13 results
An energetic signature for breaking inception in surface gravity waves
- Daniel G. Boettger, Shane R. Keating, Michael L. Banner, Russel P. Morison, Xavier Barthélémy
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- Journal:
- Journal of Fluid Mechanics / Volume 959 / 25 March 2023
- Published online by Cambridge University Press:
- 23 March 2023, A33
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A dynamical understanding of the physical process of surface gravity wave breaking remains an unresolved problem in fluid dynamics. Conceptually, breaking can be described by inception and onset, where breaking inception is the initiation of unknown irreversible processes within a wave crest that precede the visible manifestation of breaking onset. In the search for an energetic indicator of breaking inception, we use an ensemble of non-breaking and breaking crests evolving within unsteady wave packets simulated in a numerical wave tank to investigate the evolution of each term in the kinetic energy balance equation. We observe that breaking onset is preceded by around one quarter of a wave period by a rapid increase in the rate of convergence of kinetic energy that triggers an irreversible acceleration of the kinetic energy growth rate. This energetic signature, which is present only for crests that subsequently break, arises when the kinetic energy growth rate exceeds a critical threshold. At this point the additional kinetic energy convergence cannot be offset by converting excess kinetic energy to potential energy or by dissipation through friction. Our results suggest that the ratio of the leading terms of the kinetic energy balance equation at the time of this energetic signature is proportional to the strength of the breaking crest. Hence this energetic inception point both predicts the occurrence of breaking onset and indicates the strength of the breaking event.
On the breaking inception of unsteady water wave packets evolving in the presence of constant vorticity
- Julien Touboul, Michael L. Banner
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- Journal:
- Journal of Fluid Mechanics / Volume 915 / 25 May 2021
- Published online by Cambridge University Press:
- 09 March 2021, A16
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The recent numerical study of Barthelemy et al. (J. Fluid Mech., vol. 841, 2018, pp. 463–488) investigated the local properties of two-dimensional (2-D) and three-dimensional (3-D) nonlinear unsteady gravity wave packets in deep and uniform intermediate depth water. Their study focused on the breaking inception transition zone separating maximum recurrence and marginal breaking, and reported that a suitably normalized energy flux localized at the steepest crest in the packet provides a robust breaking threshold parameter. Our present study uses the fully nonlinear boundary integral element method solver developed by Touboul & Kharif (Nat. Haz., vol. 84, issue 2, 2016, pp. 585–598) to investigate breaking inception of 2-D deep water nonlinear water wave packets propagating in the presence of a background current that varies linearly with depth. We seek to validate whether the proposed generic breaking inception threshold holds for the case of constant background vorticity. Results are presented for different packet bandwidths and background vorticity levels.
Crest speeds of unsteady surface water waves
- Francesco Fedele, Michael L. Banner, Xavier Barthelemy
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- Journal:
- Journal of Fluid Mechanics / Volume 899 / 25 September 2020
- Published online by Cambridge University Press:
- 17 July 2020, A5
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Intuitively, crest speeds of water waves are assumed to match their phase speeds. However, this is generally not the case for natural waves within unsteady wave groups. This motivates our study, which presents new insights into the generic behaviour of crest speeds of linear to highly nonlinear unsteady waves. While our major focus is on gravity waves where a generic crest slowdown occurs cyclically, results for capillary-dominated waves are also discussed, for which crests cyclically speed up. This curious phenomenon arises when the theoretical constraint of steadiness is relaxed, allowing waves to change their form, or shape. In particular, a kinematic analysis of both simulated and observed open-ocean gravity waves reveals a forward-to-backward leaning cycle for each individual crest within a wave group. This is clearly manifest during the focusing of dominant wave groups essentially due to the dispersive nature of waves. It occurs routinely for focusing linear (vanishingly small steepness) wave groups, and it is enhanced as the wave spectrum broadens. It is found to be relatively insensitive to the degree of phase coherence and focusing of wave groups. The nonlinear nature of waves limits the crest slowdown. This reduces when gravity waves become less dispersive, either as they steepen or as they propagate over finite water depths. This is demonstrated by numerical simulations of the unsteady evolution of two- and three-dimensional dispersive gravity wave packets in both deep and intermediate water depths, and by open-ocean space–time measurements.
