a peak wavelength of ~70 m, Fig. 4c–f), as already suggested by the instantaneous observations (Figs. 2 and 3). The slow waves are, on average, causing the relatively high velocity wind above, to accelerate and move upward as it approaches crests, and to decelerate (sheltering) and move downward past the crests (panels a and b). We observe a phase shift of ~0 (resp. −π/2) between the maximum horizontal (resp. vertical) airflow velocity and the water surface elevation in these slow waves. We note that intense separated sheltering events (e.g., Fig. 2) are not directly represented in the phase average. This is likely due to the intermittency of airflow separation events30, that occur over a portion of the spectrum of waves9. Therefore the observed mean wave-coherent pattern points toward a dominance of the "nonseparated sheltering"13 mechanism for momentum and energy flux into the slow waves. The wave-coherent perturbations of the horizontal velocities are strongest within the "inner region", defined by Belcher and Hunt13 as a thin region close to the surface where the waves are expected to induce perturbations of the turbulent stress. These produce a sheltering effect that modulates the surface pressure, which, in turn, may lead to the growth of wind waves13. These in situ observations of wave-induced airflow velocities within the first millimeters above slow wind waves (with estimated wave ages cp/u* between 2.5 and 4.2) are in good agreement with past laboratory31,36 and numerical34 studies. There, similar phase shifts between wave-induced perturbations and water surface elevation were observed and modeled, albeit in simplified wave conditions (short fetch and monochromatic, respectively). Notably, the presently observed phase shifts match closest with the numerical reference case cp/u* = 0 of Sullivan et al.34, for flow over a solid wavy surface. This further supports the hypothesis that the relatively fast airflow is decoupled from the slow waves’ orbital motions, leading to sheltering as the dominant coupling mechanism.

Using the non-separated sheltering growth rate parametrization suggested by Belcher and Hunt8, we can express the non-dimensional wave energy growth rate β (e.g., Komen et al.37), as:

β = 4πr (U(Li)/c)^2 (2)

where Li is the height of the inner layer, U the mean wind profile in a frame of reference moving with the waves, and r the air–water density ratio. We find a non-dimensional non separated sheltering growth rate β between 0.015 and 0.102 (computed by using values of λ between 0.35 and 1 m). This value agrees well with historical observations of wave growth rates, as shown in Fig. 5, where the dimensionless wave growth rate β is represented as a function of inverse wave age u*/c. This agreement is consistent with the growth of the observed slow waves by the sheltering mechanism.

The fast waves (Fig. 4c, d) force orbital motions in the airflow, with phase shifts approaching π (horizontal velocity component) and π/2 (vertical component) with respect to the phase averaged water surface elevation (shown in panel e). The water orbital velocities of the fast waves are expected to be ~0.5 m/s, as estimated from linear theory. This value is consistent with a strong coupling of the water orbital motions with the measured wave-coherent airflow motions, which reach values of ~1 m/s for ~u and ~0.3 m/s for ~w (panels c and d). This result is in general agreement with past single-point observations4,10,11, and numerical simulations16,34. The fast waves observed here, as they are traveling ~1.9 m/s faster than the wind at 10 m height, are likely not influenced by dynamics near their critical layer, which, in this case, would be at a height ~100 m8.

Methods
In situ large field of view Particle Image Velocimetry

Instrumentation. A large field of view, high resolution PIV system was developed specifically for this study of airflow dynamics above ocean surface waves from FLIP. The system was composed of the following elements. Seeding particles (fog droplets, with a diameter of ~15 μm) were injected into the airflow by pumping local seawater into an array of spray nozzles, located ~3 m upwind of the imaging region. A vertical array of five, 5 Megapixel USB 3 CMOS cameras (Grasshopper 3, Point Grey Research) was installed on the first deck of FLIP, each of which was fitted with a remote lens controller for focus and aperture control (developed in-house, using an Arduino microcontroller). The top camera (large field of view), fitted with a Canon EF 50 mm lens, imaged the entire PIV region, while each of the remaining 4 cameras, fitted with a Canon EF 200 mm lens, imaged only a portion of the field of view, in order to achieve the desired resolution (300 μm/pixel). The images were stitched together prior to computing velocity vectors from the particle displacements. A downward-facing pulsed green (532 nm) Nd:YAG laser (Quantel Evergreen, 200 mJ/pulse) was positioned above the PIV field of view. PIV cameras and laser were controlled by National Instruments counter/timer hardware (PCIe 6612) connected to a computer located in the lab on the 3rd deck of FLIP. PIV measurements took place at night, in order to ensure that the only light source was the PIV laser, and thus minimize optical noise on the PIV images. The PIV acquisition was performed for intervals of 70 s, every 10 min, to allow for transfer of the buffered images from the computer memory to the hard drives. Each 70 s dataset represents a total of 1050 2D velocity fields, each with up to 6776 × 2301 measured velocity vectors, or a total of 2,416,050 (vertical) velocity profiles.

Imaging. As the laser light penetrates the water surface, the intersection of the laser sheet with the water surface delivers a high resolution (300 μm/pixel) picture of the instantaneous geometry of the water surface (upper boundary of the gray scale region in Fig. 2). The intensity variations below the interface are caused by the refraction of green PIV laser light through the rough water surface, and are as such a function of the local variations in the slope of the water surface [see also refs. 38, 39].

The suitability of the seeding particles to follow the turbulent motions of the airflow was assessed by computing the Stokes number St of the fog droplets. We find St = τp/τk ≪ 1, where τp = 1.2 ms is the Stokes timescale of the largest particles, and τk = 23.6 ms is an estimate of the Kolmogorov timescale, estimated using the measured airflow friction velocity and a length scale of 1 m (cutoff wavelength for the slow waves)40.

One of the challenges with in situ (outdoor) airflow PIV is the difficulty to achieve high seeding particle density within the entire field of view of the cameras. Some of the raw PIV images inevitably contained patches with low seeding density. An image variance based algorithm was developed and used to remove these patches automatically before computing PIV velocity fields. Low seeding density was observed predominantly over the troughs of peak (fast) waves with wave heights ~1 m. Hence the very near surface airflow measurements presented in this paper are mostly acquired above the crests of the fast waves. Therefore the results presented for slow wind waves are valid for waves riding on the crests of the fast waves.

Procedure. Prior to starting the PIV measurements, the dominant wind direction was monitored live using a sonic anemometer. Once the wind direction was approximately aligned with the laser sheet (direction perpendicular to the starboard boom), the PIV data acquisition started. This procedure ensured the presence of seeding particles within the laser light sheet, and that the PIV technique captured the dominant wind velocity components.

