VOLUME 29 JOURNAL OF PHYSICAL AUGUST 1999

Wind Growth and Dissipation in the Open

JEFFREY L. HANSON The Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland

OWEN M. PHILLIPS The Johns Hopkins University, Baltimore, Maryland

(Manuscript received 12 December 1997, in ®nal form 17 June 1998)

ABSTRACT sea growth and dissipation in a -dominated, open ocean environment is investigated to explore the use of wave parameters in air±sea process modeling. Wind, wave, and whitecap observations are used from the Gulf of Alaska surface scatter and air±sea interaction experiment (Critical Sea Test-7, Phase 2), conducted 24 February through 1 March 1992. Wind sea components are extracted from buoy directional wave spectra using an inverted catchment area approach for peak isolation with both wave age criteria and an equilibrium range threshold used to classify the wind sea spectral domain. Dimensionless wind sea energy is found to scale with inverse wave age independently of swell. However, wind trend causes signi®cant variations, such as underde- veloped during rising . These important effects are neglected in wind-forced air±sea process models. The total rate of wave energy dissipation is conveniently estimated using concepts from the Phillips equilibrium range theory. Replacing wind speed with wave dissipation rate in the standard power-law description of oceanic whitecap fraction decreases the range of data scatter by two to three orders of magnitude. The improved modeling of whitecaps demonstrates that wave spectral parameters can be used to enhance air±sea process models.

1. Introduction lationships, Donelan et al. (1992) made extensive wind and wave measurements on Lake St. Clair out to a fetch The detailed physical mechanisms by which wind of approximately 21 km. They note a very high degree waves grow and evolve remain an intriguing unsolved of correlation of nondimensional wind sea energy eЈϭ mystery of ¯uid mechanics. Most ®eld observations of 2 4 eg /U c with Uc/cp, where the total energy (variance) is growth characteristics have been made in de®ned by integrating the directional wave spectrum well-de®ned geometrical scenarios with steady prevail- S(␻, ␪) over frequency (␻) and direction (␪): ing winds, well-understood fetch, and no swell. An anal- ysis of fully developed wind seas by Pierson and Mos- kowitz (1964) veri®ed earlier theoretical notions that e ϭ ͵͵S(␻, ␪) d␻ d␪. there is a universal similarity in spectral shape (Kitai- ␻␪ gorodskii 1962) with an asymptotic upper bound (Phil- The effect of swell on wind wave growth has been a lips 1958). However, a peak enhancement effect ob- topic of active research for many years with inconsistent served during the Joint North Sea Wave Project (JON- results. Selected ®ndings are summarized in Table 1. SWAP) was found to have no correlation with various Although numerous well-documented experiments fetch relationships (Hasselmann et al. 1973). In a study show unequivocally that short laboratory wind waves of fetch-limited waves on Lake Ontario, Donelan et al. exhibit reduced amplitudes when in the presence of lon- (1985) noted that the peak enhancement depends on ger paddle-generated waves, the details are often con- inverse wave age Uc/cp, where Uc is the component of tradictory among investigations. Furthermore, there re- the 10-m-elevation wind speed (U10) in the mean di- main a variety of competing theories to explain these rection of the waves at the spectral peak, and cp is the phenomena. Most surprising, perhaps, is that modi®- wave phase speed. To further re®ne the wave fetch re- cation of wind-driven gravity waves by swell has yet to be demonstrated in the real ocean. This is partially due to the dif®culties of separating naturally observed wind sea from swell. Note that only a single study from Corresponding author address: Dr. Jeffrey L. Hanson, Applied Physics Laboratory, The Johns Hopkins University, Johns Hopkins Table 1 was conducted in oceanic conditions (Dobson Road, Laurel, MD 20723. et al. 1988). In a fetch-limited coastal environment, E-mail: [email protected] Dobson and colleagues do not report any signi®cant

᭧ 1999 American Meteorological Society 1633

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC 1634 JOURNAL OF VOLUME 29

TABLE 1. The modi®cation of wind waves by swell: selected results. Reference Investigation Relevant conclusions Cox (1958) Laboratory Short wave mean square slope is highest just ahead of long wave peaks. Longuet-Higgins and Theoretical Short waves become shorter and steeper at the crest of superposed long waves owing to Stewart (1960) interactions. Mitsuyasu (1966) Laboratory Wind wave energy attenuation depends on steepness of aligned swell waves. Phillips and Banner (1974) Laboratory/ Enhanced short wave breaking near long wave crests results from intensi®ed drift of theoretical aligned and opposed swell. Wright (1976); Laboratory/ Drift-enhanced dissipation theory does not agree with observations. Plant and Wright (1977) theoretical Hatori et al. (1981) Laboratory An unidenti®ed nonlinear process transfers energy from wind waves to superposed long waves. Donelan (1987) Laboratory Energy input by wind is unaffected by superposed long waves. Resonant nonlinear inter- action ``detuning'' may cause wind wave energy loss. Dobson et al. (1988) Field Fetch-limited wind sea growth is not in¯uenced by opposed swell. Smith (1990) Theoretical Physical model including drift-enhanced dissipation roughly agrees with observations. Mitsuyasu (1992) Laboratory Wind sea is intensi®ed by opposed swell. Chu et al. (1992) Laboratory Wind seas are shortened and attenuated by aligned swell; wind sea slope remains nearly constant. growth effects resulting from the presence of an op- mentum ¯ux from breaking waves provides an energy posing swell. They present results that are statistically source for enhanced turbulence and mixing in the upper identical to the Lake Ontario results of Donelan et al. ocean with turbulent kinetic energy (TKE) dissipation (1985). They attribute this similarity to the short fetches rates that are one or two orders of magnitude above involved with both studies. levels expected from a wall-bounded shear ¯ow. Using Breaking surface waves are observed on any open laboratory data (Loewen and Melville 1991; Rapp and body of water over which the wind exceeds approxi- Melville 1990) and theoretical arguments (Phillips mately 3 m sϪ1. In a recent review, Melville (1996) notes 1985), Melville (1994) concluded that the surface layer that breaking waves contribute to wave evolution by should be well mixed to a depth comparable to the effectively dissipating excess energy originally input by breaking with TKE dissipation rates in the the wind. The importance of this role is evidenced in range observed by Agrawal et al. (1992). the radiative transfer equation, which describes the con- The entrainment of air is another important attribute servation of wave action spectral N(k) ϭ of surface wave breaking. Using electrical conductivity gS(k)/␻ of waves interacting with a current of velocity sensors to map the air content, or void fraction distri- U (Phillips 1977; Komen et al. 1994) in wave number bution, under breaking laboratory waves of different (k) space: amplitudes, Lamarre and Melville (1991) observed that void fractions of Ͼ20% were sustained for up to one- Nץ dN T(k) ϩ S Ϫ D, (1) half wave period after breaking. Furthermore, the initial ´ ١N ϭϪ١´(ϭϩ(cgkwϩ U t volume of entrained air was found to scale with the totalץ dt energy dissipated by each breaking event; this led them where cg is the wave group velocity; Ϫ١k ´ T(k) is the action spectral ¯ux due to nonlinear wave±wave inter- to conclude that wave parameters obtained by techniques may be used to quantify air entrain- actions; Sw represents action input by the wind; and D is the dissipation, primarily due to wave breaking. Since ment and gas transfer in the ®eld. an explicit de®nition of D is not yet available, wave Whitecaps are a well-known surface signature of the evolution models such as WAM rely on a tunable dis- and air entrainment processes. Monahan sipation source term. As assessed by Banner and Young and Lu (1990) classify whitecaps as either active (1994), shortcomings in the dissipation source term lead (formed by the aerated spilling crest of a breaking wave to signi®cant differences between predicted and ob- in progress) or mature (the residual foam patch that served spectral properties of fetch-limited waves. remains after the active break). Combining several sets In addition to the role in wave evolution, wave break- of observations, Wu (1992) notes a clear power-law de- ing has important dynamical roles in facilitating air±sea pendence on wind forcing such that transfers. The breaking process acts to transfer momen- W ϳϳu*3(CU 1/2U )3 ϳ 3.75, (2) tum and energy from the waves to the upper ocean; 1010 10 Melville and Rapp (1985) showed that the momentum where W is the whitecap fraction, u* is the friction ve- ¯ux by breaking may be comparable to that transferred locity, and C10 is the 10-m-elevation atmospheric drag 1/2 directly from the wind. As revealed in numerous ob- coef®cient, assumed to scale withU 10 . Wu points out servations of turbulent dissipation beneath surface that the relationships given by Eq. (2) are dynamically waves, collated and presented by Agrawal et al. (1992) consistent sinceu*3 is proportional to the energy ¯ux and further analyzed by Terray et al. (1996), the mo- from the wind. Using modeled wave spectra, Cardone