Predicting the breaking strength of gravity water waves in deep and intermediate depth
- Morteza Derakhti, Michael L. Banner, James T. Kirby
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- Journal:
- Journal of Fluid Mechanics / Volume 848 / 10 August 2018
- Published online by Cambridge University Press:
- 06 June 2018, R2
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We revisit the classical but as yet unresolved problem of predicting the strength of breaking 2-D and 3-D gravity water waves, as quantified by the amount of wave energy dissipated per breaking event. Following Duncan (J. Fluid Mech., vol. 126, 1983, pp. 507–520), the wave energy dissipation rate per unit length of breaking crest may be related to the fifth moment of the wave speed and the non-dimensional breaking strength parameter $b$. We use a finite-volume Navier–Stokes solver with large-eddy simulation resolution and volume-of-fluid surface reconstruction (Derakhti & Kirby, J. Fluid Mech., vol. 761, 2014a, pp. 464–506; J. Fluid Mech., vol. 790, 2016, pp. 553–581) to simulate nonlinear wave evolution, with a strong focus on breaking onset and postbreaking behaviour for representative cases of wave packets with breaking due to dispersive focusing and modulational instability. The present study uses these results to investigate the relationship between the breaking strength parameter $b$ and the breaking onset parameter $B$ proposed recently by Barthelemy et al. (J. Fluid Mech., vol. 841, 2018, pp. 463–488). The latter, formed from the local energy flux normalized by the local energy density and the local crest speed, simplifies, on the wave surface, to the ratio of fluid speed to crest speed. Following a wave crest, when $B$ exceeds a generic threshold value at the wave crest (Barthelemy et al. 2018), breaking is imminent. We find a robust relationship between the breaking strength parameter $b$ and the rate of change of breaking onset parameter $\text{d}B/\text{d}t$ at the wave crest, as it transitions through the generic breaking onset threshold ($B\sim 0.85$), scaled by the local period of the breaking wave. This result significantly refines previous efforts to express $b$ in terms of a wave packet steepness parameter, which is difficult to define robustly and which does not provide a generically accurate forecast of the energy dissipated by breaking.
On the threshold for wave breaking of two-dimensional deep water wave groups in the absence and presence of wind
- Arvin Saket, William L. Peirson, Michael L. Banner, Xavier Barthelemy, Michael J. Allis
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- Journal:
- Journal of Fluid Mechanics / Volume 811 / 25 January 2017
- Published online by Cambridge University Press:
- 15 December 2016, pp. 642-658
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The threshold for the onset of breaking proposed by Barthelemy et al. (arXiv:1508.06002v1, 2015) has been investigated in the laboratory for unidirectional wave groups in deep water and extended to include different classes of wave groups and moderate wind forcing. Thermal image velocimetry was used to compare measurements of the wave crest point (maximum elevation and also the point of maximum) surface water particle velocity ($U_{s}$) with the wave crest point speed ($C$) determined by an array of closely spaced wave gauges. The crest point surface energy flux ratio $B_{x}=U_{s}/C$ that distinguishes maximum recurrence from marginal breaking was found to be $0.840\pm 0.016$. Increasing wind forcing from zero to $U_{\unicode[STIX]{x1D706}/4}/C_{0}=1.42$ systematically increased this threshold by 2 %. Increasing the spectral bandwidth (decreasing the Benjamin–Feir index from 0.39 to 0.31) systematically reduced the threshold by 1.5 %.