Environmental conditions and supporting measurements
The PIV images for Fig. 2 were acquired on 17 October, 2017 at 10:27 pm, local time. The local 10-m wind speed was 6.6 m/s. The data for Figs. 3 and 4 were acquired on 20 October, 2017, at 7:13 pm. The local wind speed was then 8.4 m/s. Short wind waves (with wavelengths ~1 m) were typically traveling in the direction of the local wind. Alignment of the peak wave travel direction with the local wind direction was checked using directional wave field information provided by a waverider buoy moored within 1 km of FLIP’s location.

A suite of sonic anemometers (including the one visible in Fig. 1b, just above the PIV imaging region) and wave gauges provided additional, single-point, fixed height wind-wave measurements, co-located with the PIV imaging region. Two 3D anemometers (Gill Windmaster) measured wind velocities with a sampling frequency of 20 Hz at fixed heights above the mean water level (2.6 and 4.6 m, respectively). A weather station (measuring 2D wind speed, temperature, relative humidity, atmospheric pressure) was positioned at a height of 10.6 m above mean water level. The latter measurement was used to estimate the friction velocity (u*), needed for the calculations of wave age and growth rate, via the COARE bulk flux algorithm (Edson et al. 19, Fairall et al. 41, 42). During the same time period, Ortiz-Suslow et al. 43 also performed wind speed measurements (vertical profiles of the wind speed), on the port boom of FLIP. Their observations point to the existence of a constant flux layer at the time of our measurements, and are in good agreement with our total momentum flux estimates43. Two down-looking distance sensors were used as wave gauges (sonic and LIDAR, respectively), acquiring time series of the water surface elevation at a spanwise distance of 60 cm from the PIV field of view, and with a sampling frequency of 20 Hz. A motion sensor (VectorNav VN-100 Rugged IMU) was placed next to the PIV laser on FLIP’s starboard boom, and acquired the motions of FLIP at a frequency of 20 Hz. A frequency spectrum of the water surface elevations obtained from different methods, at the location of the PIV measurements is provided in Fig. S1 in the supplementary material. The water surface profiles obtained from the PIV images provide two data products. First, any column of the images can be used as a single point wave gauge, yielding a time series (with a sampling frequency of 15 Hz, the PIV pair acquisition frequency) of the water surface elevation. Here, the middle of the PIV field of view was used (black curve). Second, wavenumber spectra can be computed from the spatial surface snapshots of each PIV image (0.69 m wide, with a resolution of 300 μm/pixel); these were subsequently averaged yielding the purple curve.

A cross-spectral analysis (Fig. S2) of the sonic anemometer wind speed measurements (ua, wa) with the water surface elevation measurements (η), co-located with the PIV measurements, supports the phase shift observations from the phase-averaged PIV fields for the fast waves in Fig. 4c, d. By computing the cross-spectral densities between the horizontal (resp. vertical) airflow velocity components and the water surface elevations, denoted Sa uη (resp. Sa wη), we find that the coherence function γa uη = |Sa uη|2 / (Saa uu Sηη) (resp. γa wη = |Sa wη|2 / (Saa ww Sηη)) is maximum at the peak wave age (c/u* = 33). At this wave age, their respective phase shifts (φa uη = arg(Sa uη), φa wη = arg(Sa wη)) are ~0.9π and 1.2π/2. This result supports the hypothesis that (linear) wave orbitals induce the wave-coherent motions in the airflow, in accordance with linear theory, which predicts phase shifts of π and π/2, respectively4.

Wave phase detection and averaging
For the fast waves, instantaneous wave phases were defined as the argument of the Hilbert transform of the water surface elevation time series, for each along-wind (x-direction) location in PIV snapshot j, φj(x) = arg[H{ηj(x)}], where η(x) represents the surface elevation at along-wind position x (see also Buckley and Veron31, Melville44). An example of wave phase detection from Hilbert analysis is shown in Fig. S3b, applied to a time series of surfaces detected on the PIV images, and to sonic wave gauge data (panel a). Here, each point of the time series of “PIV surfaces” is the middle of the detected surface within each PIV image. Panel a shows the relatively good agreement between the wave gauge and imagery water surface elevation measurements. This agreement also holds for the phase averaged water surface elevations (Fig. S4c). In addition, we checked the validity of the PIV velocity measurements by comparing the airflow velocities obtained at the top of the PIV field of view (at a height of z = 1.5 m above the mean water level) with the airflow velocity observations from the lowest sonic anemometer (z = 2.6 m). Figure S4a, b shows the phase averages of these quantities (horizontal and vertical components, respectively).

In the case of the slow waves, the spatial water surface elevation profile from each PIV snapshot was first high-pass filtered to isolate the slow waves (with a cut-off wavelength of λ = 1 m). A Hilbert transform was then applied to the filtered profiles, yielding a wave phase estimate for each point along the imaged water surface40. The velocity fields were mapped from the cartesian frame of reference (x, z) to a surface-following frame of reference (x, ζ), where ζ = z − η(x, t) (as was previously done in laboratory studies, for example by Grare et al. 45, Tenhaus et al. 46). For the comparatively more regular, fast waves, the phase averaging was performed in the cartesian frame of reference.

