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DATES COVERED (From -To) 12-07-2007 Journal Article _ 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Spectral Signature Wave Breaking in Surface Wave Components of Intermediate Length Scale 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 0602435N 6. AUTHOR(S) 5d. PROJECT NUMBER Paul A. Hwang 5e. TASK NUMBER 5f. WORK UNIT NUMBER 73-6628-85-5 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER Naval Research Laboratory NRL/JA/7330-05-5262 Oceanography Division Stennis Space Center, MS 39529-5004 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) Office of Naval Research ONR 800 N. Quincy St. Arlington, VA 22217-5660 11. SPONSOR/MONITOR'S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release, distribution is unlimited. 13. SUPPLEMENTARY NOTES 14. ABSTRACT This paper investigates the length scale of ocean surface breaking waves in the spectral range of intermediate wavelength components a few centimeters to a few meters long. The spectral properties of wave breaking are examined first with the dissipation function of the wave action density conservation equation. The analysis reveals a strong breaking signature in wave components between 0.15 and 1.5 m long in the form of a quasi- singular behavior of the dissipation function using the present formulation of the wind-generation and breaking dissipation functions. Independent studies of more-direct breaking observations of radar tracking of sea spikes in the past have shown close correlation between sea spiked and scatterers traveling at the speed of surface waves a few meters long and much shorter than the dominant wavelength. The intermediate-scale waves are the primary contributor of the ocean surface mean-square slope, the close correlation between the gas transfer rate and the mean-square slope has been demonstrated repeatedly. A better understanding of the wave dynamics of intermediate-scale waves is important for clarification of various gas transfer mechanisms. 15. SUBJECT TERMS wave breaking, surface roughness, intermediate-length scale, dissipation, sea spikes 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 18. NUMBER 19a. NAME OF RESPONSIBLE PERSON a. REPORT b. ABSTRACT c. THIS PAGE ABSTRACT OF Paul A. Hwang PAGES Unclassified Unclassified Unclassified UL 10 19b. TELEPHONE NUMBER (include area code) 202-767-0800 Standard Form 298 (Rev. 8/98) Prescribed by ANSI Std, Z39,18 Available online at www.sciencedirect.com JOURNAL OF - ScienceDirect M A R I N E SYSTEMS ELSEVIER Journal of Marine Systems 66 (2007) 28- 37 www.clsevier.com'Iocatewiiiarsys Spectral signature of wave breaking in surface wave components of intermediate-length scale Paul A. Hwang * Bldg, 2. Roon 244E. Naval Researuh Laboratoir 4555 Overlook Avenue SW Ifitshington. DC 20375. U.S,4. Received 12 September 2005; accepted I I November 2005 AMailable online 7 September 2006 Abstract This paper investigates the length scale of ocean surface breaking waves in the spectral range of intermediate wavelength components a few centimeters to a few meters long. The spectral properties of wave breaking are examined first with the dissipation function of the wave action density conservation equation. The analysis reveals a strong breaking signature in wave components between 0. 15 and 1.5 m long in the form of a quasi-singular beha, ior of the dissipation function using the present fornnulation of the wind-generation and breaking dissipation functions. Independent studies of more-direct breaking observations of radar tracking of sea spikes in the past have shown close correlation between sea spikes and scatterers traveling at the speed of surface waves a few meters long and much shorter than the dominant wavelength. This feature of sea-spike properties is consistent with the breaking signature of the dissipation function in similar wavelengths. The intermediate-scale waves are the primary contributor of the ocean surface mean-square slope. The close correlation between the gas transfer rate and the mean-square slope has been demonstrated repeatedly. A better understanding of the wave dynamics of intermediate-scale waves is important for clarification of various gas transfer mechanisms. ,,c 2006 Else\,ier B.V. All rights reserved. Keywords: Wave breaking; Surface roughness; Intermediate-length scale: Dissipation; Sea spikes 1. Introduction 1994; Monahan, 2002; Asher et al., 2002). Clarification of the spectral properties of breaking surface waves may Wave breaking has profound impacts on the upper- contribute to a better understanding of the gas transfer ocean turbulence properties, the disruption of the ocean process in the