On the microphysical behaviour of wind-forced water surfaces and consequent re-aeration
- William L. Peirson, James W. Walker, Michael L. Banner
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- Journal:
- Journal of Fluid Mechanics / Volume 743 / 25 March 2014
- Published online by Cambridge University Press:
- 05 March 2014, pp. 399-447
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A detailed laboratory investigation of the mechanical and low-solubility gas coupling between wind and water has been undertaken using a suite of microphysical measurement techniques. Under a variety of wind conditions and in the presence and absence of mechanically generated short waves, approximately fetch-independent surface conditions have been achieved over short laboratory fetches of several metres. The mechanical coupling of the surface is found to be consistent with Banner (J. Fluid Mech. vol. 211, 1990, pp. 463–495) and Banner & Peirson (J. Fluid Mech. vol. 364, 1998, pp. 115–145). Bulk observations of re-aeration are consistent with previous laboratory studies. The surface kinematical behaviour is in accordance with the observations of Peirson & Banner (J. Fluid Mech. vol. 479, 2003, pp. 1–38). Also, their predictions of a strong enhancement of low-solubility gas flux at the onset of microscale breaking is confirmed and direct observations show a concomitant onset of very thin aqueous diffusion sublayers. It is found that the development of strong parasitic capillary waves towards the incipient breaking limit does not noticeably enhance constituent transfer. Across the broad range of conditions investigated during this study, the local instantaneous constituent transfer rate remains approximately log-normally distributed with an approximately constant standard deviation of $0.62\pm 0.15({\mathrm{log}}_e(\mathrm{m}~ {\mathrm{s}}^{-1}))$. Although wind-forced water surfaces are shown to be punctuated by intense tangential stresses and local surface convergence, localized surface convergence does not appear to be the single critical factor determining exchange rate. Larger-scale orbital wave straining is found to be a significant constituent transfer process in contrast to Witting (J. Fluid Mech. vol. 50, 1971, pp. 321–334) findings for heat fluxes, but the measured effects are consistent with his model. By comparing transfer rates in the presence and absence of microscale breaking, low-solubility gas transfer was decomposed into its turbulent/capillary ripple, gravity-wave-related and microscale breaking contributions. It was found that an efficiency factor of approximately $17\, \%$ needs to be applied to Peirson & Banner’s model, which is extended to field conditions. Although bulk thermal effects were observed and thermal diffusion layers are presumed thicker than their mass diffusion counterparts, significant thermal influences were not observed in the results.
Rain-induced attenuation of deep-water waves
- William L. Peirson, José F. Beyá, Michael L. Banner, Joaquín Sebastián Peral, Seyed Ali Azarmsa
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- Journal of Fluid Mechanics / Volume 724 / 10 June 2013
- Published online by Cambridge University Press:
- 29 April 2013, pp. 5-35
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A laboratory investigation has been undertaken to quantify water wave attenuation rates as a function of rainfall rate. Vertical artificial rainfall is shown to generate weak near-surface velocity fluctuations that decline systematically away from the free surface and are independent of rainfall rate across the range of rainfall rates investigated (40–$170~\mathrm{mm} ~{\mathrm{h} }^{- 1} $). In the absence of rain, the observed attenuation of gravity waves is at levels consistent with classical viscous theory, but with a systematic finite-amplitude effect observed above a mean steepness of 0.10. Wave attenuation rates were found to be independent of the mean wave steepness and identical when artificial rainfall rates of 108 and $141~\mathrm{mm} ~{\mathrm{h} }^{- 1} $ were applied. Reassessment of complementary theoretical and experimental studies of individual droplets impacting on undisturbed water surfaces indicates that above a weak threshold rainfall rate of $30~\mathrm{mm} ~{\mathrm{h} }^{- 1} $, the surface irradiation becomes so frequent that droplet-generated violent surface motions directly interact with the incoming droplets. Present evidence is that a matching of time scales develops between the incoming surface irradiation and surface water motions generated by antecedent droplets as the rainfall rate increases. Consequently, at high rainfall rates, a highly dissipative surface regime is created that transmits little of the incident rainfall kinetic energy to the aqueous layers below. Rainfall-induced wave attenuation rates are compared with measurements of other wave attenuation processes to obtain a hierarchy of strength in both the laboratory and the field. Comparison is also made with wave attenuation theories that incorporate momentum and energy flux considerations. Rain-induced wave attenuation rates are weak or very strong depending on whether they are expressed in terms of energy scaling obtained from above or below the surface respectively, due to the high dissipation rate that occurs in the vicinity of the interface.