Platform motion. The airflow velocity and surface displacement measurements presented here were corrected to account for the motions of the platform, and projected into earth coordinates. This was achieved by using a combination of motion sensor measurements47, water surface imagery on the PIV images, as well as images of the lowest anemometer captured by the large field of view PIV camera.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this study, the authors used a PIV system installed on the FLIP ocean research platform to measure ocean wind\nturbulence. The authors observed that the boundary layer separated for relatively short-wavelength, “slow” component\nwaves, and argued for the importance of the sheltering mechanism in wind wave development. The successful PIV\nmeasurement of oceanic wind turbulence in actual sea areas suggests the possibility of new research developments in the\nfuture, and the academic value of this work is high. In particular, if the separation of the boundary layer plays an important\nrole in wind wave development, it is even possible that it will overturn the previous theoretical research that explains wind\nwave development. The reviewer highly evaluates the novelty and academic value of this paper, and therefore evaluates\nthis paper as Minor Revision.\nThe method of measurement using PIV is unclear.\nIn contrast to tank experiments, the difficulty of PIV measurement in real sea areas is to set the downwind direction\nappropriately for wind waves with directional propagation. Therefore, in order to achieve continuous PIV measurement, it is\nnecessary to monitor the wind direction in real time and adjust the direction of laser beam irradiation as needed. In this\npaper, there is no description of how the downwind direction was set and the measurement was performed. This is an\nunclear point regarding the in-situ PIV method, so I recommend that it be described. Since the measurement time is only 70\nseconds, will the data analysis results only be shown if the irradiation direction of the laser sheet coincides with the\ndownwind direction?\nIn order to calculate the growth rate of the wind wave, it is necessary to define the friction velocity. Firstly, is a constant\nflux layer confirmed? If a data sample is in the 70s, is statistical representativeness guaranteed? And how has it been\nconfirmed?\nComparison with previous research\nIn order to make the validity of the PIV measurements more robust, it is recommended to compare the results of this study\nwith the results of previous research. For example, Sullivan et al. (2000, JFM) show the turbulent intensity and Reynolds\nstress distribution at the wavy boundary obtained by DNS. It would be better to show to what extent the turbulent\ncharacteristics obtained in this study agree with them.\nAs a conclusion of this study, it is difficult to understand the position of the Miles mechanism (1958) and the sheltering\nmechanism proposed by Jeffreys (1925) in the development of wind waves. While it is stated that the contribution of the\nsheltering mechanism to the wind wave growth rate is large, the importance of the Miles mechanism is claimed in the critical\nlayer of a few millimetres.", "reviewer_2": "Review of Buckley et al, Direct observations of airflow separation over ocean surface\nwaves\nThis paper presents field measurements of the airflow separation over short and long waves during a campaign with FLIP\noutside the coast of California. The results point to two regimes for how surface waves are coupled to the airflow. The short\nwaves are observed to experience a sheltering mechanism, whereas the long (70m and more) affect the airflow. The results\nare important and the reporting is timely since the general problem of wave growth is one which has direct implications for\nnumerical weather prediction and climate modeling. The problem remains far from solved, but there is general agreement\nthat a critical layer theory is the most efficient mechanism by which momentum is transferred between the atmosphere and\nthe wave field. The authors are thus presenting a somewhat contrarian view, in that the sheltering seems to be quite\nimportant. They also claim to observe a direct momentum transfer from the long waves to the lower atmosphere. This latter\nmechanism has been studied experimentally (see Semedo et al, 2009), and is potentially of importance for swell attenuation.\nThe middle ground, however, is not well covered by this study. That is, we are presented with very long waves that outrun\nthe local wind and very short waves that are strongly forced by the wind. The critical layer theory is supposedly filling in the\nintermediate scales, but the authors state that the critical layer falls either too close to the wavy surface to be resolved for\ntheir short waves or is too high up in the case of long waves. This is a weakness of the study since the community would\nbenefit from knowing how well the critical layer theory holds up in such experiments. We acknowledge that the extent to\nwhich this is feasible may be limited by the experimental setup, but we would encourage the authors to look for evidence of\nthis middle ground where critical layer theory should apply. Moreover, it is not entirely clear from the manuscript how long\nthe experiments went on; this should be clarified in the revisions.\nHaving said that, the paper is well written, relevant and important, and we would recommend publication following a round of\nrevisions.\nMajor comments and questions\nThe literature review should be expanded to set the current experiments and results in context. This could be done either in\nthe introduction or in the supplementary materials.\nCan the analysis be extended to also cover mid-range wavelengths for which the critical layer would presumably coincide\nwith the range of the PIV measurements?\nSpecific comments by section\nIntroduction\n(As above) More in depth information about existing theories and contradictions between competing theories would be\nhelpful to set the context for the current analysis and its importance, especially since the journal (Nature Communications)\nhas a wide interdisciplinary scope. Therefore many readers are unlikely to have a strong background in the subject. If word\nlimits prohibit the introduction from being expanded significantly, a more in-depth review of the literature covering the critical\nlayer and sheltering mechanisms could be added to the supplementary materials for interested readers.\nThe dataset was collected already in 2017. Is this the first paper to analyze the dataset, or have there been other\npublications using the same data?\n2.1 Airflow separation events\nFig. 2: Does the green laser penetrate the water surface? Do the gray regions beneath the air-sea interface in Fig. 2\nrepresent the water column under the surface, or is it a re-projection of the surface reflection?\nFig. 2: Is the example short wave riding the crest or trough of a long wave? One would assume the former based on the text\nin the Methods section, but it would be helpful to state this more clearly also in the main text. Are the axes rotated relative to\nthe instantaneous long-wave slope?\n2.2 Instantaneous structure of the airflow over fast waves\nFig. 3: Are both the wave crest and (mean) wind propagating from left to right? Is windward/leeward defined with respect to\nthe crest velocity? This could be specified in the caption.\n2.3 Wave-induced motions\nHow many individual slow and fast waves were used to generate the ensemble-averaged airflow profiles? What is the full\nduration of the experimental dataset?\nDo the slow wave ensemble averages contain breaking waves? If not, how do (or would) the mean airflow profiles differ for\nbreaking waves?