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC AUGUST 1999 HANSON AND PHILLIPS 1635

(1970) found that W is better correlated with theoretical ious surface wave parameters was investigated by Fel- energy dissipation estimates than with wind speed alone. izardo and Melville (1995). They isolate wind sea spec- Furthermore, Kraan et al. (1996) recently observed a tra from full energy±frequency spectra by locating a wave-age dependence of W, although with much scatter spectral minimum between wind sea and swell peaks to their results. and then ®ltering the lower frequencies from the data.

Wave breaking and the bubble structures associated They note a high correlation between AN and wind sea with breaking are now known to in¯uence a variety of rms amplitude that was comparable to that between wind processes of global and operational signi®cance (Banner speed U and AN. The correlation of AN to various es- and Donelan 1992; Melville 1996). For example, air± timates of wave dissipation rate, obtained from the wind sea gas ¯ux is enhanced by a factor of 2 or more above and wave observations using the separate ideas of Phil- molecular diffusion in the open ocean when waves are lips (1985) and Hasselmann (1974), were also quite suc- breaking (Wallace and Wirick 1992; Farmer et al. 1993). cessful. These results, along with those obtained by Wal- In addition, Jessup et al. (1990) reported strong micro- lace and Wirick, suggest that properly chosen wave pa- wave returns from breaking waves in the ®eld. They rameters can be used to augment or replace wind forcing note that the contribution of breaking waves to the radar parameters to improve the predictions of air±sea process cross section increases approximately asu*3 , in agree- models. ment with theoretical arguments by Phillips (1988). Fur- The primary objectives of the work reported here thermore, the bubbles entrained by breaking waves are were to investigate wind sea growth and dissipation in found to be the dominant natural source of underwater the open ocean and to determine if wave parameters are ambient noise when winds are above the 3 m sϪ1 break- more appropriate than wind speed parameters for esti- ing threshold (Kerman 1988, 1993; Buckingham and mation of wave breaking phenomena. These were ac- Potter 1995). It is thought that ambient noise could be complished using a spectral partitioning method for the an indicator of air±sea gas transfer (Melville 1996). Fi- isolation of distinct wind sea and swell wave compo- nally, near-surface bubble populations are now known nents from directional wave spectra obtained from a to be the dominant contributor to low-frequency (Յ1000 heave, pitch, and roll buoy. Statistics generated from Hz) acoustic scatter and reverberation near the ocean the wind sea partitions were employed to explore the surface (Ogden and Erskine 1994; McDaniel 1993). in¯uence of wind history and background swell on wave In place of a detailed physical representation of break- growth in the open ocean environment. ing waves and the subsequent development of bubble Furthermore, the equilibrium range theory of Phillips , empirical process models for air±sea gas ¯ux, (1985) was employed to estimate the total rate of wave sonar and radar performance, etc., typically employ dissipation by breaking and to explore the relationships wind speed expressions to describe the wave-induced among wave dissipation, related air±sea parameters, and effects. Examples include the thin-®lm model for air± oceanic whitecap coverage. We believe the results have water gas transfer (JaÈhne 1990), which includes a wind- important implications for the use of surface wave pa- speed-dependent diffusion coef®cient; the Wenz curves rameters in air±sea process models. for ambient noise (Wenz 1962), which yield a power- law dependence of ambient noise on wind speed; and 2. Observations the Ogden±Erskine model for low-frequency acoustic backscatter (Ogden and Erskine 1994), which employs Open ocean wind and wave observations were ob- wind speed as the only environmental variable in a mul- tained during the Gulf of Alaska Surface Scatter and tiparameter ®t to experimental data. The use of short- Air±Sea Interaction Experiment, conducted from 24 term averaged wind speed to describe wave-related pro- February through 1 March 1992, as part of the Critical cesses will lead to prediction inaccuracies as the state Sea Test Program (Tyler 1992; Hanson and Erskine of wind wave development at any given time represents 1992; Hanson 1996). Located in the central Gulf of an integrated effect of both the previous wind history Alaska at 48Њ45ЈN, 150Њ00ЈW, the experiment was spe- and its spatial variability (Huang 1986). ci®cally designed to study the in¯uence of the air±sea Attempts have been made to augment or replace wind boundary zone on underwater acoustic scatter and re- speed with wave parameters in air±sea process model- verberation at frequencies below 1000 Hz. Here we fo- ing. These have usually failed when bulk wave statistics cus on the wind, wave, and whitecap observations made were chosen; average wave parameters tend to smear during this experiment. The collection and processing the information from distinct wind sea and swell wave of these data, described elsewhere (Hanson 1996; Mon- systems. Wallace and Wirick (1992), however, note a ahan and Wilson 1993), are brie¯y summarized below better correlation of mixed-layer saturation lev- for completeness. els with wave height than with wind speed. Their results do not match the standard thin-®lm gas diffusion model a. Atmospheric measurements but are more comparable to predictions from a model by Thorpe (1984) that include enhanced transfer by bub- A MINIMET meteorological buoy (Coastal Climate bles. The correlation between ambient noise AN and var- Co.) was deployed by C.S.S. John P. Tully to obtain

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC 1636 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 29 wind speed and direction, air , sea surface wind sea peaks are included. All remaining partitions temperature, relative , and barometric with energy are swell. measurements at 1-Hz resolution. The data were aver- Spectral partitioning provides a preliminary isolation aged over 30-min windows and input to a stability-de- of spectral peaks that lie within the wind-forced spectral pendent marine atmospheric boundary layer model domain. During times of ¯uctuating winds, however, (Hanson and White 1991; Smith 1988) to obtain esti- young swell components may also occupy this spectral mates of vector-averaged wind velocity at a 10-m height region. Here the equilibrium range theory of Phillips (U ) and wind friction velocity (u ). Similar meteo- (1985) is employed to identify the ``active'' portion of 10 * rological observations, obtained by a shipboard mete- the wind sea spectrum directly involved with ``local'' orological station mounted on R/V Cory Chouest, show energy transfers, including wave dissipation by break- excellent agreement with the MINIMET observations ing. For wind-generated gravity waves, Phillips argued (Hanson et al. 1993). for the existence of a spectral equilibrium range where