ocean. Wave breaking is also an important surface cool skin, the generation and entrainment of air subject in many different ocean remote sensing applica- bubbles into the water column, and the composition of the tions, for example, sea spikes in radar scatter from the ocean surtfce roughness. All factors cited above arc ocean surface (e.g., Lee et al., 1996; Frasier et al., 1998; known to produce significant modifications of the gas Liuetal., 1998; Phillips et al., 2001) and bubble effects on transfer rate across the air-sea intertfce (e.g., Phillips, underwater acoustics (e.g., Ding and Farmer, 1994; Deane 1985; Wallace and Wirick, 1992; Thorpe, 1993; Melville, and Stokes, 2002; Melville and Matusov, 2002). In this paper, experimental results on the length scale of breaking waves are examined. Section 2 describes the • Iel.: 1I 202 767 0800W fax: 1 202 767 5599. indirect approach of breaking wave analysis through the E-mciladd.vs.: phxNangeaccs.nrl.navy.mil. investigation of the dissipation function of the wave 0924-7963/S -scc front matter i(ý 2006 Iseier 1V. All rights reserved, do i:1 0. l0 16,'j.j.m ars s.2005.l .015 U; TUT B; ON 3T AT 7 iT 7N T A Appi Oved 0or Public Pelease U161ribution Unlimited PA, Iti ang / Journalo ! Marine S~stems 66 (2007) 28 37 29 action density conservation equation (e.g., Phillips, source functions due to nonlinear wave wave interac- 1984. 1985). The method has been applied to the spectra tion, wind input and breaking dissipation. N is related to of intermediate-scale waves (from 0.02 to 6.3 m long) the 2D wave displacement spectral density, z(k), by N collected in the ocean using a free-drifting measurement (k) =gX(k)i/r, g the gravitational acceleration, and a the technique to mitigate the problem of Doppler frequency intrinsic frequency of the wave component. In the shift in converting the measured encounter-frequency following, the result applicable to the omni-directional spectrum to the wavcnurnber domain (Hwang and spectrum,X(k)=iX(k)kdO and N(k)-gZ(k)/1r, is Wang, 2004). Interesting features of the spectral discussed. properties of intermcdiate-scalc surface waves in the Theoretical and experimental studies of the energy ocean derived from the analysis are discussed. In transfer from wind to waves have led to the following Section 3, the wind-speed dependence of the wave parameterization function for the wind input source spectral density is presented. The topic is of great function (Plant, 1982; Phillips, 1984) interest in many areas of research including wave dynamics, air sea interaction and microwave remote Sw(k) nmu(-.N(k). (2) sensing of the ocean. Results from earlier studies on surface waves of length scales from long gravity waves where n 0.04. For gravity waves several times shorter to short capillary wvaves are found to be in good than the spectral peak component. the nonlinear wave agreement with the intermediate-scale wave data. In SSeeccttiioonn n44t, ,ththtei leddi issssiippaattioionn fnfu ncticotionn ddeerirvvede dffarmotma . tt he wttee armvems in((PPteh riailllc itpipos, n , 1t1e 9r7m77 . i,s 1m998u84 c)h). sTmhhae lldedryy n thaaman i nct h ce b bao ltahane crce et wooof action density conservation equation is described. The intermediate- and short-scale gravity waves, therefore, is most interesting result is that the dissipation function mainly determined by the wind-input and breaking displays a quasi-singular property in the middle range dissipation terms. Phillips (1984, 1985) suggested the (about 0.15 to 1.5 in) of the intennediate-length scale. following expression for the omni-directional dissipa- Such a feature is interpreted as a distinct signature of tion sink term wave breaking in wave components of intennediate- length scale. Results on the length scale of wave D = gkf1(B). (3) breaking obtained from more-direct wave breaking measurement techniques, including tracking of bubble- where B=k3X=k3aN/g is the dimensionless wave generated acoustic noise (Ding and Fanner, 1994), radar spectrum representing the degree of saturation (Phillips, sea spikes (Lee et al., 1996; Liu et al., 1998; Frasier 1985). Eq. (2) can be expressed in terms of B, et al., 1998; Phillips et al., 2001), whitecaps (Melville,,,\2 and Matusov, 2002), and high-speed photographs of Sw(k) = i(n gk 3B(k). (4) bubble plume formation (Deane and Stokes, 2002) are investigated in Section 5. It is shown that the length At equilibrium dNidt=0. Equating (3) and (4), Phillips scales of wave breaking derived from direct and indirect (1984) concluded that the solution to the unknown methods are in very good agreement. Additional dissipation functionfi(B) relies on the knowledge of the