\nEq. 1: How were the inner layer heights L_i determined or defined?\nFig. 4: (How) Does the long-wave modulation of the short waves affect the mean airflow patterns? Does the mean airflow of\nthe slow waves cover all long-wave phases? Would the authors expect there to be a difference in the short-wave airflow at\ndifferent long-wave phases due to long-wave modulation of the short waves (e.g. crest vs trough of long waves)?\nFig. 4: Alternate layout suggestion: Keep 2-column layout, but with the left column consisting of 4 subpanels in each row,\nand the right panel consisting of one high panel (current f panel). Left column: 4-panel column with c+d on top 2 rows of left\ncolumn. Include the wave form in the same way as in a+b (so that all subpanels include 0 on the y axis). On 3rd and 4th row\nof left column, show current a+b panels, with e.g. a box showing the horizontal and vertical scales of the short waves vs the\nlong waves.\nThe authors summarize their results, which show that short/slow waves are coupled to a sheltering/separation response in\nthe nearfield airflow, whereas the long/fast waves induce orbital wakes in the airflow. This result is essentially (redundantly)\nstated twice back-to-back. What is lacking for readers with basic (or limited) background in the subject is a clear statement of\nhow the presented results change or update our understanding of the process of wave growth by wind. As stated above, this\nshould preferably be explained more thoroughly in the introduction, but more details could be added to the Supplementary\nmaterials.\n4.1 In situ Large field of view Particle Image Velocimetry (PIV)\nWill the code for the PIV algorithm used in this study be made publicly available?\nWhat level smoothing or filtering was performed on the raw PIV velocities vs. the final results shown in the manuscript?\n4.2 Environmental conditions and supporting measurements\nAre directional wave spectra available for the measurement campaign? These would be helpful for showing the relative\ndirectionality of the windsea and swell.\nWill any of the data and/or code used in the manuscript be made publicly available?\nReferences\nSemedo, A, O Saetra, A Rutgersson, K K Kahma, H Pettersson (2009). Wave-induced wind in the marine boundary layer, J\nAtmos Sci, 66(8), pp 2256-2271, doi:10.1175/2009JAS3018.1", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts."}, "author_response": "Response to the Reviewers\nReply: The authors would like to thank the reviewers for their constructive comments and suggestions\nthat have helped improve the quality of this manuscript. The manuscript has undergone a thorough\nrevision according to the reviewers’ comments. Please see our responses below. For the reviewers’\nconvenience, the reviewers’ comments are written in black, our responses are in blue, and we have\nhighlighted changes in the revised manuscript in blue.\nReviewer 1\nIn this study, the authors used a PIV system installed on the FLIP ocean research platform to\nmeasure ocean wind turbulence. The authors observed that the boundary layer separated for rela-tively short-wavelength, “slow” component waves, and argued for the importance of the sheltering\nmechanism in wind wave development. The successful PIV measurement of oceanic wind turbu-lence in actual sea areas suggests the possibility of new research developments in the future, and\nthe academic value of this work is high. In particular, if the separation of the boundary layer\nplays an important role in wind wave development, it is even possible that it will overturn the\nprevious theoretical research that explains wind wave development. The reviewer highly evaluates\nthe novelty and academic value of this paper, and therefore evaluates this paper as Minor Revision.\nComment 1 The method of measurement using PIV is unclear. In contrast to tank experiments,\nthe difficulty of PIV measurement in real sea areas is to set the downwind direction appropriately\nfor wind waves with directional propagation. Therefore, in order to achieve continuous PIV mea-surement, it is necessary to monitor the wind direction in real time and adjust the direction of laser\nbeam irradiation as needed. In this paper, there is no description of how the downwind direction\nwas set and the measurement was performed. This is an unclear point regarding the in-situ PIV\nmethod, so I recommend that it be described. Since the measurement time is only 70 seconds, will\nthe data analysis results only be shown if the irradiation direction of the laser sheet coincides with\nthe downwind direction?\nReply: Thank you for pointing this out; this should be clarified in the manuscript.\nIndeed the PIV measurements were only possible when the wind direction was aligned with the laser\nsheet. And yes, the reviewer is correct, the data analysis results are only shown when the direction of\nthe laser sheet coincides with the downwind direction. The 70 second duration was not dictated by\nthe wind direction. This imaging duration was set by the size of the computer memory (RAM), which\nwas filled after 70 seconds of PIV acquisition. The memory was subsequently emptied as the images\nwere transferred to hard drives; this operation lasted approximately 10 min. Only then was the next\n70-second run possible. This resulted in a series of 70 s datasets (each acquired at 15 Hz), every 10\nmin. Additionally, we note that, in general, when the wind direction was not aligned with the laser\nsheet, there were no seeding particles within the PIV images, rendering any PIV measurements of the\nairflow impossible.\nWe have added the following text to the manuscript:\n”Prior to starting the PIV measurements, the dominant wind direction was monitored live using a\nsonic anemometer. Once the wind direction was approximately aligned with the laser sheet (direction\nperpendicular to the starboard boom), the PIV data acquisition started. This procedure ensured the\npresence of seeding particles within the laser light sheet, and that the PIV technique captured the\ndominant wind velocity components.”\nComment 2 In order to calculate the growth rate of the wind wave, it is necessary to define the\nfriction velocity. Firstly, is a constant flux layer confirmed?\nReply: Thank you for this comment. We agree that the friction velocity estimate method should be\nspecified.\nThefrictionvelocityusedheretocomputethegrowthrate(u ∼ 0.3m/s),wasestimatedbyapplying\n∗\nthe COARE bulk flux algorithm (Edson et al. [2013], Fairall et al. [1996, 2003]) to the wind velocity\nmeasuredata10.6mheight(weatherstation). Thismeasurementwaschosenbecauseitwasourhighest\n(above the water level) wind velocity measurement on the starboard boom, thus likely minimizing the\neffect of the waves on the estimate. Ortiz-Suslow et al. [2021] performed wind speed measurements\n(vertical profiles of the wind speed) on the port boom of FLIP, during the same measurement campaign.\nTheir study suggests the existence of a constant flux layer at the time of our measurements, with an\nestimated friction velocity of (u ∼ 0.29 m/s) [Ortiz-Suslow et al., 2021].\n∗\nWe have added the following text to the methods section of the manuscript:\n”The latter measurement was used to estimate the friction velocity (u ), needed for the calculations\n∗\nof wave age and growth rate, via the COARE bulk flux algorithm (Edson et al. [2013], Fairall et al.\n[1996, 2003]). During the same time period, Ortiz-Suslow et al. [2021] also performed wind speed\nmeasurements (vertical profiles of the wind speed), on the port boom of FLIP. Their observations point\nto the existence of a constant flux layer at the time of our measurements, and are in good agreement\nwith our total momentum flux estimates [Ortiz-Suslow et al., 2021].”