9 results
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:
- 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.
Growth and dissipation of wind-forced, deep-water waves
- Laurent Grare, William L. Peirson, Hubert Branger, James W. Walker, Jean-Paul Giovanangeli, Vladimir Makin
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- Journal:
- Journal of Fluid Mechanics / Volume 722 / 10 May 2013
- Published online by Cambridge University Press:
- 28 March 2013, pp. 5-50
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The input of energy by wind to water waves is compared with the observed growth of the waves using a suite of microphysical measurement techniques in the laboratory. These include measured tangential stresses in the water and air immediately adjacent to the interface with corresponding form drag measurements above wind-forced freely propagating waves. The drag data sets are consistent but the comparison has highlighted important issues in relation to the measurement of fluctuating pressures above freely propagating waves. Derived normalized wind input values show good collapse as a function of mean wave steepness and are significantly in excess of the assembly of net wave growth measurements by Peirson & Garcia (J. Fluid Mech., vol. 608, 2008, pp. 243–274) at low steepness. Sheltering coefficients in the form of Jeffreys (Proc. R. Soc. Lond. Ser. A, vol. 107, 1925, pp. 189–206) are derived that are consistent with values previously obtained by Donelan & Pierson (J. Geophys. Res., vol. 92, 1987, pp. 4971–5029), Donelan (Wind-over-Wave Couplings: Perspectives and Prospects, Clarendon, 1999, pp. 183–194) and Donelan et al. (J. Phys. Oceanogr., vol. 36, 2006, pp. 1672–1689). The sheltering coefficients exhibit substantial scatter. By carefully measuring the associated growth of the surface wave fields, systematic energy budgets for the interaction between wind and waves are obtained. For non-breaking waves, there is a significant and systematic misclose in the radiative transfer equation if wave–turbulence interactions are not included. Significantly higher levels of turbulent wave attenuation are found in comparison with the theoretical estimates by Teixeira & Belcher (J. Fluid Mech., vol. 458, 2002, pp. 229–267) and Ardhuin & Jenkins (J. Phys. Oceanogr., vol. 36, 2006, pp. 551–557). Suitable normalizations of attenuation for wind-forced wave fields exhibit consistent behaviour in the presence and absence of wave breaking. Closure of the surface energy flux budget is obtained by comparing the normalized energy loss rates due to breaking with the values previously determined by Banner & Peirson (J. Fluid Mech., vol. 585, 2007, pp. 93–115) and Drazen et al.(J. Fluid Mech., vol. 611, 2008, pp. 307–332) when expressed as a function of mean wave steepness. Their normalized energy loss rates obtained for non-wind forced breaking wave groups are remarkably consistent with the levels found during this present study when breaking waves are subject to wind forcing.
On the wind-induced growth of slow water waves of finite steepness
- WILLIAM L. PEIRSON, ANDREW W. GARCIA
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- Journal:
- Journal of Fluid Mechanics / Volume 608 / 10 August 2008
- Published online by Cambridge University Press:
- 11 July 2008, pp. 243-274
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Determining characteristic growth rates for water waves travelling more slowly than the wind has continued to be a key unresolved problem of air–sea interaction for over half a century. Analysis of previously reported and recently acquired laboratory wave data shows a systematic decline in normalized wave growth with increasing mean wave steepness that has not previously been identified. The normalized growth dynamic range is comparable with previously observed scatter amongst other laboratory data gathered in the slow wave range. Strong normalized growth rates are observed at low wave steepnesses, implying an efficient wave-coherent tangential stress contribution. Data obtained during this study show quantitative agreement with the predictions of others of the interactions between short wind waves and the longer lower-frequency waves. Measured normalized wave growth rates are consistent with numerically predicted growth due to wave drag augmented by significant wave-coherent tangential stress.
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
- Published online by Cambridge University Press:
- 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.
Water wave attenuation due to opposing wind
- WILLIAM L. PEIRSON, ANDREW W. GARCIA, STEVEN E. PELLS
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- Journal:
- Journal of Fluid Mechanics / Volume 487 / 25 June 2003
- Published online by Cambridge University Press:
- 25 June 2003, pp. 345-365
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A laboratory investigation of the attenuation of mechanically generated waves by an opposing wind has been completed. Wave attenuation was quantified by measurements of the decline in surface variance. These measurements show higher effective levels of monochromatic wave attenuation than predicted by air-side measurements: approximately an order of magnitude higher than measurements by Young & Sobey (1985) and, a factor of 3 higher than those of Donelan (1999) for waves in a JONSWAP spectrum. Furthermore, they show that theoretical estimates currently underestimate the attenuation rates by a factor of at least 3. This study has shown that the magnitude of wave attenuation rates due to opposing winds is approximately 2.5 times greater than the magnitude of wave growth rates for comparable wind forcing. At high wave steepnesses, detailed analysis suggests that air-side processes alone are not sufficient to induce the observed levels of attenuation. Rather, it appears that energy fluxes from the wave field due to the interaction between the wave-induced currents and other subsurface motions play a significant role once the mean wave steepness exceeds a critical value. A systematic relationship between the energy flux from the wave field and mean wave steepness was observed. The combination of opposing wind and wind-induced water-side motions is far more effective in attenuating waves than has previously been envisaged.
Aqueous surface layer flows induced by microscale breaking wind waves
- WILLIAM L. PEIRSON, MICHAEL L. BANNER
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- Journal:
- 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.
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.