discussions on issues of wave dynamics are given in dependence of B on the wind speed. Experimental data Section 6 and a summary is presented in Section 7. show that the dependence of the spectral density on wind speed can be represented by a power-law function 2. Analysis (Hwang and Wang. 2004) Wave breaking is the dominant dissipation mecha- B(-) ((5) nismn in the source function balance of the action or C / energy conservation equation of surface waves. The conservation equation of wave action, N(k), can be Assuming a power-law relation for the unknown expressed as (e.g., Phillips, 1984, 1985) function in the dissipation term (Phillips, 1984, 1985) f(B) = AdB"" (6) dN e'I S dt (cid:127)I the expressions for ad and Ad become simply where k is the wavenumber vector with modulus k. The ad I J 2 Ad - 1. (7a. b) three terms on the right-hand side of (I) represent the a0 30 PA. Hiwang "Inournal t lMarine SYitewns 66 (2007) 28 37 3. Spectral dependence on wind speed by two separate sensor systems. The first system is a two- dimensional scanning laser slope sensor that generates The approach described above is most suitable for directly the wavenumber spectrum from the spatial applications in the region of intermediate- and short- images of the surface slopes over an area 0.1 m x 0.1 m. scale waves where the magnitude of the nonlinear The second system constitutes of thin-wire wave gauges wave-wave interaction term is much smaller than that at fixed stations that provide the frequency spectrum of of the wind input or the breaking dissipation term. surface waves measured at essentially the same wind fttch Obtaining reliable measurements of intermediate- and as that of the scanning slope sensor system. The labo- short-scale waves in the ocean is a complicated task. ratory measurements further confirn the robust power- One of the most difficult issues is the Doppler frequency law relationship of B(u,!c) as illustrated by the examples shift that renders the interpretation of the length scale of shown in Fig. lb. From these field and laboratory data, .,4o measured encounter frequency spectrum an uncertain and ao can be obtained by least-square fitting of the task (Hwang, 2006). This problem can be mitigated by spectral measurements for each wavenumber component. free-drifting operation that provides measurements in a The results arc given in Fig. Ic and d, respectively. An frame moving with the advecting currents that caused interesting feature in the results of At and au is their the Doppler frequency shift. Phillips (1984) method of nomnonotonic dependence on k, as clearly illustrated in analysis described in the last section is applied to the the field data. The results from laboratory experiment (all spectra of intermediate-scale waves (wavelengths be- wind-sea conditions) show a similar dependence of A, tween 0.02 and 6.3 m) measured in the ocean using and an on k in the wavenumber range comparable to those wave gauges mounted on a free-drifting platform of the field data, but because the length scale of laboratory (Htwang and Wang, 2004). The results show that B(u,! wind-generated waves is much shorter than that in the c) can be represented by a power-law function (5). An field, the interesting nonmonotonic feature revealed by example is shown in Fig. Ia . the field data cannot be detected in the laboratory results. Recently, laboratory experiments were conducted in Also, there is an apparent wavenumber downshift in the the large wind- wave facility at the Institut de Recherche cluster of laboratory data derived from temporal measure- sur les Phenomenes Hors Equilibre (IRPHE), Marseille, menits by stationary sensors when compared to the result France. The wind-generated surface waves are measured derived from spatial measurements. This is likely due to (a) (c) -_ __ __ __-_..._II Field drifling (k= 16) 0 Field (0Aind ,wad "I0 Field (mixed sa,) "- Fquilihnuin aymptole " Lahoraory iemporal 10-20- 10o1 full MIoit 2 (b) (d) k( r.udm a tLah spalial (k=452) 1.5 E * Lah temporal (k=264) 10-2 A (cid:127) + a (1.5 100 10.1 Io0 i00 I01 102 (t,/C ) k (rad/rn) Fig. I. Examples of the power-law dependence ofBltinrj: (a) field measurements by wave gauges mounted on a free-driffing platform, (b) laboratory measurements by sLalionary wave gauges (temporal) and scanning laser slope sensor (spatial). The wavenumber dependence of(c) the proportionality coetficient. A,, and (d) the exponent, a(. of the power-law function derised from both field and laboratory experiments. P.A. HIwang Journalo l Marine Systerns 66 (200') 28 37 31 the Doppler frequency shift induced by the orbital summarized by many researchers (e.g., Toba, 1973; velocity of