Swinburne Research Bank

Transcription

1 Swinburne Research Bank htt://researchbank.swinburne.edu.au Babanin, A. V., Young, I. R. (2006). Field study of energy source/sink terms for wind-generated waves. Paer resented at the Fundamental and Environmental Fluid Mechanics: Fluxes and Structures in Fluids, Moscow, Russia, June 2005 Coyright 2006 Alexander Babanin and Ian Young. This is the author s version of the work. It is osted here in accordance with the coyright olicy of the ublisher for your ersonal use. No further distribution is ermitted. Accessed from Swinburne Research Bank: htt://hdl.handle.net/1959.3/4998

2 FIELD STUDY OF ENERGY SOURCE/SINK TERMS FOR WIND- GENERATED WAVES Alexander Babanin and Ian Young Swinburne University of Technology Melbourne, Victoria 3122 Australia Натурные исследования функций источников/стоков энергии для ветровых волн. Натурный эксперимент по одновременному изучению функций источников/стоков энергии ветровых волн в условиях ограниченной глубины был проведён на озере в Австралии. Прямые измерения накачки энергии от ветра, трения волн о дно и диссипации волновой энергии из-за обрушения волн осуществлялись синхронно интегральной измерительной системой. Также проводились другие синхронизированные записи, позволяющие получить пространственно-временной спектр волн, характеристики пограничного слоя атмосферы и свойства турбулентности в воздухе и в воде. Наблюдения осуществлялись в течение трёх лет, с сентября 1997 г. по август 2000 г. Результаты позволили выявить новые физические механизмы в процессах диссипации волновой энергии и мелкомасштабного обмена энергией и импульсом между атмосферой и океаном, которые были параметризованы как спетральные функции для применения в моделях. 1. Introduction Sectral evolution of the wind-generated wave field is commonly described by the radiative transfer equation (Hasselmann, 1960): df( = I( + N( + D( + B( (1) dt where the total derivative of the frequency ( -wavenumber ( sectrum F( on the left hand side is balanced by the sum of energy source I, sinks D, and sectral redistribution N terms on the right. In the finite deth, energy sink due to wave interaction with the bottom B is usually considered exlicitly. Here, only energy terms for wind inut I, dissiation in the water column D, bottom friction B, and four-wave non-linear interactions N are mentioned, as they are usually the dominant terms. Equation (1) is the basic equation used in most hase-average numerical wave rediction models. A field exeriment to study the sectral balance of the source terms for wind-generated waves in finite water deth was carried out in Lake George, Australia (Fig. 1). The measurements were made from a shore connected latform at varying water deths from 1.2 m down to 20 cm. Wind conditions and the geometry of the lake were such that fetch-limited conditions with fetches ranging from aroximately km down to 1 km revailed. The resulting waves were intermediate-deth wind waves with inverse wave ages, measured by the ratio of wind seed at m height above the sea level, U to the seed of the dominant (sectral ea waves, c, in the range 1 < U / c < 8. The atmosheric inut, bottom friction and whiteca dissiation were measured directly and synchronously by an integrated measurement system. In addition, simultaneous data defining the directional wave sectrum, atmosheric boundary layer rofile and atmosheric and underwater turbulence were available. The contribution to the sectral evolution due to nonlinear interactions of various orders is investigated by a combination of bisectral analysis of the data and numerical modelling. The relatively small scale of the lake enabled exerimental conditions such as the wind field and bathymetry to be well defined. The observations were conducted over a three-year eriod from