the source terms for wind input (Sw), wave dissipation (D), and nonlinear wave±wave interactions (S ) are in b. Wave buoy data nl a state of statistical balance such that Surface wave observations were obtained by a Da- S ϩ S Ϫ D ϭ 0. tawell WAVEC buoy deployed from John P. Tully. The w nl iterative eigenvector (IEV) method of Marsden and Using theoretical arguments for Snl and experimental Juszko (1987) was employed by Juszko et al. (1995) to evidence for Sw, Phillips derived an expression for the compute 236 half-hourly directional wave spectra over wave frequency spectrum in the equilibrium range: a 0.05±0.56 Hz band from the buoy heave, pitch, and S(␻) ϭ ␣u g␻Ϫ4, (4) roll time series. A data-adaptive technique, the IEV * method has the advantage of exceptional peak resolution where ␣ ranged from 0.06 to 0.11 in experimental data within multimodal spectra such as those obtained from reviewed by Phillips. This range also ®ts with the ob- the swell-dominated Gulf of Alaska. In robust compar- servations reported here. isons with direct maximum likelihood (ML) and itera- The concept of an equilibrium range is used to dis- tive maximum likelihood (IML) methods, using both criminate between actively generating wind sea spectral simulated data and more than 350 real spectra, the IEV components, which should be maintained above a min- method produced low errors comparable to the IML imum threshold level set by ␣ ϭ 0.06 in Eq. (4), and method and was superior at producing narrower, more swell components, which are not maintained in local sharply de®ned peaks at all noise levels (Marsden and equilibrium and hence may fall below the energy thresh- Juszko 1987). old. A wave partitioning and swell tracking method (Han- Indeed, examination of the Gulf of Alaska wind wave son 1996) was employed to isolate wind sea from swell partitions indicates that active wind seas are typically in the buoy observations. Based on an inverted catch- separated from young swell by gaps in the spectrum ment area approach (Hasselmann et al. 1994; Voorrips where energy values fall below the ␣ ϭ 0.06 threshold et al. 1997), wave partitioning is accomplished by di- level. A typical case is depicted in Fig. 1. The original viding each directional wave spectrum into distinct sub- ``parent'' spectrum (dashed line) exhibits a dominant sets, or partitions, by de®ning partition boundaries as swell peak and a lesser wind sea peak. The wind wave the minima between peaks. Recombining statistically spectrum isolated by the spectral partitioning process is similar peaks yields a set of individual partitions that depicted by a solid curve in Fig. 1. The actively gen- represent the wave energy contributed from speci®c erating wind sea components, isolated using the equi- wind generation events. Peak separation and recombi- librium range threshold criteria, are identi®ed as that nation criteria are tunable for a particular observation part of the solid curve with open circles. A lower-fre- set; this leads to consistent results obtainable with dif- quency peak, contained in the original wind wave par- ferent buoy platforms and spectral processing methods. tition, has been excluded by the ␣ ϭ 0.06 threshold We have applied this technique to several different ob- criterion and is regarded as young swell. This excluded servation sets originating from a variety of buoy types peak has a wave age cp/U10 ϭ 1.1, which is slightly less (Datawell, Seatec, and National Data Buoy Center plat- than the cp/U10 ϭ 1.2 point of full development as de- forms), and employing various processing techniques termined by Pierson and Moskowitz (1964). This is un- (IEV, ML, maximum entropy) with consistently good derstandable since winds were steadily increasing prior results (Hanson and White 1997; Kline and Hanson to the observation depicted in Fig. 1 and seas were most 1995). Wind sea peaks lie within the parabolic boundary certainly duration limited. de®ned by Results of the wind sea isolation process appear in Fig. 2. Bulk signi®cant wave heights H , as determined c Յ 1.5U cos␦, (3) s p 10 from the full original spectra prior to partitioning, are where ␦ is the minimum angle between the wind and plotted with U10 in Fig. 2a. Although Hs depicts an the waves. The factor of 1.5 ensures that all possible increasing trend with U10, there is much scatter in the

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC AUGUST 1999 HANSON AND PHILLIPS 1637

FIG. 1. Typical Gulf of Alaska wave spectrum (dimensionless) showing the full original parent spectrum (dashed line), partitioned wind wave spectrum (solid line), and actively generating wind sea with young swell components removed (open circles). Equilibrium range model representations for ␣ ϭ 0.06 and 0.11 are included. correlation. Furthermore, when wind speeds diminish to derived from the active wind sea spectral subsets, are Ϫ1 less than 5 m s , wave heights of at least 2 m remain. plotted with U10 in Fig. 2b. The wind sea signi®cant 2 These traits are due to the considerable amount of swell wave heights exhibit nearly aU 10 dependence; this is present in the Gulf of Alaska. These swells originated in agreement with the JONSWAP results (Hasselmann from storms up to 5000 km distant and, therefore, were et al. 1973). The scatter of Hws values is principally not directly associated with the local wind forcing (Han- attributed to wave age and wind history effects. These son 1996). The wind sea signi®cant wave heights Hws, factors are further addressed in the following section.

FIG. 2. Correlation of wind speed to signi®cant wave heights as determined from (a) full original spectra

and (b) active wind sea subsets. High values of Hs during low winds are a result of swell in the wave records. 2 Swell removal results in a U dependence of Hws as observed during JONSWAP.

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC 1638 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 29

Ϫ3.22 U10 ewsЈϭ0.0020 , (5) ΂΃cp with a correlation of r ϭ 0.94. Also included on Fig. 3 is a regression from the Lake St. Clair observations of Donelan et al. (1992):

Ϫ3.3 U10 eLЈϭ0.0022 , (6) ΂΃cp where the L subscript is used to denote lake data. The open ocean observations are statistically identical with the Lake St. Clair results. This agreement is remarkable considering the drastic differences between the two sites: one a swell-dominated open ocean environment and the other a sheltered lake setting with no swell. From these results there is no directly discernible effect of swell on wind sea growth. There is, however, suf®- cient scatter beyond the 90% con®dence limits to war- FIG. 3. Nondimensional energy of actively generating wind sea rant additional investigation of these data. In the fol- Ϫ1 observations obtained with U10 Ն 5.0ms . Regressions through lowing sections we examine, ®rst, the effect of wind these data (solid line) and those of Donelan et al. (1992) (dashed history variability on wind sea growth and then look in line) are included. greater detail at wind sea modi®cation by swell. c. Whitecap video observations a. Wind history effects An additional estimate of breaking wave intensity was Since the response of the ocean surface to wind speed obtained by continuous video recordings of the sea sur- and direction changes is not instantaneous, it is likely face during daylight hours using video camera systems that some of the remaining scatter in Fig. 3 is attributable mounted in heated instrument shelters on the sides of to the recent wind history prior to each observation. John P. Tully and Cory Chouest (Monahan and Wilson Speci®cally, the mean rate at which wind speeds are 1993). The video images were analyzed using an image rising or falling prior to each wave observation ought processing technique to evaluate the fraction of the sea to determine, in addition to the current wind speed, the surface with Stage A (active spilling crest) whitecaps state of sea development. Indeed, it was noted by Toba (Monahan 1993) during the experiment. et al. (1988) that the equilibrium range spectral level ␣ becomes smaller for accelerating wind conditions and vice versa. To quantify the wind history conditions for 3. Wind sea growth in the open ocean each Gulf of Alaska wave observation, a 3-h averaging From comprehensive observations of wind wave window was used to compute the mean wind speed U 10. growth on Lake St. Clair, Donelan et al. (1992) report The mean rate of change or acceleration of the wind a high correlation of nondimensional wave energy eЈϭ was then computed for each observation: 2 4 eg /U c with inverse wave age Uc/cp. For our analysis, a U ϭ⌬U 10/⌬t, (7) U10 has been used in place of Uc since wave-induced motions of ¯oating meteorological stations have been where ⌬t represents a 15-min interval. A comparison found to induce error into the directional resolution of of the U10, U 10, and a U records from the Gulf of Alaska attached wind sensors (Dugan 1991). Indeed, attempts appears in Fig. 4. to use Uc in these analyses resulted in poorer correla- The nondimensional wind sea energies observed dur- Ϫ2 tions. Furthermore, observations made with U10 Ͻ 5.0 ing rising (a U Ͼ 0.0002 m s ) and falling (a U Ͻ msϪ1 were dropped from the record because of the Ϫ0.0002 m sϪ2) wind conditions appear in Fig. 5 with greater uncertainty in buoy measurements of small, separate symbols and regression lines for each. Again, Ϫ1 high-frequency waves. observations made with U10 Ͻ 5ms are excluded The Gulf of Alaska results, appearing in Fig. 3, depict from the analysis. A distinct grouping of the two ob- a high correlation of wind sea energy to inverse wave servation sets indicates that wind seas under falling wind age. The 90% con®dence interval for these observa- conditions are more developed both in energy content tions, estimated using the approach of Skafel and Do- and location of the spectral peak. The latter is evident nelan (1983), appears on the plot. A least squares re- by the shift of falling wind observations to larger inverse gression curve on the plot is given by wave ages. Although not shown (to preserve clarity), a