\nComment 3 If a data sample is in the 70s, is statistical representativeness guaranteed? And how\nhas it been confirmed?\nReply:\nThank you for this comment. We recognize that this relatively short acquisition duration can be\nconcerning. We have added the following to the methods section:\n”Each 70 s dataset represents a total of 1050 2D velocity fields, each with up to 6776 x 2301\nmeasured velocity vectors, or a total of 2,416,050 (vertical) velocity profiles.”\nFor the slow wave results, each phase average value (figure 4, panels a and b) results from an\naverage over at least 2507 instantaneous velocity measurements. The total number of slow waves is\nestimated to be over 2000. The maximum 95% confidence interval shows no significant difference from\nthe average over all data (see figure R 1).\nA similar analysis was performed for the previous 70 s PIV dataset (acquired approximately 10 min\nprior to the one presented in this study, due to hardware restrictions, as mentioned above). The wind\nand wave conditions were similar (U = 7.9 m/s, u = 0.29 m/s, C = 10 m/s) as in the present study\n10 ∗ p\n(U = 8.3 m/s, u = 0.3 m/s, C = 10.4 m/s). The results show no significant difference with respect\n10 ∗ p\nto the phase averaged contours of the horizontal and vertical velocity components (see figure R 2).\nForthefastwaves,thetotalnumberofwavessampledwithin70sisonlyapproximately11(seefigure\nS3, in the supplementary material). However, the standard deviation is low, as these long, fast waves\nconsistently force the airflow in a quasi linear way. This is confirmed by the confidence interval figure\nbelow (figure R 3), where no significant difference is visible. Again, a comparison with the conditions\n10 min prior, shows that the shown results are robust (figure R 4).\nComment 4 Comparison with previous research\nIn order to make the validity of the PIV measurements more robust, it is recommended to\ncompare the results of this study with the results of previous research. For example, Sullivan et al.\n(2000, JFM) show the turbulent intensity and Reynolds stress distribution at the wavy boundary\nobtained by DNS. It would be better to show to what extent the turbulent characteristics obtained\nin this study agree with them.\nReply: Thank you for this suggestion. Regarding the turbulence, the computation of the turbulent\nstress tensor components from the PIV within the wave boundary layer requires several additional data\nprocessing steps that are beyond the scope of this study. So far, we were not able to obtain satisfying\nresults for this, likely because of the limited duration of the dataset.\nHowever, we were able to compare the wave-coherent velocity fields with those of Sullivan et al.\n[2000]. For the fast wave results, a comparison to previous research is mentioned in the manuscript:\n”This result is in general agreement with past single-point observations [Hristov et al., 2003, Grare\net al., 2013a, Zippel et al., 2024], and numerical simulations [Sullivan et al., 2000, 2008].”, where we\nhave now also added the originally omitted reference to Sullivan et al. [2000].\nFor the slow waves, we have now added the following text to the manuscript:\n”These in situ observations of wave-induced airflow velocities within the first millimeters above\nslow wind waves (with estimated wave ages c /u between 2.5 and 4.2) are in good agreement with\np ∗\npast laboratory [Buckley and Veron, 2016, 2019] and numerical [Sullivan et al., 2000] studies. There,\nsimilar phase shifts between wave-induced perturbations and water surface elevation were observed and\nmodeled, albeit in simplified wave conditions (short fetch and monochromatic, respectively). Notably,\nthepresentlyobservedphaseshiftsmatchclosestwiththenumericalreferencecasec /u = 0ofSullivan\np ∗\net al. [2000], for flow over a solid wavy surface. This further supports the hypothesis that the relatively\nfast airflow is decoupled from the slow waves’ orbital motions, leading to sheltering as the dominant\ncoupling mechanism.”\nComment 5 As a conclusion of this study, it is difficult to understand the position of the Miles\nmechanism (1958) and the sheltering mechanism proposed by Jeffreys (1925) in the development\nof wind waves. While it is stated that the contribution of the sheltering mechanism to the wind\nwave growth rate is large, the importance of the Miles mechanism is claimed in the critical\nlayer of a few millimetres.\nReply: Thank you for this comment. We recognize that this part is confusing and meddles with the\nclarity of the message. We have removed the following paragraph from the Results and Discussion\nsection:\n”It should nonetheless be noted that a critical layer in the vicinity of the top of the viscous sublayer\ncan be dynamically significant, even for strongly wind-forced waves of similar age (see for example\nCarpenter et al. [2022], who found a significant role of the critical layer just 2 mm above the surface).\nHence it is possible that the critical layer for the slow waves and its associated dynamical role are not\nfully resolved here, since the mean viscous sublayer thickness here is approximately 0.5-0.7 mm (law of\nthe wall).”\nWe have re-written the Conclusion section and added the following text:\n”For intermediate wave ages, (e.g., for 14 ≲ c/u ≲ 25 [Belcher and Hunt, 1998]), the competing\n∗\ndynamical roles of turbulent (e.g., sheltering) versus linear (e.g., Miles’ critical layer theory, [Miles,\n1957]) mechanisms, remain a topic of active research. New methods are being developed, to quantify\nthese processes from our high resolution airflow observations, within this previously inaccessible region\nof the atmosphere-ocean boundary layer.”\nReviewers 2 and 3\nThis paper presents field measurements of the airflow separation over short and long waves during\na campaign with FLIP outside the coast of California. The results point to two regimes for how\nsurface waves are coupled to the airflow. The short waves are observed to experience a sheltering\nmechanism, whereas the long (70m and more) affect the airflow. The results are important and the\nreporting is timely since the general problem of wave growth is one which has direct implications\nfor numerical weather prediction and climate modeling. The problem remains far from solved,\nbut there is general agreement that a critical layer theory is the most efficient mechanism by\nwhich momentum is transferred between the atmosphere and the wave field. The authors are thus\npresenting a somewhat contrarian view, in that the sheltering seems to be quite important. They\nalso claim to observe a direct momentum transfer from the long waves to the lower atmosphere.\nThis latter mechanism has been studied experimentally (see Semedo et al, 2009), and is potentially\nof importance for swell attenuation. The middle ground, however, is not well covered by this study.\nThatis,wearepresentedwithverylongwavesthatoutrunthelocalwindandveryshortwavesthat\nare strongly forced by the wind. The critical layer theory is supposedly filling in the intermediate\nscales, but the authors state that the critical layer falls either too close to the wavy surface to\nbe resolved for their short waves or is too high up in the case of long waves. This is a weakness\nof the study since the community would benefit from knowing how well the critical layer theory\nholds up in such experiments. We acknowledge that the extent to which this is feasible may be limited by the experimental setup, but we would encourage the authors to look for evidence of\nthis middle ground where critical layer theory should apply. Moreover, it is not entirely clear from the\nmanuscript how long the experiments went on; this should be clarified in the revisions.