longer waves. Because the Jacobian connect- Phillips, 1985; Forristall, 1981; Donelan ct al., 1985: ing the wavenumber-to-frequency conversion is nonlinear Hwang et al., 2000). Based on the 2D wavenumber with respect to the advecting current, the Doppler fre- spectrum derived from the spatial 3D surface wave qucncy shift due to the background orbital velocity does topography of a steady and equilibrium wind-generated not vanish on averaging over integral cycles of long wave field obtained by an airborne scanning lidar system, waves. Instead, the advection by orbital velocity produces Hwang et al. (2000) reported b z5.26 x 10 2. The a net downshifl in the resulting encounter frequency for a analysis of intenrediate-scale wave spectra also yields given wavcnumber component (Hwang. 2006). similar values of the proportionality coefficient and The nonmonotonic behavior of the spectral dcpen- exponent (A1. and a() in the lower limit of the resolved dence on wind speed as quantified by au is noteworthy. wavenumber range (I!< k_< 316 rad/m) (Fig. Ic -d). Discussions of this feature have been given by Hwang and Banner ct al. (1989) reported wavenumber spectra of Wang (2004) and they are briefly summarized in the surface waves derived from 3D surface topography following. As illustrated in Fig. Id , tbr both conditions of measured by stereo photography. The resolved wavc- wind sea and mixed sea, the wind speed dependence of the lengths are between 0.2 and 1.6 m (31 Ž k Ž4 rad/m). The wave spectral density approaches linear toward the long range of wind speeds is between 5.5 and 13.3 mns. Their gravity wave region. This is in agreement with many results show a very weak wind-speed dependence of the earlier investigations on the wind-speed dependence of wave spectrum, with B(k) -u,1 (indicated by a short the surface wave spectrum in the equilibrium range, line-segment in Fig. 2). The analysis of intermediate-scale wave spectra expands the resolved wavelengths to a range -2. (8) from 0.02 to 6.3 m (I _k<_< 316 rad/m). For wind sea, the C wind-speed exponent drops sharply from approaching 1.0 The corresponding dimensionless spectrum is (linear) for long gravity waves to about 0.22 neark= 5 rad/ m; at, remains to be less than 0.5 through k=40 rad/m. In b (91) mixed sea, the minimum value of ao is also about 0.22, ' B(cid:127),(k) h " (9) and a,, < 0.3 fork between 8 and 25 rad/m, and ao- :0.5 tbr k between 3 and 80 radim (Fig. 2). The range of h varies approximately within a factor-of- For short gravity waves and capillary waves, field data two range based on field observations, as has been are usually obtained by radar backscatter measurements 3 1.... 1.1 . . ... I . . .I .I .. .I 1 1 1 11 11 - Slerco Phodo (B89) 0 - Driffing gauge, wind sca (W04) 2.5 --- " " ixed % -a 0 Radar. )>O.@6in (fom Fig. 5, H97) 0 "O.A>X,>0.2 in * 0.2A>>0.05 in 2 o 0.05>X.>O.03 inI *0 0 0 0.03>".02 il 0.02A.r>0.001 in o~o j1.5 - Fquilibrium asymptote + 00 0 #a 0 , ,, I 1 II 1 I0W 10I 102 103 k Iraid/tn) Fig. 2. The wvind-specd exponent of a given wase spectral component obtained by different methods including radar return (Jones and Schroeder, 1978, Stewart, 1985; Masuko et al.. 1986; Phillips, 1989; Weissinan ctal., 1994; Colton ci al., 1995; summnarized in Fig. 5 of4lwang. 1997), stereo photography (Banner ct al.. 1989), and ffre-drifiing wVave gauge (I hvang and Wang. 2004); ., is the radar wavelength. 32 PA. Hwang /,Journal of Marine Systens 66 (2007) 28 37 using diftcrent radar frequencies and incident angles (e.g., short waves. The results suggest that the spectral Jones and Schroeder, 1978; Stewart, 1985: Masuko et al., signature of wave breaking is localized in the wave- 1986; Phillips, 1988; Weissman et al., 1994; Colton et al., number space in the intermediate-length scale. [Detailed 1995). Fig. 5 of Hwang (1997) summarized the radar data breaking wave observations also show the obvious with incidence angles between 250 and 600, in which signature at the dominant-wave length scale (e.g., range the dominant scattering mechanism is the Bragg Banner et al., 2000, 2002). The results presented here resonance so the radar cross section is proportional to the do not resolve wavelengths near the spectral peak spectral density of the resonant roughness spectral component. The focus of the present research is on component. The radar data are shown in Fig. 2 together surface waves in the intermediate-length scale. These with the result derived from the analysis of intermediate- intennediatc-scale waves contribute more than 78% to scale wave spectra described above. Despite the large the total mean-square slope of gravity waves generated scatter in the