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC AUGUST 1999 HANSON AND PHILLIPS 1639

FIG. 4. Various wind parameters used in the evaluation of wind history effects: 15-min average

wind (U10), 3-h average wind (U 10), and 3-h average wind acceleration (a U).

FIG. 5. Nondimensional wind energy in falling and rising wind conditions.

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC 1640 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 29

TABLE 2. Sorting of wave observations by swell conditions. Most of the observations fall under the confused sea Number of category, indicating the simultaneous existence of two Wave category Selection criteria observations or more swell systems with comparable steepness. No swell ⌿ Ͻ 0.5⌿ 81 Nondimensional wind sea energy as a function of s1 ws inverse wave age for the opposed swell and aligned Aligned swell ews Ͼ 0

⌿s2 Ͻ 0.5⌿s1 42 swell categories (Table 2) appears in Fig. 6. Also ap- 0Њ Յ |␪sϪws| Յ 45Њ pearing on the plot is the best-®t regression of the no- Opposed swell e Ͼ 0 ws swell observations, given by ⌿s2 Ͻ 0.5⌿s1 15 135Њ Յ |␪ | Յ 180Њ sϪws U Ϫ3.02 Confused sea All other conditions 98 eЈϭ0.002210 , (10) ΂΃cp with a correlation of r ϭ 0.94. The results suggest that regression through a steady wind observation subset the relationship of nondimensional wind sea energy to (Ϫ5 ϫ 10Ϫ5 Ͻ a Ͻ 5 ϫ 10Ϫ5) is given by U inverse wave age is independent of the presence of Ϫ2.73 swell, regardless of the direction of swell propagation U10 ewsЈϭ0.0021 , (8) relative to the wind sea direction. ΂΃cp These results do not necessarily contradict the labo- which falls directly between the rising and falling wind ratory results from previous investigations. Chu et al. regressions shown in Fig. 5. These results depict a trend (1992) observed the interactions between statistically of increasing energy with decreasing wind acceleration steady wind-generated waves and groups of longer for observations at a given wave age and are in agree- waves of various slopes. During the interaction phase, ment with the ®ndings of Toba et al. (1988). This im- they noted both a reduction of wind wave amplitudes portant effect is ignored by air±sea process models that by breaking near the long wave crests and a shortening employ a short-term average wind speed forcing. of the wind waves due to straining by the wave orbital velocities of the group. The important point is that these two interaction effects are compensating, such that wind b. Interaction with swell wave slope was essentially unchanged from its original As discussed in the introduction, to date there has value before the interaction. In terms of the nondimen- been little or no evidence that swells in¯uence wind sea sionalization employed herein, swell interactions would growth, over the range of frequencies observed by wave be expected to decrease eЈ because of enhanced breaking buoys, in the open ocean. It is clear that, at least for while simultaneously decreasing the wavelength ␭ be- laboratory waves, the presence of long waves results in cause of orbital straining. Hence, assuming that the deep the attenuation of aligned wind waves. The mechanism water simpli®cation for this process is as yet unresolved; the results from gg1/2␭ 1/2 numerous laboratory and theoretical treatments are in- c ϭϭ conclusive and at times contradictory (Table 1). The p ΂΃k ΂2␲ ΃ agreement shown here between observations in the holds for this scenario, a corresponding increase in U/c swell-dominated Gulf of Alaska and those from Lake p would occur. This simultaneous decrease of eЈ and in- St. Clair suggests that the relationship between eg2/U 4 crease of U/c suggests that the occurrence of swell and U/c of natural wind waves is not affected by the p p would not change the dependence of eЈ on U/c . presence of swell. p To more fully address the interaction between swell and wind sea in the Gulf of Alaska, the information 4. Wave dissipation assimilated through the wave spectral partitioning pro- a. Equilibrium range model cess was employed. To isolate speci®c swell conditions, the wave observations were sorted based on ratios be- The equilibrium range theory of Phillips (1985) pro- tween wind sea signi®cant slope ⌿ws, dominant swell vides the necessary framework for obtaining estimates, partition signi®cant slope ⌿s1, the signi®cant slope of from actual wave observations, of the total wave energy the second largest swell partition ⌿s2, and the angle ␪sϪws dissipation rate ␧t. By assuming a dependence of each between the wind sea and dominant swell directions. term on the developing spectrum, Phillips employed the- Here the signi®cant slope (Huang 1986) oretical and empirical arguments to derive the equilib-

2 rium range wave number and frequency spectral forms: Hs ␻psH ⌿ϭ ϭ (9) ⌿(k) ϭ ␤(cos␪)pugϪ1/2 kϪ7/2, (11) ␭p 2␲g * is computed using the peak frequency (␻ ) and H sta- Ϫ4 p s S(␻) ϭ 4␤I(p)ug* ␻ , (12) tistics from the appropriate spectral partition. Four wave condition categories were formed as identi®ed in Table 2. where I(p) is a spreading function given by

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC AUGUST 1999 HANSON AND PHILLIPS 1641

FIG. 6. Nondimensional wind sea energy during conditions of swell opposed with wind sea (open circles) and swell aligned with wind sea (solid circles). Although the no-swell observations are omitted for clarity, a regression through these observations is included on the plot.