\nHaving said that, the paper is well written, relevant and important, and we would recommend\npublication following a round of revisions.\nMajor comments and questions\nThe literature review should be expanded to set the current experiments and results in context.\nThis could be done either in the introduction or in the supplementary materials.\nReply: Thank you for this comment, we realize that the introduction was too specialized. We have\nnow significantly expanded the literature review in the introduction. We have introduced both airflow\nseparation dynamics over short, slow waves, and wave-induced airflow motions over long, fast waves,\nbothrelevantconceptsforthisstudy. Wehavealsoaddeddetailsonthedebateoverwavegrowthmech-anisms. We have mentioned very fast-running waves (swells) and their possible net upward momentum\nflux effect.\nCan the analysis be extended to also cover mid-range wavelengths for which the critical layer\nwould presumably coincide with the range of the PIV measurements?\nReply: Thank you for this question. This is ongoing work that has, so far, not been successful, in\nspite of many efforts in this direction. Other datasets (acquired a few hours before/after the presented\ndataset) contain conditions, where we expect the critical layer of the dominant waves to fall within the\nfield of view of the PIV. However, we were not able to extract clear (converging), meaningful results\nfor these conditions. We speculate that this is due to the presence of both sheltering and critical\nlayer mechanisms, but the resolution of this issue will require new techniques that have not yet been\ndeveloped. This is for future work and is now mentioned in the conclusions:\n”For intermediate wave ages, (e.g., for 14 ≲ c/u ≲ 25 [Belcher and Hunt, 1998]), the competing\n∗\ndynamical roles of turbulent (e.g., sheltering) versus linear (e.g., Miles’ critical layer theory, [Miles,\n1957]) mechanisms, remain a topic of active research. New methods are being developed, to quantify\nthese processes from our high resolution airflow observations, within this previously inaccessible region\nof the atmosphere-ocean boundary layer.”\nUsing our 3D anemometer and wave gauge data, we were able to identify critical layers using cross-spectral analysis when the anemometer is at the critical height of the dominant waves, similarly to\nHristov et al. [2003], Grare et al. [2013b], Wu et al. [2018], but during those times, the PIV field of\nview does not extend high enough to encompass the critical layer.\nSince this study shows new, statistically robust results for sheltering past slow short waves, as well\nas new, 2D PIV velocity field-based results for the longer waves, we believe it is worth reporting here,\neven without providing an answer so far for other wind-wave regimes, such as intermediate wave ages.\nSpecific comments by section\nIntroduction (As above) More in depth information about existing theories and contradictions\nbetween competing theories would be helpful to set the context for the current analysis and its\nimportance, especially since the journal (Nature Communications) has a wide interdisciplinary\nscope. Therefore many readers are unlikely to have a strong background in the subject. If word\nlimits prohibit the introduction from being expanded significantly, a more in-depth review of the\nliteraturecoveringthecriticallayerandshelteringmechanismscouldbeaddedtothesupplementary\nmaterials for interested readers.\nReply: Thank you for this comment. We agree and have added additional details on wave growth\nmechanisms in the introduction, and also more clearly referred to the recent reviews on the topic:\n”Wind wave growth results from a difference in airflow pressure between the leeward and windward\nsides of the wave [Phillips, 1977, Hristov et al., 2003]. However, the mechanisms that trigger this\npressureperturbation,remainthesubjectofdebate[Pizzoetal.,2021,AyetandChapron,2022,Sullivan\nand McWilliams, 2010]. Physical interpretations are largely based on one of two competing theories,\n”critical-layer theory” [Miles, 1957], a linear shear-flow instability mechanism that takes place within\nthe critical layer (thin region in the airflow, where the mean airflow speed matches that of the waves),\nand the ”sheltering” mechanism, a turbulent process analogous to turbulent boundary modulations over\nlow hills [Belcher and Hunt, 1998], whereby slow, wind-forced waves create a sheltered zone (from the\nwind) on their lee-side [Buckley et al., 2020]1.\nField observations [Hristov et al., 2003, Grare et al., 2013a, Zippel et al., 2024] and high resolution\nlaboratory measurements [Carpenter et al., 2022] suggest that waves travelling faster than the wind\nvery near the surface, but slower than the wind at ∼10-m height, receive a significant amount of energy\nthrough the critical layer mechanism. However, recent laboratory measurements show frequent, highly\nturbulent airflow separation or ”separated sheltering” [Belcher and Hunt, 1993] events over strongly\nforced wind waves [Buckley et al., 2020]; these are incompatible with linear critical-layer theory. On\nthe other hand, longer waves that travel faster than the wind, are expected to cause sheltering effects\non their windward side [Belcher and Hunt, 1998] (though observational evidence is scarce), and very\nfast-running waves (swells) can return momentum back to the atmosphere in the form of wave-induced\n1For a more extensive review of wind-wave coupling mechanisms, the reader is referred to reviews by Pizzo et al.\n[2021], Sullivan and McWilliams [2010], and Ayet and Chapron [2022].\nwinds [Semedo et al., 2009, Hanley and Belcher, 2008, Sullivan et al., 2008, Smedman et al., 1999,\nGrachev and Fairall, 2001].\nWhen the wind forcing increases, wave steepening, breaking, and related turbulent processes are\nassociated with an increase in air-sea exchanges of momentum and scalars [Sullivan and McWilliams,\n2010, Edson et al., 2013, Veron, 2015, Richter and Veron, 2016, Brumer et al., 2017, Deike and\nMelville, 2018]. In high to very high wind conditions, momentum and CO fluxes across the ocean\n2\nsurface eventually stop increasing [Powell et al., 2003, Donelan et al., 2004, French et al., 2007,\nCurcic and Haus, 2020, Bell et al., 2013]. Airflow separation past wave crests has been suggested as a possible\nreason for this flux saturation [Donelan et al., 2004, Janssen and Bidlot, 2023, Bell et al., 2013]. Yet\ndirect, in situ observational evidence of airflow separation is lacking, due to difficulties in measuring\nairflow within centimeters of the wavy ocean surface.”\nThe dataset was collected already in 2017. Is this the first paper to analyze the dataset, or have\nthere been other publications using the same data?\nReply: Thank you for pointing this out. We agree that this is a long time for a first publication on\nthese exciting measurements. This is the first manuscript to analyze the dataset. There are no other\npublications using this data. The relatively long delay is linked to the challenges that came with the\ndata processing methods developed for this study. These novel, in situ airflow PIV measurements over\nthe ocean waves, required the development of new image and data processing methods tailored to these\nfield measurements. And, as mentioned above, we did spend a considerable amount of time and effort\nlooking for critical layers and associated airflow velocity phase shifts within the PIV measurements, but,\nso far, without success.