3 Setember, 1997 to August, 2000, with a designated intensive measurement eriod (AUSWEX) carried out in August-Setember High data return was achieved (Young et al., 2005). Fig.1 (left) Location of the Lake George site; (right) onshore view of the site. Elevated walkway, comuter shed, measurement bridge and anemometer mast are seen 2. Wind Inut Nearly all of the momentum delivered from wind to waves comes about through waveinduced ressure acting on the sloes of waves - form drag. Direct field measurements of the wave-induced ressure in air flow over water waves are difficult and consequently rare. In order to measure microscale oscillations of induced ressure above surface waves, a high-recision wave follower system was develoed at the University of Miami, Florida (Donelan et al., 2005a). The rincial sensing hardware included Elliott ressure robes, hot film anemometers and Pitot tubes. The wave-follower recordings were sulemented by a comlete set of relevant measurements in the atmosheric boundary layer, on the surface and in the water body. The recision of the feedback wave-following mechanism did not imose any restrictions on the measurement accuracy in the range of wave heights and frequencies relevant to the roblem. Thorough calibrations of the ressure transducers and moving Elliott robes were conducted. As a result of this study, it was shown for the first time that the resonse of the air column in the connecting tubes rovides a frequency-deendent hase shift, which must be accounted for to recover the low-level induced ressure signal. 2.1 Wind inut sectral function Previously reorted measurements of the wave-induced air ressure are for dee water conditions and conditions in which the level of forcing is quite weak: U / c < 3. The data reorted here, obtained during AUSWEX, have the range of 1 < U / c < 8. The roagation seeds of the dominant waves were limited by deth and the waves were corresondingly stee. This wider range of forcing and concomitant wave steeness revealed some new asects of the rate of wave amlification by wind - the so-called wind inut source function I in the energy balance equation for wind-driven water waves (1) (Donelan et al., 2005b). The nondimensional growth rate is customarily exressed in terms of the fractional energy increase γ, which is a sectral function ρ w 1 F( γ ( =. (2) ρ a ωf( t Here, ρ w and ρ a are densities of water and air resectively. Once the growth rate function γ( is known and the ower sectrum F( is available, the dimensional wind energy inut is I( = ρ aωgγ ( F( (3) where g is the gravitational constant. Two new features of the wind-wave interaction were discovered as a result the of Lake George study. Firstly, it was found that the exonential growth rate arameter γ deended on the

4 sloe of the waves, ak (a is the wave amlitude). Secondly, it was found that for very strong forcing a condition of full searation occurs, where the air flow detaches from the crests and re-attaches on the windward face leaving a searation zone over the leeward face and the troughs. In a sense, the outer flow does not see the troughs and the resulting wave-induced ressure erturbation is much reduced, leading to a reduction in the wind inut source function comared to that obtained by extraolation from more benign conditions. The two features affect the momentum transfer in oosing ways, increasing it in moderate forcing conditions and reducing it in strong forcing conditions. The validity of the arameterisation across the sectrum was verified by indeendent measurements of the integrated momentum flux across the interface. The latter feature may also have significant imlications for descritions of air-sea interaction at strong wind conditions. This result, along with recently discovered by Donelan et al. (2004) effect of limiting value of aerodynamic roughness at extreme winds, oint out to an imortant conclusion, not comletely unexected. The drag coefficient deendences obtained at moderate wind conditions and then extraolated into strong-wind situations may significantly overestimate the drag and air-sea momentum exchange. The source function arameterised on wave steeness and degree of searation is shown to be in agreement with revious field and laboratory data obtained in conditions of much weaker forcing and wave steeness. The strongly forced steady-state conditions of AUSWEX have enabled us to define a generalised wind inut source function that is designed to work in the entire range of wave generation by wind: from light and moderate to very strong winds; from young waves to mature seas. An analogue of this arameterisation, exressed in terms of the wave sectrum and suitable for use in wave sectral models, has form (Donelan et al., 2005b): U 2 γ = G Bn ( 1), c (4) U 2 G = 1.80 tanh( Bn ( 1) 11). c 5 ω F( Here, B n ( = A( is the sectral saturation (Banner et al., 2002) and A( is the 2 2g directional sreading function (Babanin and Soloviev, 1998). 