Wave breaking onset and strength for two-dimensional deep-water wave groups
- MICHAEL L. BANNER, WILLIAM L. PEIRSON
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- Journal:
- Journal of Fluid Mechanics / Volume 585 / 25 August 2007
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- 07 August 2007, pp. 93-115
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The numerical study of J. Song & M. L. Banner (J. Phys. Oceanogr. vol. 32, 2002, p. 254) proposed a generic threshold parameter for predicting the onset of breaking within two-dimensional groups of deep-water gravity waves. Their parameter provides a non-dimensional measure of the wave energy convergence rate and geometrical steepening at the maximum of an evolving nonlinear wave group. They also suggested that this parameter might control the strength of breaking events. The present paper presents the results of a detailed laboratory observational study aimed at validating their proposals.
For the breaking onset phase of this study, wave potential energy was measured at successive local envelope maxima of nonlinear deep-water wave groups propagating along a laboratory wave tank. These local maxima correspond alternately to wave group geometries with the group maximum occurring at an extreme carrier wave crest elevation, followed by an extreme carrier wave trough depression. As the nonlinearity increases, these crest and trough maxima can have markedly different local energy densities owing to the strong crest–trough asymmetry. The local total energy density was reconstituted from the potential energy measurements, and made dimensionless using the square of the local (carrier wave) wavenumber. A mean non-dimensional growth rate reflecting the rate of focusing of wave energy at the envelope maximum was obtained by smoothing the local fluctuations.
For the cases of idealized nonlinear wave groups investigated, the observations confirmed the evolutionary trends of the modelling results of Song & Banner (2002) with regard to predicting breaking onset. The measurements confirmed the proposed common breaking threshold growth rate of 0.0014±0.0001, as well as the predicted key evolution times: the time taken to reach the energy maximum for recurrence cases; and the time to reach the breaking threshold and then breaking onset, for breaking cases.
After the initiation and subsequent cessation of breaking, the measured wave packet mean energy losses and loss rates associated with breaking produced an unexpected finding: the post-breaking mean wave energy did not decrease to the mean energy level corresponding to maximum recurrence, but remained significantly higher. Therefore, pre-breaking absolute wave energy or mean steepness do not appear to be the most fundamental determinants of post-breaking wave packet energy density.
However, the dependence of the fractional breaking energy loss of wave packets on the parametric growth rate just before breaking onset proposed by Song & Banner (2002) was found to provide a plausible collapse to our laboratory data sets, within the experimental uncertainties. Further, when the results for the energy loss rate per unit width of breaking front were expressed in terms of a breaker strength parameter b multiplying the fifth power of the wave speed, it is found that b was also strongly correlated with the parametric growth rate just before breaking. Measured values of b obtained in this investigation ranged systematically from 8 × 10−5 to 1.2 × 10−3. These are comparable with open ocean estimates reported in recent field studies.
The influence of wave breaking on the surface pressure distribution in wind—wave interactions
- Michael L. Banner
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- Journal of Fluid Mechanics / Volume 211 / February 1990
- Published online by Cambridge University Press:
- 26 April 2006, pp. 463-495
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In reviewing the current status of our understanding of the mechanisms underlying wind-wave generation, it is apparent that existing theories and models are not applicable to situations where the sea surface is disturbed by breaking waves, and that the available experimental data on this question are sparse. In this context, this paper presents the results of a detailed study of the effects of wave breaking on the aerodynamic surface pressure distribution and consequent wave-coherent momentum flux, as well as its influence on the total wind stress.