radar data, there are apparent similarities in by winds up to 20 rn/s (Hwang, 2005).] From the point- the results obtained by these fundamentally different of-view of the spectral response to wind input, as shown approaches of obtaining the wind-speed exponent of the in Fig. I d or Fig. 2, the presence of a localized region in wave spectral component. the wavenumber space where the spectral density is only weakly dependent on the forcing wind condition 4. Dissipation function suggests a localized region where the wave growth is quenched by strong dissipation. Further discussions of Fig. 3 shows the coefficients (7) of the dissipation this point will be described in Section 6. The range of function (6) obtained from field and laboratory wavelengths with at<0.3 is about 0.15 _<), _ 1.5 m. measurements. The breaking dissipation function dis- These wave components are sufficiently long such that plays a quasi-singular behavior in the neighborhood of the energy loss due to viscous dissipation (Lamb, 1945) meter-long wave components. In mixed sea, the or generation of parasitic capillary waves (Longuet- breaking scale shifts toward smaller breaker size and Higgins, 1992, 1995) may be neglected. It is reasonable the size range expands in comparison with those of the to assume that wave breaking is the major dissipation wind sea, reflecting the modification by long waves and mechanism for the observed peculiarity in the dissipa- interaction between background orbital velocity and tion function of intermediate-scalc waves. (a) (b) -- Field (MS) aLab temp. op, Lah spatial IoEqui.asymp. < I * A' it 6a* OF F~ig _i.T rhe wavcnumber dependence of (a) the proportionality coefficient. Ad, and (b) the exponent, u,j, of the power-law represe2ntation of"the dissipation l'unction, I(B). Results from free-driffing measurements in the field in wind sea and mixed sea as well as laboratory data by stationary temporal and spatial measurements are presented. PA. Htwanig Journal o/ Marine Systems 66 (2007) 28 37 33 Microwave observations of the ocean surface over breaking events as a function of the breaker phase speed. the last fe~w decades indicate that Doppler shifts at HH The length scales of breaking waves can be calculated (horizontal transmitting, horizontal receiving) polariza- from the reported statistics, they range from about 0. I to tion and low grazing angles are due to scatterers 3 in at 4 mis wind speed and from 3 to 20 m at 15 m/s traveling at the speed of surface waves of a few meters wind speed (Fig. 4a). Two major factors contribute to long (e.g., Lee et al., 1996; Frasier et al., 1998; and the the observed wide range of the breaking length scales at references therein). This feature is consistent with the a given wind speed. The first is the dynamic range of the strong signature of wave breaking in the intermediate- sensors. In particular, the passive acoustic tracking of length wave components. In the next section, some breaking events cannot detect small-scale breakings due recent breaking-wave observations made by more-dircct to the problem of ambient noise (Ding and Fanner, measurement techniques are summarized to compare 1994). The second factor is the stage of wave with the result using the indirect approach of dissipa- development. The experiments reported by Lee et al. tion-function analysis. (1996) were conducted in a lake and a protected bay with limited wind tiztch so the wave field is relatively 5. Breaking length scale young compared to the wave conditions of the others obtained in the open ocean environment. The second In the last decade or so, many more-direct measure- factor can be compensated somewhat by normalizing ments of breaking waves have been reported, using the breaking length scale, h.a,b y the dominant techniques such as passive acoustic tracking of the wavelength of the wave field, .P.W ith this normaliza- ambient noise produced by bubbles generated by tion, the majority of radar data are clustered in the -bi!X 1 breaking waves (Ding and Farmer, 1994), radar tracking range between 0.04 and 0.2 over the full range of wind of sea spikes (Lee et al., 1996: Frasier et al., 1998; Liu speeds encountered in the experiments (Fig. 4b). The et al., 1998, Phillips et al., 2001), and video tracking of mean value with a standard deviation is 2ýi;.-o=0.092 1 whitecap evolution (Melville and Matusov, 2002). 