2.2 Enhancement of the wind inut due to wave breaking, and other effects In the finite deth environment of Lake George, breaking waves lay an imortant role in the momentum exchange between wind and waves. Direct evidences were found of the influence of wave breaking on the wave-induced ressure in the air flow over water waves, and hence the energy flux to the waves (Young and Babanin, 2001). These measurements allowed an assessment of the magnitude of any breaking-induced searation enhancement and rovided a basis for arameterising the effect. Overall, areciable levels of wave breaking occurred for the strong wind forcing conditions revailing during the observational eriod. Associated with these breaking wave events, we observed a significant hase shift in the local wave-coherent surface ressure. This roduced an enhanced wave-coherent energy flux from the wind to the waves with a mean value of 1.9 times the corresonding energy flux to the non-breaking waves. We roose that the breaking-induced enhancement of the wind inut to the waves can be arameterised by the roduct of the non-breaking inut and the breaking robability. Further analysis of the wind-wave energy inut, revealed a fine scale inhomogeneity of such inut, both in time (over a few wave eriod time scale) and in sace (over a few wave lengths) (Agnon et al., 2005). Such oscillations aear to be correlated with fluctuations of wave skewness and asymmetry and have a otential to essentially alter the average inut estimates if are roerly accounted for (Donelan et al., 2005b). 3. Sectral dissiation of wave energy due to whitecaing and eddy viscosity Sectral wave energy dissiation reresents the least understood art of the hysics relevant to wave modelling. There is a general consensus that the major art of this dissiation is

5 suorted by the wave breaking, but hysics of this breaking rocess, articularly for the sectral waves, is oorly understood. Theoretical and exerimental knowledge of the sectral wave dissiation is so insufficient that, to fill the ga, sectral models have been used to guess the sectral dissiation function D in eq.(1) as a residual term of tuning the balance of better known source functions to fit known wave sectrum features. This is the only source function in (1) which has so far been inferred indirectly by modelling the evolution of the wave sectrum rather than by arameterising known hysical features directly. Two different methodologies were used in the Lake George study to investigate the dissiation function. The first emloyed the acoustic noise sectrograms to identify segments of breaking and non-breaking dominant wave trains (Babanin et al., 2001). The average ower and directional sectra for breaking and non-breaking waves were thus obtained, and the difference was attributed to the dissiation due to wave breaking (Young and Babanin, 2005). This method rovides an estimate of the sectral effects, both in frequency and directional domains, of the dominant wave breaking. As an indeendent second aroach, a assive acoustic method of detecting individual bubble-formation events was develoed. This method was found romising for obtaining both the rate of occurrence of breaking events at different wave scales and the severity of wave breaking (Manasseh et al., 2005). A combination of the two methods should lead to direct estimates of the sectral distribution of wave dissiation. If the wave energy dissiation at each frequency were due to whitecaing only, it should be a function of the excess of the sectral density above a dimensionless threshold sectral level, below which no breaking occurs at this frequency (Babanin et al., 2001, Banner et al., 2002). This was found to be the case around the wave sectral eak. A more comlex mechanism aears to be driving the dissiation at scales different to those of the dominant waves. Dissiation at a articular frequency above the eak demonstrates a cumulative effect, deending on the rates of sectral dissiation at lower frequencies. In terms of the dissiation function S ds such an effect will mean a two-hase behaviour: S ds being a simle function of the wave sectrum at the sectral eak and having an additional cumulative term at all frequencies above the eak (Babanin and Young, 2005). The following arameterisation of the dissiation term was suggested: ω n D( = a1 ρ w gω(( F( Fthr ( ) A( ) + a2ρ wg ( F( q) Fthr ( q)) A( q) dq (5) where ω is the sectral eak frequency, a i