Two complementary experimental configurations were used to focus on the details and consequences of the pressure distribution over breaking waves under wind forcing. The first utilized a stationary breaking wave configuration and confirmed the presence of significant phase shifting, due to air flow separation effects, between the surface pressure and surface elevation (and slope) distributions over a range of wind speeds. The second configuration examined the pressure distribution, recorded at a fixed height above the mean water surface just above the crest level, over short mechanically triggered waves which were induced to break almost continuously under wind forcing. This allowed a very detailed comparison of the form drag for actively breaking waves and for waves of comparable steepness just prior to breaking (‘incipiently’ breaking waves). For these propagating steep-wave experiments, the pressure phase shifts and distributions closely paralleled the stationary configuration findings. Moreover, a large increase (typically 100%) in the total windstress was observed for the breaking waves, with the increase corresponding closely to the comparably enhanced form drag associated with the actively breaking waves.
In addition to further elucidating some fundamental features of wind-wave interactions for very steep wind waves, this paper provides a useful data set for future model calculations of wind flow over breaking waves. The results also provide the basis for a parameterization of the wind input source function applicable for a wave field undergoing active breaking, an important result for numerical modelling of short wind waves.
Wind-induced growth of mechanically generated water waves[dagger]
- W. Stanley Wilson, Michael L. Banner, Ronald J. Flower, Jeffrey A. Michael, Donald G. Wilson
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- Journal of Fluid Mechanics / Volume 58 / Issue 3 / 8 May 1973
- Published online by Cambridge University Press:
- 29 March 2006, pp. 435-460
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An experimental study was conducted to measure the growth rates of mechanically generated surface water waves when subjected to a fully developed turbulent channel airflow. The study was designed to test the accuracy of the growth rates predicted by Miles's (1962b) theory. For a series of wave frequencies (from 2·04 to 6·04 Hz at 0·50 Hz increments) and centre-line wind velocities (0·20, 1·12 and 1·84 m/s) wave amplitudes were measured at three stations (2–21, 3–43 and 4·65 m) downwind from a wave generator. In addition, for centre-line velocities of 1–12 and 1·84 m/s, U* (the velocity at the outer edge of the viscous sublayer) and U1, (the shear velocity) were obtained from measured mean velocity and Reynolds stress profiles. The wave amplitude measurements at the wind velocity of 0·20 m/s provided attenuation rate estimates which agreed reasonably well with theoretical attenuation rates based on viscous effects both on the walls and in the bulk of the water. The amplitude measurements at the wind velocities of 1·12 and 1·84m/s provided growth rate estimates which were compared with theoretical growth rates (computed using the wave frequency, U1 and U* predicted by Miles's (1962b) theory. At 1·12m/s Miles's growth rateswere two to five times larger than those measured; at 1·84 m/s Miles's growth rates were about two times larger.
Aqueous surface layer flows induced by microscale breaking wind waves
- WILLIAM L. PEIRSON, MICHAEL L. BANNER
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- Journal of Fluid Mechanics / Volume 479 / 25 March 2003
- Published online by Cambridge University Press:
- 01 April 2003, pp. 1-38
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Microscale breaking wind waves cover much of the surface of open waters exposed to moderate wind forcing. Recent studies indicate that understanding the nature and key features of the surface skin flows associated with these small waves is fundamental to explaining the dramatic enhancement of constituent exchange that occurs in their presence. We describe a laboratory study in which velocity measurements were made within a few hundred micrometres of the surface of microscale breaking wind waves without bubble entrainment, using flow visualization and particle image velocimetry (PIV) techniques for a range of wind speed and fetch conditions. Our measurements show that for each experiment, the mean surface drift directly induced by the wind on the upwind faces and crests of these waves is ($0.23\,{\pm}\,0.02$)${u}^a_\ast$ in the trough increasing to ($0.33\,{\pm}\,0.07$)${u}^a_\ast$ at the crest, where ${u}^a_\ast$ is the wind friction velocity. About these mean values, there is substantial variability in the instantaneous surface velocity up to approximately ${\pm}\,0.17{u}^a_\ast$ in the trough and ${\pm}\,0.37{u}^a_\ast$ at the crest. This variability can be attributed primarily to the modulation of the wave field, with additional contributions arising from fluctuations in wind forcing and near-surface turbulence generated by shear in the drift layer or by the influence of transient microscale breaking.