␲/2 ␲/2 dk I(p) ϭ (cos␦)p d␦, (13) ␧(␻) ϭ 2 k ␧(k) d␦ . (18) ͵ d␻ 2 ͵ Ϫ␲/2 Ηkϭ␻ /g Ϫ(␲/2) and ␤ is related to Toba's constant (␣) and I(p)by Substituting Eq. (15) into the above and solving yields u3 ␣ 3 * ␤ ϭ . (14) ␧(␻) ϭ 4␥␤ I(3p) (19) 4I(p) ␻ 2 The equilibrium range concepts allow for the ex- for k ϭ ␻ /g. pression of each source term as a function of the equi- The spectral dissipation rate can be cast in terms of librium range spectrum. The spectral rate of energy loss the equilibrium range spectrum by ®rst solving equation in the equilibrium range is given by (12) for u* and then inserting this result into Eq. (19): ␥I(3p) ␧(k) ϭ ␻D(k) ϭ ␥␤3(cos␦)3pu*3 kϪ2. (15) ␧(␻) ϭ ␻11S(␻) 3 . (20) 16[I(p)]33g This expression indicates that breaking waves provide energy for near-surface turbulence over the full range Assuming that the equilibrium range extends from ␻p of scales in the equilibrium range. Equating the dissi- to higher frequencies, integrating over this range and pation rate to the rate of energy input by the wind reveals putting in the water density factor yields the dimen- sionally correct total rate of wave energy dissipation ␥␤2 ഠ m ഠ 0.04, (16) ␳␥I(3p) ␧ϭ w ␻11S(␻) 3 d␻. (21) and combining Eqs. (14) and (16), t 16[I(p)]33g ͵ ␻p ␣ 2 Felizardo and Melville (1995) use this expression to ␥ ഠ 0.04 . (17) 4I(p) compare wave dissipation rate estimates with ambient ΋΂΃ sound signatures of breaking waves. They use wind sea The equilibrium range ideas can be used to develop frequency spectra, obtained by ®ltering out what was an expression for the total rate of wave dissipation ␧t considered to be swell energy from observed wave fre- in terms of a measured directional wave spectrum quency spectra, in place of S(␻) in Eq. (21), along with S(␻, ␪). First it is necessary to express the spectral dis- constant I(p) spreading terms. Felizardo and Melville sipation rate [Eq. (15)] in terms of frequency. This trans- compare results of using Eq. (21) with those obtained formation is given by (Phillips 1977, 1985) using a dissipation expression proposed by Komen et

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC 1642 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 29 al. (1984). This alternate approach follows theoretical b. Open ocean dissipation estimates arguments of Hasselmann (1974) that spectral dissipa- tion should approach a linear proportionality with S(␻) Directional wave spectra over the equilibrium range and exhibit a damping coef®cient proportional to ␻ 2. are required to satisfy the dissipation model assumption. In Felizardo and Melville's correlations of spectral dis- The wave partitioning process resulted in the isolation sipation rate with ambient noise levels, Eq. (21) per- of a wind-forced spectral domain as de®ned by the wave formed at a level comparable to, if not slightly better age criterion of Eq. (3) and the ␣ threshold criterion than, the Komen et al. approach (see Fig. 19 in Felizardo (see Fig. 1). From these actively generating wind seas and Melville 1995). Thus we will proceed with the de- the equilibrium range SER(␻, ␪) is now de®ned as all velopment of Eq. (21), however noting the existence of spectral components that extend from the spectral peak an alternate method that has been shown to produce to the high-frequency cutoff f c ϭ 0.5 Hz. statistically similar results. The total rate of wave energy dissipation (in units of Perhaps the most signi®cant limitation of the equi- kg sϪ3) was estimated by applying Eqs. (24)±(27) to the librium range theory is the I(p) directional spread factor Gulf of Alaska equilibrium-range directional spectra. de®ned by Eq. (13). This factor has its roots in the Plant These estimates represent the dissipation rate expected (1982) wind input equation, which reasonably uses cos over the observed range of frequencies. The resulting ␦ to obtain the component of wind stress that is in the Gulf of Alaska ␧t and I1 records, along with wind speed direction of wave propagation. However, the use of this and direction, appear in Fig. 7. As expected, dissipation method to calculate I(p) yields a spreading function that rate is highest during the elevated wind events. As for assumes a symmetrical wave spectrum developed the spreading parameter, trends in I appear to be an- through a hypothetical u stationarity. As directional 1 * ticorrelated with wind speed. Lower I1 values, indicative distributions of wave spectra are now routinely mea- of directionally aligned seas, occur during the higher sured, it is conceivable that the I(p) terms of Eq. (21) wind events when seas are more fully developed. could also be replaced with observational data. As Fig. 8 indicates, the dissipation rate estimates ob- A convenient directional spread indicator that has the tained from the wave spectra are fairly well correlated same limits as cos , yet is derived from observations, ␦ with wind speed. The data are ®t by is the normalized direction spectrum Ϫ5 3.74 S(␪) ␧t ϭ 4.28 ϫ 10 U 10 , (28) S(␪) ϭ , (22) N S( ) ␪p with a correlation of r ϭ 0.82. Also appearing on the where the wave direction spectrum in the equilibrium ®gure are sample data points from Felizardo and Mel- range is de®ned by ville (1995), which from here on is referred to as FM95. The FM95 dissipation estimates fall within the range of scatter of the Gulf of Alaska estimates and exhibit a S( ) S( , ) d (23) ␪ ϭ ͵ ␻ ␪ ␻ similar wind speed dependence. However, there is a ␻p nearly constant offset between the wind regressions of and S(␪p) represents the equilibrium range peak. New each observation set. Explanations for this offset are spreading functions are de®ned as given in the discussion. As demonstrated earlier, wind history effects can sig- ␪ ϩ␲/2 p ni®cantly in¯uence wind sea growth (Fig. 5). Similarly, I ϭ S(␪) d␪, (24) 1 ͵ N it is found that a signi®cant portion of the scatter in the ␪pϪ␲/2 correlation of ␧t with U10 (Fig. 8) can be attributed to ␪pϩ␲/2 wind history trends not represented by the half-hour U10 I ϭ [S(␪)]3 d␪. (25) 3 ͵ N averages. Figure 9 shows the correlation of mean ␪pϪ␲/2 (3-hourly) wind acceleration (a U), introduced earlier as

a crude indicator of wind trend, with sorted ␧t obser- Substitution of I1 and I3 in place of I(p) and I(3p), respectively, in Eq. (21) yields an estimate of the total vations in three speci®c wind speed bins. The wave rate of wave energy dissipation based on attributes of dissipation rate exhibits a strong dependence on a U, with the directional wave spectrum: higher rates of dissipation when winds are falling. It is clear that wave dissipation estimates represent the in- ␳␥I ␧ϭ w 3 ␻11S(␻) 3 d␻, (26) tegrated effect of the previous wind forcing history. This t 33 16Ig1 ͵ important information is lost when a short-term aver- ␻p aged wind speed is used to describe air±sea processes. with This has signi®cant implications for the use of wave 2 parameters to augment wind speed in air±sea process ␣ ␥ ϭ 0.04 . (27) modeling. An example of this, using whitecap obser- 4I ΋[]1 vations from the Gulf of Alaska, is explored next.

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC AUGUST 1999 HANSON AND PHILLIPS 1643

FIG. 7. Gulf of Alaska wind, wave dissipation rate, and spreading function records. c. Whitecaps Can wave dissipation rate estimates, obtained from surface wave observations, be used in place of wind speed to model ocean surface whitecaps? Cardone

FIG. 8. Correlation of dissipation rate estimated from surface wave FIG. 9. Dependence of dissipation rate on mean wind acceleration spectra with wind speed. at selected wind speeds.

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC 1644 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 29

FIG. 10. Correlation of 30-min average whitecap fraction subset with wind speed. The power ®t is computed over all W Ͼ 5 ϫ 10Ϫ5. The points not included in this ®t are identi®ed by a dot in the circle FIG. 11. Correlation of 30-min average whitecap fraction subset center. with dissipation rate.