are exerimental constants yet to be comrehensively obtained, F thr ( is the dimensional threshold, and it is likely that n=1 (see Babanin and Young (2005) regarding details relating to the last three arameters mentioned). The nature of the induced dissiation above the eak can be due to either enhanced induced wave breaking or additional turbulent eddy viscosity or both. Babanin and Young (2005) showed that there are indications that the turbulent viscosity becomes significant at small wave scales, where the cumulative term of the function (5) dominates. Once this is true, the dimensionless sectral threshold below which no dissiation occurs, may not be universal across the sectrum. This comlex issue needs further research. Young and Babanin (2005) also comared directional sectra of the breaking and nonbreaking waves whose difference should be indicative of the directional distribution of the dissiation. They showed that directional dissiation rates at oblique angles are higher than the dissiation in the main wave roagation direction and therefore the breaking tends to make the wave directional sectra narrower. If confirmed, this conclusion may have very significant imlications for the directional shae of D: unlike I, it would be bimodal with resect to the wind direction, and the main wave direction would be characterized by a local minimum of the directional sectrum of dissiation. ω 4. Wave-bottom interaction and total dissiation in the water column

6 Field observations carried out at Lake George were sulemented with laboratory exeriments conducted in a wave flume and water tank at the Australian Defence Force Academy (ADFA), Canberra to accurately estimate the bottom friction term B in eq.(1). Measurements in the bottom boundary layer were erformed by means of acoustic and laser Doler velocimeters, as well as by means of a secially designed shear late caable of measuring the bottom stresses directly. Given the substantial body of knowledge in this field for monochromatic waves, tests were conducted to create an emirical link between monochromatic and sectral conditions to enable this existing knowledge be alied to sectral conditions. In the laboratory studies, for bed conditions ranging from smooth to rough and for JONSWAP-like wave sectra, it was found that, in terms of the loss of wave energy due to the bottom friction B, the sectrum can be reresented by a monochromatic wave, the bottom velocity amlitude of which is equal to 1.88u rms and with a eriod equal to the sectral eak eriod (Mirfenderesk and Young, 2003). Two additional sets of laboratory exeriments were conducted to study conditions of rile formation on a silt-covered bottom and to study the effects of direct injection of turbulence into the bottom boundary layer by breaking waves (Babanin et al., 2005). Bottom of the ADFA s tank was covered by a layer of Lake George silt, and thus the bottom interaction term was estimated for Lake George silt-bottom conditions, and the estimates were indeendently verified by means of comarisons with other energy sources and sinks, simultaneously measured while in situ, which together had to satisfy the energy balance (1). The friction factor for the Lake George silt was obtained in a series of exeriments in the uni-directional flow tank. Variability of the bottom roughness and conditions of rile formation in the fine-sediment silt were analysed. It was shown that, as the mean flow velocity grows, the friction factor lateaus until it abrutly increases 60 times once the riles are formed. Also, the effect of wave breaking on the bottom boundary layer was examined. When a wave breaks, articularly if it is a lunging breaker, it injects a turbulent jet into the water column. The jet has a vertical comonent, and if it can reach the bottom, it will enhance the turbulent mixing, thus reducing the vertical velocity gradient in the boundary layer and, corresondingly, the bottom stress τ 0. The exeriment was conducted at the ADFA s wave flume where the waves were forced to break at a given location and τ 0 was directly measured by means of the shear late. The reduction was found to be of the order of %, and it may become noticeable in field conditions in case of frequent wave breaking at finite deths. Overall, the bottom dissiation term was found to be an imortant art of the total energy balance in the finite deth wave field, measuring u to 20% of