0.051, thus the representative breaking length scale is These remote sensing techniques usually process a about one order of magnitude shorter than the dominant very large population of breaking events, on the order of wavelength of the wave field based on sea-spike tens of thousands. From these analyses, the authors observations. [Although the normalized breaking length report statistics of the frequency of occurrences of scale seems to bring together data sets from very (a) (b) o Video whitecaps MM, 2 o tydrol.hone. 1)F94 *Radar PO I 0 o 0 Radar irisingswellh. F98 ( 00°o . Radar (sicad ) / o 0 0 0 10 2 . Radarideca)ing) / 00 * Radar 1[96 00 0 Wire (vwind sea)1I)I 4o - - Wire onixed seas)/,+ -- Well dkwehoc(cid:127)d' O °i 0 0 01 00 101 s 0- -- 4 10 E• o I g 4 h r n li0gbtih scale , obt.in. y d nict m.h. . . i b i o 0 - 0 -- .. ÷ )"(cid:127)............... .. ........".:. I "I ' i0-I II, ,I alyiisgahdaboe1.0h1I0D mniols brakn legtI 0 scale, 1(,10 (cid:127).I01 [tl ot( IS) ( 11 i0 nit(cid:127)s Fig. 4. (a) Theli representative breaking length scale, )-b, obtained by different more-direct measurement techniques of wave breaking including tiacking (if acoustic noisc' , whitecaps and sea spike~s. Estimiation of thc upper and lower hounds of the breaking length scales froin the dissipation analysis is graphed as boxes. (b) Dimensionless breaking length scale, A+)P. 34 PA. HIwang .Journalo l Marine Sysntms 66 (2007) 28 37 different wave development stages, it should be pointed acceleration and the surface tension divided by the water out that for open ocean measurements the data scatter density, and is almost constant in sea water without with breaking length given in dimensional form is much surface slicks), the reduced scatter in the dimensional smaller than that given in dimensionless forn (Fig. 4). representation of the breaking length scale would be The cause and significance of this interesting result is sensible. However, as discussed earlier, the range of the not obvious at this stage but it seems to suggest that the length scales of nonmonotonic behavior is between 0.15 peak wavelength is not necessarily the proper scaling and 1.5 m, and far away from the capillary influence. A factor for intermediate-length wave components several better explanation remains elusive.] times shortcr than the spectral peak wavelength. If the The breaking length scale can be estimated from the scaling length is the wavelength at minimum phase indirect breaking analysis using the dissipation function speed (determined by the ratio of the gravitational by setting a threshold in the result of Ad(k) or a (k) 1 Fig. 5. Pictures from high-speed photography of hubbtc plume linnalion under breaking waves (Fig. 2 of' Dearie and Stokes, 2002). PA. /lhang Journal ol Marime Svstemns 66 (2007) 28 37 35 shown in Fig. 3. For example, applying a threshold of models. In most applications, the action density 106 times less than the peak value of Ad, one can derive conservation equation fornulated as Eq. (1) is sufficient. the breaking length scales from the lower and upper In coastal areas, the bottom dissipation function needs to bounds of the wave numbers that Ad, exceeds the be included on the right-hand side of the equation. For threshold. The result is shown in Fig. 4. The breaking intermediate-scale waves, the situation is not as clear. A length, Lb,i s between 0.6 and 1.5 m for wind sea, and key question is whether wind forcing is the sole source between 0.15 and 1.2 ril for mixed sea. The ratio A8//v0 of wave generation. The results from radar sea-spike ranges between 0.013 and 0.025 for wind sea, and from analyses are very instructive. Many of those experi- 0.008 to 0.05 for mixed sea. Similar results can be ments are accompanied with detailed video recording of derived by using a threshold (of about 7) in ad. These the wave field in the radar field-of-view (e.g., Frasier values of breaking length scales are smaller than those et al., 1998; Liu et al., 1998). The close association of derived from sea-spike measurements. It is likely that sea spikes with (large-scale, or dominant) wave sea-spike tracking overestimates the breaking length breaking or steep waves is convincingly established, scale because the tracking procedure requires a finite yet the phase velocity of the breakers derived from dwell time of the breaking event in the field of tracking sea spikes is much slower than the phase speed measurements. For example, Frasier et al. (1998) set a of the dominant wave component. The logical explana- threshold of I-s minimal dwell time for the sea-spike tion of this result is in the distinction of wave breaking event to be included in the breaking analysis, thus events (as in dominant wave breaking) vs. breaking excluding shorter breaking events in the final statistics. patches (as in sea spikes or the length scale of the This problem is similar to the ambient-noise limitation dissipation function). The breaking patches are obvi- on the