(1970) observed that wave dissipation estimates, ob- in wind history, surface properties, and atmospheric sta- tained from modeled wind seas, were better correlated bility may also contribute to the extreme variability in 3 with whitecap fraction estimates than with wind speed. this range. Nevertheless, ␧t ϳ u* should continue to Furthermore, the power-law ®t of wind speed to wave hold even if, at low wind speeds, the breaking is not dissipation rate, given by Eq. (28), additionally suggests energetic enough to produce air entrainment and foam that the answer to this question is yes. The U10 exponent but is instead in the form of small-scale breaking and of 3.74 is nearly identical to that noted by Wu (1992), perhaps sporadic splashing with few bubbles entrained. and appearing in Eq. (2), for the correlation of whitecap The use of the Gulf of Alaska wave dissipation rate fraction W to U10. This agreement supports the labo- estimates [Eqs. (26) and (27)] in place of wind speed ratory ®ndings of Lamarre and Melville (1991), who improves the power-law description of whitecap frac- noted that the initial volume of air entrained by breaking tion. The dependence of W on ␧t appears in Fig. 11. is proportional to the energy dissipated by the wave. The whitecap power-law model Whitecaps are breaking events marked by the generation Ϫ3 1.5 of foam, and as long as they represent the dominant W ϭ 3.4 ϫ 10 ␧t (31) energy dissipation mechanism, one would expect that ®ts all the observations with an improved correlation of

W would be directly proportional to ␧t such that r ϭ 0.86. The scatter of W with ␧t is approximately two 3 3.75 orders of magnitude less than that with U10, and the W ϳ␧t ϳϳu* U . (29) ``kink'' in the W versus U10 distribution (Fig. 10) is The dependence of the Gulf of Alaska 30-min average removed by using ␧t. As will be further addressed in W observations on U10 appears in Fig. 10. A power ®t the discussion, the use of wave dissipation rate in place to all of these points gives of wind speed removes the uncertainty caused by at- Ϫ9 5.16 mospheric forcing variability. The power of 1.5 on ␧ , W ϭ 3.66 ϫ 10 U 10 , t rather than a power of unity as implied by (29), is likely which is much steeper than the correlation (29) given a result of the fact that not all of the dissipation is by Wu. The observational data used by Wu exclude any represented by W. This is especially true with breaking Ϫ5 values of W Ͻ 5 ϫ 10 , and if we also exclude these at very small scales, which would likely produce surface points, we obtain the best-®t solid line in Fig. 10 rep- manifestations too small for the detection capability of resented by a ship-mounted whitecap video system. Ϫ7 3.61 W ϭ 2.04 ϫ 10 U 10 , (30) with a correlation of r ϭ 0.72. This is very close to 5. Discussion Wu's result. It is evident from Fig. 10 that when W Ͻ a. Wave dissipation estimates 5 ϫ 10Ϫ5, the scatter becomes very large and unsys- tematic, as each point represents an observation of only Estimates of the total rate of wave energy dissipation a few isolated whitecaps in the ®eld of view. Variations by breaking surface waves in the Gulf of Alaska have

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC AUGUST 1999 HANSON AND PHILLIPS 1645 been conveniently obtained from wave buoy observa- 2) ISOLATION OF THE EQUILIBRIUM RANGE tions. On average, the Gulf of Alaska dissipation rates fell below those estimated from wave measurements off The theoretical concepts discussed earlier specify the the coast of Oregon by FM95 (Fig. 8). Several factors equilibrium range to be a spectral region where the ac- could contribute to the increase in FM95 wave dissi- tion ¯ux due to wind input, nonlinear transfer, and wave pation estimates over those obtained from the Gulf of dissipation are all in balance and proportional to each Alaska, including 1) exclusion of dissipation in the spec- other. This refers to that portion of the spectrum where tral tail region, 2) the method employed to isolate the active exchanges are occurring and, hence, speci®es the equilibrium range, and 3) geographic and seasonal range over which the waves are breaking. Observations trends in atmospheric forcing. Each of these will be by Farmer and Vagle (1988) indicate a wide range of discussed in turn. breaking scales, supporting the concept here that the equilibrium range extends from near the wind sea spec- tral peak out through the observed spectral tail. 1) DISSIPATION IN THE SPECTRAL TAIL REGION FM95 isolated wind sea frequency spectra by locating FM95 used wire wave gauges to estimate wave fre- a minimum between wind sea and swell peaks and ®l- quency spectra; they present these estimates out to a tering out spectral components at frequencies below this minimum. It appears that all spectral components above cutoff frequency f c ϭ 2.0 Hz. If they estimated equi- librium range dissipation out to 2.0 Hz, then their dis- the minimum were considered to be wind sea. They sipation estimates include more of the spectral tail re- de®ned the equilibrium range, for estimation of dissi- pation rate, as extending from the peak of the ®ltered gion than those presented for the Gulf of Alaska ( f c ϭ 0.5 Hz) and, hence, would be expected to be higher. But wind seas to the end of the spectral tail at f c. To this how much higher? To determine the importance of dis- they applied a constant directional spreading of I(p) ϭ sipation in the spectral tail, a simple relationship can be 2.4. established assuming an ␻Ϫ5 spectral falloff in this re- As described, the Gulf of Alaska directional wind sea gion as observed by Donelan et al. (1985). The total spectra were isolated using an automated spectral par- dissipation rate given in Eq. (26) can be expressed as titioning approach. An ␣-threshold test was employed to identify and remove young swell components that were found to exist within the wind-forced spectral do- ␧ϭP ␻11S(␻) 3 d␻, (32) t ͵ main. The premise here is that rapidly varying wind ␻p conditions can lead to a close spectral mix of wind sea where P simply refers to the term in front of the integral. and swell components and that these swell components, In line with Donelan et al. (1985), assume moving at speeds comparable to or slightly greater than the wind speed, are not actively involved in the equi- S(␻) ϳ ␻Ϫ5 ϭ C␻Ϫ5. (33) librium range exchanges. The removal of young swell Substituting this into Eq. (32) and solving over the spec- components from isolated wind sea spectra would likely tral tail region, result in dissipation rate estimates that are lower than those obtained by the FM95 method. Although the con- ␧Ä ϭ P ␻11(C␻Ϫ53) d␻ (34) stant I(p) spectral spreading employed by FM95 would t ͵ ␻ 0 not contribute to a bias of the mean, it could result in an increased level of data scatter about the mean due ϭ PC͵ 3␻Ϫ4 d␻ (35) to wind direction variability. ␻ 0 1 ϭ PC 3␻Ϫ3|ϱ , (36) 3) GEOGRAPHIC AND SEASONAL EFFECTS 3 ␻ 0 As was demonstrated by Fig. 9, wind history trends where the integral has been evaluated from the radian factor prominently in the distribution of ␧t with U10. 5 cutoff frequency ␻ 0 ϭ 2␲f c out to ϱ. Since C ϭ S(␻)␻ , The FM95 data were obtained during September at a the total dissipation rate in the spectral tail can be ex- location approximately 130 km off the Oregon coast. pressed as a function of S(␻ 0): The atmospheric forcing trends, and the responses of 1 the ocean to these trends, are expected to be different ␧Ä ϭ P␻ 12S 3(␻ ). (37) than those observed in the Gulf of Alaska during winter. t 3 00 Indeed, inspection of the FM95 wind records indicates Application of the tail dissipation correction factor to that wind speeds varied on much slower timescales than the Gulf of Alaska dissipation estimates results in just those experienced in the Gulf of Alaska. Furthermore, a few percent increase in log(␧t). As the FM95 estimates the FM95 wind directions were reasonably steady dur- are some 30%±40% higher than the Gulf of Alaska ing most of their experiment. As a result, the FM95 estimates, spectral dissipation in the tail region is not wave ®eld, at a given wind speed, tended more toward the primary cause of this offset. full development and, hence, would be expected to ex-