On the determination of the onset of breaking for modulating surface gravity water waves
- MICHAEL L. BANNER, XIN TIAN
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- Journal of Fluid Mechanics / Volume 367 / 25 July 1998
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- 25 July 1998, pp. 107-137
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Determining the onset of wave breaking in unforced nonlinear modulating surface gravity wave trains on the basis of a threshold variable has been an elusive problem for many decades. We have approached this problem through a detailed numerical study of the fully nonlinear two-dimensional inviscid problem on a periodic spatial domain. Two different modes of behaviour were observed for the evolution of a sufficiently steep wave group: either recurrence of the initial state or the rapid onset of breaking, each of these involving a significant deformation of the wave group geometry. For both of these modes, we determined the behaviour of dimensionless growth rates constructed from the rates of change of the local mean wave energy and momentum densities of the wave train, averaged over half a wavelength. These growth rates were computed for wave groups with three to ten carrier waves in the group and also for two modulations with seven carrier waves and three modulations with ten carrier waves. We also investigated the influence of a background vertical shear current.
Two major findings arose from our calculations. First, due to nonlinearity, the crest–trough asymmetry of the carrier wave shape causes the envelope maxima of these local mean wave energy and momentum densities to fluctuate on a fast time scale, resulting in a substantial dynamic range in their local relative growth rates. Secondly, a universal behaviour was found for these local relative growth rates that determines whether subsequent breaking will occur.
Tangential stress beneath wind-driven air–water interfaces
- MICHAEL L. BANNER, WILLIAM L. PEIRSON
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- Journal:
- Journal of Fluid Mechanics / Volume 364 / 10 June 1998
- Published online by Cambridge University Press:
- 10 June 1998, pp. 115-145
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The detailed structure of the aqueous surface sublayer flow immediately adjacent to the wind-driven air–water interface is investigated in a laboratory wind-wave flume using particle image velocimetry (PIV) techniques. The goal is to investigate quantitatively the character of the flow in this crucial, very thin region which is often disrupted by microscale breaking events. In this study, we also examine critically the conclusions of Okuda, Kawai & Toba (1977), who argued that for very short, strongly forced wind-wave conditions, shear stress is the dominant mechanism for transmitting the atmospheric wind stress into the water motion – waves and surface drift currents. In strong contrast, other authors have more recently observed very substantial normal stress contributions on the air side. The availability of PIV and associated image technology now permits a timely re-examination of the results of Okuda et al., which have been influential in shaping present perceptions of the physics of this dynamically important region. The PIV technique used in the present study overcomes many of the inherent shortcomings of the hydrogen bubble measurements, and allows reliable determination of the fluid velocity and shear within 200 μm of the instantaneous wind-driven air–water interface.
The results obtained in this study are not in accord with the conclusions of Okuda et al. that the tangential stress component dominates the wind stress. It is found that prior to the formation of wind waves, the tangential stress contributes the entire wind stress, as expected. With increasing distance downwind, the mean tangential stress level decreases marginally, but as the wave field develops, the total wind stress increases significantly. Thus, the wave form drag, represented by the difference between the total wind stress and the mean tangential stress, also increases systematically with wave development and provides the major proportion of the wind stress once the waves have developed beyond their early growth stage. This scenario reconciles the question of relative importance of normal and tangential stresses at an air–water interface. Finally, consideration is given to the extrapolation of these detailed laboratory results to the field, where the present findings suggest that the sea surface is unlikely to become fully aerodynamically rough, at least for moderate to strong winds.