\n2.1 Airflow separation events Fig. 2: Doesthegreenlaserpenetratethewatersurface? Dothe\ngray regions beneath the air-sea interface in Fig. 2 represent the water column under the surface,\nor is it a re-projection of the surface reflection?\nReply: Thank you for this question; we recognize that these types of images can be confusing, and\nthat the manuscript benefits from explaining this better. The green laser light penetrates the water\nsurface, creating a light source below the surface. This light is then refracted through the rough water\nsurface. Therefore, on the images, the gray regions that are visible beneath the air-sea interface, do not\nrepresent the water column under the surface, they are a representation of the slope of the portion of\nthe sea surface that is between the camera and the laser sheet. The representation remains qualitative\nbecause this portion of the image is not within the focal plane of the camera lens. We realize that this\nwas unclear in the text and have added the following text to the methods section:\n”As the laser light penetrates the water surface, the intersection of the laser sheet with the water\nsurface delivers a high resolution (300 µm/pixel) picture of the instantaneous geometry of the water\nsurface (upper boundary of the gray scale region in Fig. 2). The intensity variations below the interface\nare caused by the refraction of green PIV laser light through the rough water surface, and are as such a\nfunction of the local variations in the slope of the water surface [see also Liu and Duncan, 2003,\nDuncan et al., 1999].”\nFig. 2: Is the example short wave riding the crest or trough of a long wave? One would assume\nthe former based on the text in the Methods section, but it would be helpful to state this more\nclearly also in the main text. Are the axes rotated relative to the instantaneous long-wave slope?\nReply: Thank you, this was indeed not very clear in the text. Yes, the short wave is at the crest of a\nlonger wave. We have added the following to the caption of figure 2:\n”The age of this wave (with a wavelength ∼ 1 m) is c/u = 6.4 or c/U = 0.22, which classifies it\n∗ 10\nas a ”slow” wave with respect to the wind speed blowing over it [Belcher and Hunt, 1998]. It is riding\non the crest of a longer wave (with a wavelength ∼ 70 m).”\nThe images are all projected into earth coordinates (vertical z-axis). We would not expect any\nsignificant changes in the results, were the axes rotated relative to the instantaneous long-wave slope,\nbecause the long-wave slopes remain small.\n2.2 Instantaneous structure of the airflow over fast waves Fig. 3: Are both the wave crest\nand (mean) wind propagating from left to right? Is windward/leeward defined with respect to the\ncrest velocity? This could be specified in the caption.\nReply: Thank you, this was indeed confusing. We have added the following to the figure caption:\n”Both the mean wind, and the wave, with a wavelength ∼ 70 m, are propagating from left to right.”\nAnd we have added some clarification on windward/leeward in the text:\n”Contrary to the slow wave case where the sheltered region is to the right of the crest (leeward side\nwith respect to the mean wind), the magnitude of the horizontal velocity (panel a) decreases here on\nthe left side of the wave, which is travelling faster than the local, near-surface wind.”\n2.3 Wave-induced motions How many individual slow and fast waves were used to generate\nthe ensemble-averaged airflow profiles? What is the full duration of the experimental dataset?\nReply: Thank you for asking this. As mentioned to Reviewer 1, we recognize that this relatively short\nacquisition duration can be concerning. The duration of the presented dateset is 70 seconds. This\nimaging duration was set by the size of the computer memory (RAM), which was filled after 70 seconds\nof PIV acquisition. The memory was subsequently emptied as the images were transferred to hard\ndrives; this operation lasted approximately 10 min. Only then was the next 70-second run possible. This\nresulted in a series of 70 s datasets (each acquired at 15 Hz), every 10 min.\nWe have added the following to the methods section:\n”Each 70 s dataset represents a total of 1050 2D velocity fields, each with up to 6776 x 2301\nmeasured velocity vectors, or a total of 2,416,050 (vertical) velocity profiles.”\nFor convenience, we have also copied part of our response to Reviewer 1 here:\nFor the slow wave results, each phase average value (figure 4, panels a and b) results from an\naverage over at least 2507 instantaneous velocity measurements. The total number of slow waves is\nestimated to be over 2000. The maximum 95% confidence interval shows no significant difference from\nthe average over all data (see figure R 1).\nA similar analysis was performed for the previous 70 s PIV dataset (acquired approximately 10 min\nprior to the one presented in this study, due to hardware restrictions, as mentioned above). The wind\nand wave conditions were similar (U = 7.9 m/s, u = 0.29 m/s, C = 10 m/s) as in the present study\n10 ∗ p\n(U = 8.3 m/s, u = 0.3 m/s, C = 10.4 m/s). The results show no significant difference with respect\n10 ∗ p\nto the phase averaged contours of the horizontal and vertical velocity components (see figure R 2).\nForthefastwaves,thetotalnumberofwavessampledwithin70sisonlyapproximately11(seefigure\nS3, in the supplementary material). However, the standard deviation is low, as these long, fast waves\nconsistently force the airflow in a quasi linear way. This is confirmed by the confidence interval figure\nbelow (figure R 3), where no significant difference is visible. Again, a comparison with the conditions\n10 min prior, shows that the shown results are robust (figure R 4).\nDo the slow wave ensemble averages contain breaking waves? If not, how do (or would) the\nmean airflow profiles differ for breaking waves?\nReply: In the presented dataset, we do not observe any air-entraining breaking waves. At other times\noutside of this dataset, we have observed intense separated sheltering events (airflow separation) past\nthe crest of slow, air-entraining breaking waves. (Unfortunately the quality of the PIV measurement\nis reduced above such waves, due to intense light reflections.) Based on our past work in wind-wave\ntunnels, where we have measured airflow dynamics over breaking and non-breaking waves, we would\nexpect similar results for the wave-induced perturbations over breaking waves, see for example Buckley\nand Veron [2019], figure 4, panels f and i. There, with a mean wind speed of 16.63 m/s, we expect\nfrequent wave breaking events. Interestingly, in spite of dramatic airflow separation events (with flow\nreversal in the sheltered region), the average flow is generally not reversed. This result contrasts with\nresults from numerical simulations over monochromatic waves or artificially narrow-banded breaking\nwave conditions [Yang and Shen, 2010, Sullivan et al., 2018], where phase averages show flow reversal\nin the average. We should mention here that airflow separation events over real wind waves (including\nlaboratory waves) are very turbulent, intermittent events, and with a broad range of spatial scales (the\nsheltered area varies rapidly in space and time). We have found that phase averages of the airflow\nvelocities do not generally represent this variability (in the laboratory as well as in situ).\nEq. 1: How were the inner layer heights L determined or defined?\ni\nReply: Thank you for this question, we realize that this should have been detailed in the manuscript.