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC 1646 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 29 hibit higher dissipation rates than were observed in the estimated from the Gulf of Alaska wind sea partitions highly variable Gulf of Alaska environment. using concepts from the Phillips (1985) equilibrium range theory [Eq. (24)±(27)]. Equilibrium ranges of di- rectional wave spectra were isolated using a wave-age- b. Whitecap fraction correlations dependent partitioning approach with an ␣-threshold Whitecap fraction has been shown to exhibit a better criterion for the removal of young swell components power-law relationship with wave dissipation rate than near the wind sea peak. Furthermore, the I(p) spreading with wind speed (Figs. 10 and 11). The use of ␧t to functions in the Phillips theory have been replaced by describe W effectively removes the uncertainty due to directional spread indicators obtained from the wave wind trend that is present when U10 is used as the in- observations. dependent variable. Although surface wave parameters Dissipation estimates obtained with this approach have been previously used to characterize the acoustics show a similar dependence on wind speed as reported of breaking (Ding and Farmer 1994; FM95), the results by FM95. Furthermore, whitecap fraction estimates reported here appear to be the ®rst to show that observed from ship-board video records obtained during the Gulf surface wave parameters can be successfully used to of Alaska experiment were used to evaluate power-law characterize the whitecap signatures of wave breaking descriptions of whitecaps using wind speed and wave in the ®eld. dissipation rate. Replacing wind speed with ␧t in the What of the remaining scatter in W as a function of standard power-law description of whitecap fraction W

␧t (Fig. 11)? Possibly, this variability is either dominated resulted in a new proportionality, by measurement noise or represents limitations in the 1.5 W ϰ ␧t , (38) equilibrium range estimates of ␧t. There are, however, additional air±sea attributes that are thought to in¯uence that reduces the scatter of W about the independent var- wave dissipation rates and air entrainment by breaking iable by 2 to 3 orders of magnitude. These improve- waves. These include, but are not limited to, atmo- ments result primarily from the removal of wind trend spheric turbulence, atmospheric stability, water tem- effects that add uncertainty to wind speed relationships. perature, biological surfactants, directionality of the These open ocean results support the laboratory ®ndings wave ®eld, and the interaction with swell and surface of Lamarre and Melville (1991); those authors observed currents. Of these effects, only the wave ®eld direc- a proportionality between the energy dissipated by tionality is addressed by the equilibrium range model. breaking and the initial amount of air entrained. The successful description of whitecaps by our dissipation rate estimates lends credibility to the equilibrium range 6. Conclusions theory as a viable approach to modeling air±sea ex- A wave spectral partitioning approach has allowed changes. an investigation of wind sea growth and dissipation in Remote sensing techniques, wave buoy arrays, and a swell-dominated open ocean environment. When regional wave modeling efforts are continually being scaled by eg2/U 4, Gulf of Alaska wind seas exhibit the re®ned so that soon high-quality directional wave spec- same functional dependence on inverse wave age U/cp tra will be routinely available on a global scale (Beal that was observed in a relatively benign lake setting by 1991). It is conceivable that air±sea process models for Donelan et al. (1992). It is concluded that the chosen such mechanisms as gas ¯ux, radar backscatter, under- scaling compensates for wind sea modi®cation by swell; water ambient noise, and near-surface acoustic rever- a decrease of eg2/U 4 through swell interactions is ac- beration will soon experience signi®cant improvements companied by a compensating increase of U/cp. This due to the use of surface wave spectral parameters in ®nding is consistent with the laboratory results of Chu place of external forcing parameters. Since wave-related et al. (1992) that show wind sea slope is preserved dur- processes are dynamically linked to intrinsic properties ing interactions between wind sea and swell. of the wave ®eld (not necessarily to properties of the Using the 3-h average wind acceleration as a crude external forcing on the waves from winds, currents, ba- indicator of wind trend, it was found that the dependence thymetry, etc.), use of wave parameters should improve 2 4 of eg /U on U/cp is signi®cantly in¯uenced by wind model performance. history. At a given wave age, wind seas are more de- veloped during falling winds due to the recent history Acknowledgments. We are grateful to the many in- of high winds, and they are less developed during rising dividuals who contributed to the logistics, acquisition, winds for the opposite reason. This effect is not ac- and processing of the ®eld data. In particular, wave spec- counted for in empirical process models for air±sea gas tra were provided by Richard F. Marsden, whitecap vid- ¯ux (JaÈhne 1990), acoustic reverberation (Ogden and eo observations were provided by Ed Monahan, and Erskine 1994), and ambient noise (Wenz 1962; Cato et meteorological observations were obtained by Larry al. 1995). It is likely that accounting for wind history White. We wish to thank Hans Graber for insightful effects would improve the accuracy of these models. discussions on wind±wave dynamics and Ken Melville

The total rate of wave energy dissipation (␧t) was for suggesting the wave dissipation calculations. We