the total dissiation in extreme wave cases. To obtain the total dissiation, vertical rofile of the volumetric rate of total kinetic energy dissiation ε(z) was analysed (Young and Babanin, 2005, Babanin et al., 2005). This led to a new arameterisation of the deth distribution of ε(z): const z 0.4H s 1 ε ( z) = z z > 0.4H U < 7.5 (6) s 2 z z > 0.4H s U 7.5 In this arameterisation, the total dissiation rate is a function of distance from the water surface z, significant wave height H s, and wind seed U. The latter comes into imortance due to the fact that once the waves start to break at U >7.5m/s, they significantly enhance the background turbulence level in the water column (Terray et al., 1996). 5. Summary Sectral terms for wind inut I, whiteca dissiation D and bottom friction B (1) were exerimentally aroached in a detailed study at Lake George, Australia. The field study was sulemented by a series of laboratory exeriments. A number of new hysical features of

7 behaviour of the source/sink functions were revealed. These features were arameterised in forms suitable for adoting in wave sectral models. Acknowledgements The authors gratefully acknowledge the financial suort of the U.S. Office of Naval Research (grants no. N and N ) and of the Australian Research Council (grant no. A002965) References Agnon, Y., A.V. Babanin, I.R. Young, D. Chalikov, 2005: Fine scale inhomogeneity of wind-wave energy inut, skewness and asymmetry, Geohys. Res. Lett., 32, L12603, doi:.29/2005gl022701, 4 Babanin, A.V., and Yu.P. Soloviev, 1998: Variability of directional sectra of windgenerated waves, studied by means of wave staff arrays. Marine and Freshwater Res., 49, 89-1 Babanin, A.V., I.R. Young, and M.L. Banner, 2001: Breaking robabilities for dominant surface waves on water of finite constant deth. J. Geohys. Res., C6, Babanin, A.V., I.R. Young, 2005: Two-hase behaviour of the sectral dissiation of wind waves, in Proceedings Ocean Waves Measurement and Analysis, Fifth h International Symosium WAVES2005, 3-7 July, 2005, Madrid, Sain, Eds. B. Edge and J.C. Santas, aer no.51, 11 Babanin, A.V., I.R. Young and H. Mirfenderesk, 2005: Field and laboratory measurements of wave-bottom interaction, Proceedings of the 17 th Australasian Coastal and Ocean Engineering Conference and the th Australasian Port and Harbour Conference, Setember 2005, Adelaide, South Australia, Eds. M.Townsend and D.Walker, Banner, M.L., J.R. Gemmrich, and D.M. Farmer, 2002: Multiscale measurements of ocean wave breaking robability. J. Phys. Oceanogr., 32, Donelan, M.A., B.K. Haus, N. Reul, W.J. Plant, M. Stiassnie, H.C. Graber, O.B. Brown, E.S. Saltzman, 2004: On the limiting aerodynamic roughness of the ocean in very strong winds. Geohys. Res. Lett., 31, L18306, doi:.29/2004gl019460, 4 Donelan, M.A., A.V. Babanin, I.R. Young, M.L. Banner and C. McCormic, 2005a: Wave Follower Field Measurements of the Wind Inut Sectral Function. Part I. Measurements and Calibrations, J. Atmos. Oceanic Tech., 22, Donelan, M.A., A.V. Babanin, I.R.Young, M.L. Banner, and C. McCormick, 2005b: Wave follower measurements of the wind inut sectral function. Part 2. Parameterization of the wind inut. J. Phys. Oceanogr., submitted Hasselmann, K., 1960: Grundleiehungen der Seegangsvoraussage. Schiffstechnik, 7, Manasseh, R., A.V. Babanin, C. Forbes, K. Rickards, I. Bobevski, and A. Ooi, 2005: Passive Acoustic Determination of Wave-Breaking Events and Their Severity Across the Sectrum, J. Atmos. Oceanic Tech., acceted Mirfenderesk, H. and I.R. Young, 2003: Direct measurements of the bottom friction factor beneath surface gravity waves, Int. J. Al. Ocean Res., 25, Terray, E.A., M.A. Donelan, Y.C. Agrawal, W.M. Drennan, K.K. Kahma, A.J. Williams III, P.A. Hwang, and S.A. Kitaigorodskii, 1996: Estimates of kinetic energy dissiation under breaking waves. J. Phys. Oceanog., 26, Young, I.R. and A.V. Babanin, 2001: Wind Wave Evolution in Finite Deth Water. In Proceedings of the 14 th Australasian Fluid Mechanics Conference, Adelaide, Australia, Young, I.R. and A.V. Babanin, 2005: Sectral distribution of energy dissiation of windgenerated waves due to dominant wave breaking, J. Phys. Oceanogr., acceted Young, I.R., M.L. Banner, M.A. Donelan, A.V. Babanin, W.K. Melville, F. Veron, and C. McCormic, 2005: An Integrated System for the Study of Wind Wave Source Terms in Finite Deth Water, J. Atmos. Oceanic Tech, 22,