length-scale resolution in the acoustic tracking of ously generated by breaking of dominant waves. For a breaking-induced acoustic signature encountered by very short moment, they retain a phase speed close to or Ding and Farmer (1994). Taking this bias into exceeding that of the dominant waves (as a bound-wave consideration, it is concluded that the results from direct component). Judging from the sea-spike tracking and indirect measurements ofthe breaking length scales analysis, this duration is very short and for the are comparable. remaining part of the sea-spike (breaking) lifetime, the Deane and Stokes (2002) conducted laboratory study breaking patches propagate as free waves with phase on the generation mechanism of bubble plumes under velocities according to their sizes (in the intermediate- breaking waves. Using high-speed photography, they length scale). In other words, breaking plays double captured many interesting hydrodynamic processes in the roles in the intermediate-scale wave components: it is a active phase of wave breaking. Relevant to the present dissipation function of wave energy and an important study is the sequence of pictures depicting the develop- source function of intermediate-scale wave generation. ment of bubble plume in the first two seconds after Although it is reasonable to state that there is an formation of the air cavity trapped by the breaking jet additional source function due to breaking-wave (their Fig. 2, reproduced as Fig. 5 here). The dominant generation in the intermediate-scale spectral compo- frequency of the wave field is 0.73 liz and the nents, it remains a difficult task explaining the lack of corresponding wavelength is 2.3 m. As illustrated by response to wind-forcing in the mid-range components the sequence of pictures, after more than one wave period of intermediate-scale waves, observed by both in situ tollowing the formation of the air cavity produced by the wave measurements and remote-sensing radar scatter jet of wave breaking, the length scale of the active analyses (Fig. 2). It is generally accepted that breaking breaking region with intensive dissipation (the vortex probability increases with the cube of wind speed, so regions in the photographs) remains on the order of 0.1 m. incorporation of breaking as a generation term for This gives an estimate of the ratio )4/;,Pzz0 .025, which is intermediate-scale waves should increase the wind- in very good agreement with the results derived from the speed exponent for the wave components affected, analysis of the dissipation function shown in Fig. 4b. contradicting to the observations of decreased wind- speed exponent in the middle range of the intermediate- 6. Discussions length wave components. It remains a tough challenge to explain the observed peculiar nonmonotonic behavior Investigation of the breaking dissipation function is of the spectral properties of intermediate-scale wave of great interest to many areas of research ranging from components shown in Fig. 2. ocean and coastal engineering, wave dynamics, air-sea Eq. (1) is obviously inadequate for describing the interaction, remote sensing, and numerical wave dynamics of intermediate-scale waves. While it worked 36 P/A. twang '.Journal o(cid:127) Marine Systems 66 (2007) 28 37 nicely for identifying the breaking length scales, it is breaking in intermediate-scale spectral components emphasized that the proposed local balance of breaking can lead to a better understanding of the gas transfer dissipation and wind generation functions is a hypoth- processes. esis that leads to the prediction of enhanced dissipation in the intennediatc-length wave components. Further- Acknowledgements more, in side-by-side comparison of radar images of sea spikes and video images of ocean surface waves, it was This work is supported by the Office of Naval found that the majority of sea-spike events are Research (Naval Research Laboratory PE61153N and associated with steep waves without visible breaking PE62435N). NRL Contribution JA-7330-05-5262. whitecaps - approximately 60% 'for the young and the developed sea and 92%/, for decaying sea (Liu et al., References 1998). It is not clear whether these sea-spike-associated steep waves were undergoing microscale breaking, so Asher, W., Fdson, J.. McGillis, W., Wanninkhof, R., Jo, D.T, an unequivocal causal link between sea spikes and Litchcndorf, T.. 2002. Fractional area whitecap coverage and air sea gas transfer velocities measured during GasEx-98. In: Donclan, breaking waves is yet to be established. The observa- MA., Drennan, W.M., Saltzman, E.S., Wanninkhof. R.( Eds.). 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