\nThe inner layer height was determined using equation 26 from Belcher and Hunt [1998], which equates\nthe eddy advection time scale to that of eddy dissipation, leading to: kL (U(L )−c) = 2κu , where κ\ni i ∗\nis the von Karman constant, c the peak phase speed of the waves, k the wavenumber, U(z) the mean\nwind velocity profile. We have added more details on this in the manuscript:\n”which satisfies kL (U(L )−c) = 2κu , where κ is the von Karman constant, c the peak phase\ni i ∗\nspeed of the waves, k the wavenumber, and U(z) the mean wind velocity profile (Belcher and Hunt\n[1998] (their equation 26, see also Grare et al. [2013a], Buckley and Veron [2016])”\nFig. 4: (How) Does the long-wave modulation of the short waves affect the mean airflow\npatterns? Does the mean airflow of the slow waves cover all long-wave phases? Would the authors\nexpect there to be a difference in the short-wave airflow at different long-wave phases due to long-\nwave modulation of the short waves (e.g. crest vs trough of long waves)?\nReply: Thank you, we have been looking into this. Yes we would expect a difference in short-wave\nairflow modulations at the crests of the long waves, compared with the troughs. Unfortunately the data\nquality is not sufficient, in locations of the airflow very near the surface above long wave troughs, to\nconclude anything on this at this time. In figure R 5, we show short wave phase averaged quantities,\nfor 4 quadrants of long wave phases. We note here that the (near-surface) slow wave phase averages\nabove the trough of the fast waves do not converge toward any meaningful results. We have raised the\nissue of insufficient seeding in the methods section of the manuscript.\nFig. 4: Alternate layout suggestion: Keep 2-column layout, but with the left column consisting\nof 4 subpanels in each row, and the right panel consisting of one high panel (current f panel). Left\ncolumn: 4-panel column with c+d on top 2 rows of left column. Include the wave form in the same\nway as in a+b (so that all subpanels include 0 on the y axis). On 3rd and 4th row of left column,\nshow current a+b panels, with e.g. a box showing the horizontal and vertical scales of the short\nwaves vs the long waves.\nReply: Thank you for this suggestion. We agree that the layout of figure 4 could be improved. We\nhave now separated this figure into 2 figures, and modified the layout of the wave-coherent velocity\nplots. This now shows better the significant differences between slow wave and fast wave- coherent\nvelocities. Our updated figure(s) do not quite follow the reviewer’s suggestion for 2 reasons: First, we\nare not sure how to design a box with to-scale comparison of waves with (H,λ) scales of O(1,100)m\nvs O(1,100)cm. Second, we should have mentioned that the very near-surface wave-coherent velocities\nover the slow waves shown in figure 4, are computed in a surface-following frame of reference, before\nbeing transformed back into cartesian coordinates for this plot. For the more regular fast waves, the\naveragingwasperformedinthecartesianframeofreference. There,duetovariabilityinwaveheightsand\nin PIV seeding density near the surface, and especially just above wave troughs, we have low confidence\nin the averaged near surface values. We have included these here for the reviewer’s convenience (figure\nR 6).\nWe have added the following text to the methods section of the manuscript:\n”In the case of the slow waves [...], The velocity fields were mapped from the cartesian frame\nof reference (x,z) to a surface-following frame of reference (x,ζ), where ζ = z − η(x,t) (as was\npreviously done in laboratory studies, for example by Grare et al. [2013b], Tenhaus et al. [2024]).For\nthe comparatively more regular, fast waves, the phase averaging was performed in the cartesian frame\nof reference. There, due to variability in wave heights and in PIV seeding density near the surface,\nand especially just above wave troughs, we have low confidence in the averages below z = 0.6 m. Therefore\nthese near surface averages are not shown here (figure 4c-d).”\nReviewing this figure has also allowed us to identify an error (offset) in the vertical axis of the fast\nwave plots (figure 4, c-d), as well as in the sheltering wave growth estimate (now figure 5), which we\nhave now fixed.\nto a sheltering/separation response in the nearfield airflow, whereas the long/fast waves induce\norbital wakes in the airflow. This result is essentially (redundantly) stated twice back-to-back.\nWhat is lacking for readers with basic (or limited) background in the subject is a clear statement\nof how the presented results change or update our understanding of the process of wave growth by\nwind. As stated above, this should preferably be explained more thoroughly in the introduction,\nbut more details could be added to the Supplementary materials.\nReply: Thank you for this comment. We have removed one instance of the redundant statement and\nwe have modified both introduction and conclusion, following the reviewers’ previous comments.\n4.1 In situ Large field of view Particle Image Velocimetry (PIV) Will the code for the\nPIV algorithm used in this study be made publicly available?\nReply: Thank you for this question. It is not planned to publish the PIV algorithm for this study. We\nuseanin-housecode,butitisnotparticularlyinteresting. InfactwedonotexpecttheresultstobePIV-\nalgorithm dependent. We expect that commercially available PIV software (for example from Dantec or\nLavision) would produce similar instantaneous 2D velocity fields, provided that some important pre and\npost-processing steps are taken (e.g., image stitching, proper masking of areas without seeding, motion\ncorrection).\nWhat level smoothing or filtering was performed on the raw PIV velocities vs. the final results\nshown in the manuscript?\nReply: Figures 2 and 3 in the manuscript show direct outputs of the PIV velocity computation\nalgorithm. Within the final step of the PIV algorithm, velocity vectors with low interrogation window\ncross-correlation values (less than 50%) are removed and replaced using a 2D robust spline smoothing\nalgorithm.\n4.2 Environmental conditions and supporting measurements Are directional wave spec-\ntra available for the measurement campaign? These would be helpful for showing the relative\ndirectionality of the windsea and swell.\nReply: Thank you, we have considered this. A Datawell directional waverider buoy (CDIP #234,\nhttps://cdip.ucsd.edu/themes/cdip/news?pb=1&d2=p9&u3=v:sensors:p_id:p9:mode:all:s:\n234:st:1) was moored within 1 km of FLIP’s location. Directional wave spectra show that the domi-\nnant waves were aligned with the wind on Oct 20th. On Oct 17th, there was additionally a 12 s swell\nsystemwithadirectionperpendiculartothewindsea. Wehavenowspecifiedthe1kmdistancebetween\nthe wave buoy and FLIP in the manuscript:\n”Alignment of the peak wave travel direction with the local wind direction was checked using\ndirectional wave field information provided by a waverider buoy moored within 1 km of FLIP’s location.”\nWill any of the data and/or code used in the manuscript be made publicly available?\nReply: Thank you. We plan to share the data that is shown in all the figures, including the supple-\nmentary ones."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The author's response to my questions was clear, and I have no further questions.\nThis version is sufficient for acceptance of the paper.", "reviewer_2": "The authors have answered our concerns (this is a joint review by Rev #2 and Rev #3, an early career scientist). We\ncommend the authors on a very nice study which, despite the challenges and limitations of the experiment, will surely make\nan important contribution to the ongoing effort to understand the fiendishly difficult problem of unraveling the processes\nresponsible for wave growth.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts."}, "author_response": ""}]

Decision letter