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC AUGUST 1999 HANSON AND PHILLIPS 1647 thank the reviewers for their careful and helpful as- of the air±sea boundary zone on underwater acoustic reverber- sessments. This work was supported by the Of®ce of ation. Proc. MTS '92, Washington, DC, Marine Technology So- ciety, 835±847. Naval Research (Code 321OA) under Grant N00014- , , and M. Kennelly, 1993: Air±sea and upper ocean dy- 97-1-0075. Additional support for manuscript prepara- namics during CST-7 phase 2. The Johns Hopkins University tion came from a Johns Hopkins University Applied Applied Physics Laboratory Tech. Rep. STD-R-2281, 74 pp. Physics Laboratory Janney Fellowship Award. Hasselmann, K., 1974: On the spectral dissipation of ocean waves due to whitecapping. Bound.-Layer ., 126, 507±127. , T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, REFERENCES and Coauthors 1973: Measurements of wind±wave growth and decay during the Joint North Sea Wave Project (JONSWAP). Deutsche Hydrographische Zeitschrift, Reihe A, 8 (22), 1±95. Agrawal, Y. C., E. A. Terray, M. A. Donelan, P. A. Hwang, A. J. Hasselmann, S., K. Hasselmann, and C. Bruning, 1994: Extraction Williams III, W. M. Drennan, and Coauthors 1992: Enhanced of wave spectra from SAR image spectra. Dynamics and Mod- dissipation of kinetic energy beneath surface waves. Nature, 359, elling of Ocean Waves, Cambridge University Press, 532 pp. 219±220. Hatori, M., M. Tokuda, and Y. Toba, 1981: Experimental study on Banner, M. L., and M. A. Donelan, 1992: The physical consequences strong interactions between regular waves and wind wavesÐI. of wave breaking in deep water. Breaking Waves. M. L. Banner J. Oceanogr. Soc. Japan, 37, 111±119. and R. H. J. Grimshaw, Eds., Springer-Verlag, 3±20. Huang, N. E., 1986: An estimate of the in¯uence of breaking waves , and I. R. Young, 1994: Modeling spectral dissipation in the on the dynamics of the upper ocean. Wave Dynamics and Radio evolution of wind waves, Part I: Assessment of existing model Probing of the Ocean Surface, O. M. Phillips and K. Hassel- performance. J. Phys. Oceanogr., 24, 1550±1571. Beal, R. C., Ed., 1991: Directional Ocean Wave Spectra. The Johns mann, Eds., Plenum Press, 295±313. Hopkins Studies in Earth and Space Sciences, The Johns Hopkins JaÈhne, B., 1990: New experimental results on the parameters in¯u- University Press, 218 pp. encing air±sea gas exchange. Proc. on Air±Water Mass Transfer, Buckingham, M. J., and J. R. Potter, Eds., 1995: Sea Surface Sound Second Int. Symp., Minneapolis, MN, ASCE, 244±256. '94. World Scienti®c, 494 pp. Jessup, A. T., W. C. Keller, and W. K. Melville, 1990: Measurements Cardone, V. J., 1970: Speci®cation of the Wind Distribution in the of sea spikes in microwave backscatter at moderate incidence. Marine Boundary Layer for Wave Forecasting. New York Uni- J. Geophys. Res., 95, 9679±9688. versity, 131 pp. Juszko, B.-A., R. F. Marsden, and S. R. Waddell, 1995: Wind stress Cato, D. H., S. Tavener, and I. S. F. Jones, 1995: Ambient noise from wave slopes using Phillips equilibrium theory. J. Phys. dependence on local and regional wind speeds. Sea Surface Oceanogr., 25, 185±203. Sound '94. M. J. Buckingham and J. R. Potter, Eds., World Kerman, B. R., Ed., 1988: Natural Mechanisms of Surface Generated Scienti®c, 95±111. Noise in the Ocean: Sea Surface Sound. Kluwer Academic Pub- Chu, J. S., S. R. Long, and O. M. Phillips, 1992: Measurements of lishers, 639 pp. the interaction of wave groups with shorter wind-generated , Ed., 1993: Natural Physical Sources of Underwater Sound: Sea waves. J. Fluid Mech., 245, 191±210. Surface Sound. 2d ed. Kluwer Academic Publishers, 750 pp. Cox, C. S., 1958. Measurements of slopes of high-frequency wind Kitaigorodskii, S. A., 1962: Applications of the theory of similarity waves. J. Mar. Res., 16, 199±225. to the analysis of wind-generated gravity waves. Bull. Acad. Sci. Ding, L., and D. M. Farmer, 1994: Observations of breaking surface USSR, Geophys. Ser., 1, 105±117. wave statistics. J. Phys. Oceanogr., 24, 1368±1387. Kline, S. A., and J. L. Hanson, 1995. Wave identi®cation and tracking Dobson, F., W. Perrie, and B. Toulany, 1988: On the deep-water fetch system. Technical Report STD-R-2436, The Johns Hopkins Uni- laws for wind-generated surface gravity waves. Atmos.-Ocean, versity Applied Physics Laboratory Tech. Rep. STD-R-2436, 40 27(1), 210±236. pp. Donelan, M. A., 1987: The effect of swell on the growth of wind Komen, G. J., S. Hasselmann, and K. Hasselmann, 1984. On the waves. Johns Hopkins APL Tech. Dig., 8 (1), 18±23. existence of a fully developed wind-sea spectrum. J. Phys. , J. Hamilton, and W. H. Hui, 1985: Directional spectra of wind- Oceanogr., 14, 1271±1285. generated waves. Philos. Trans. Roy. Soc. London, 315A, 509± , L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann, and 562. P. A. E. M. Janssen, 1994: Dynamics and Modeling of Ocean , M. Skafel, H. Graber, P. Liu, D. Schwab, and S. Venkatesh, Waves. Cambridge University Press, 532 pp. 1992: On the growth rate of wind-generated waves. Atmos.- Kraan, C., W. A. Oost, and P. A. E. M. Janssen, 1996: Wave energy Ocean, 30 (3), 457±478. dissipation by whitecaps. J. Atmos. Oceanic Technol., 13, 262± Dugan, J. P., 1991: Decontamination of wind measurements from 267. buoys subject to motions in a seaway. J. Atmos. Oceanic Tech- Lamarre, E., and W. K. Melville, 1991: Air entrainment and dissi- nol., 8, 85±95. pation in breaking waves. Nature, 351, 469±472. Farmer, D. M., and S. Vagle, 1988: On the determination of breaking Loewen, M. R., and W. K. Melville, 1991: Microwave backscatter surface wave distributions using ambient sound. J. Geophys. Res., 93 (C4), 3591±3600. and acoustic radiation from breaking waves. J. Fluid Mech., 224, , C. L. McNeil, and B. D. Johnson, 1993: Evidence for the 601±623. importance of bubbles in increasing air±sea gas ¯ux. Nature, Longuet-Higgens, M. S., and R. W. Stewart, 1960: Changes in the 361, 620±623. form of short gravity waves on long waves and tidal currents. Felizardo, F. C., and W. K. Melville, 1995: Correlations between J. Fluid Mech., 8, (Part 4), 565±583. ambient noise and the ocean surface wave ®eld. J. Phys. Ocean- Marsden, R. F., and B.-A. Juszko, 1987: An eigenvector method for ogr., 25, 513±532. the calculation of directional spectra from heave, pitch and roll Hanson, J. L., 1996: Wind sea growth and swell evolution in the Gulf buoy data. J. Phys. Oceanogr., 17, 2157±2167. of Alaska. Ph.D. Dissertation, The Johns Hopkins University, McDaniel, S. T., 1993: Sea surface reverberation: A review. J. Acoust. 151 pp. Soc. Amer., 94 (4), 1905±1922. , and L. H. White, 1991: Assessment of the air±sea boundary Melville, W. K., 1994: Energy dissipation by breaking waves. J. Phys. zone during critical sea test 4. The Johns Hopkins University Oceanogr., 24, 2041±2049. Applied Physics Laboratory Tech. Rep. STD-R-1978, 116 pp. , 1996: The role of surface-wave breaking in air±sea interaction. , and F. T. Erskine, 1992: An experiment to study the in¯uence Ann. Rev. Fluid Mech., 28, 279±321.

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC 1648 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 29

, and R. J. Rapp, 1985: Momentum ¯ux in breaking waves. , and J. W. Wright, 1977: Growth and equilibrium of short gravity Nature, 317, 514±516. waves in a wind-wave tank. J. Fluid Mech., 82, 767±793. Mitsuyasu, H., 1966: Interactions between water waves and winds Rapp, R. J., and W. K. Melville, 1990: Laboratory measurements of (I). Rep. Res. Inst. Appl. Mech. Kyushu Univ., 14, 67±88. deep-water breaking waves. Philos. Trans. Roy. Soc. London, , 1992: Wave breaking in the presence of wind drift and opposed 331A, 735±800. swell. Breaking Waves, M. L. Banner and R. H. J. Grimshaw, Skafel, M. G., and M. A. Donelan, 1983: Performance of the CCIW Eds., Springer-Verlag, 147±153. wave direction buoy at ARSLOE. IEEE J. Oceanic Eng., OE- Monahan, E. C., 1993: Occurrence and evolution of acoustically rel- 8 (4), 221±225. evant sub-surface bubble plumes and their associated, remotely Smith, S. D., 1988: Coef®cients for sea surface wind stress, heat ¯ux, monitorable, surface whitecaps. Natural Physical Source of Un- and wind pro®les as a function of wind speed and temperature. derwater Sound: Sea Surface Sound. 2d ed. Kluwer Academic J. Geophys. Res., 93, 15 467±15 472. 503±517. , 1990: Modulation of short wind waves by long waves. Surface , and M. Lu, 1990: Acoustically relevant bubble assemblages Waves and Fluxes, G. L. Geerhaert and W. J. Plants, Eds., Kluwer and their dependence on meteorological parameters. IEEE J. Academic, 247±284. Oceanic Eng., 15 (4), 340±349. Terray, E. A., and Coauthors, 1996: Estimates of kinetic energy dis- , and M. Wilson, 1993: Whitecap measurements. Critical Sea sipation under breaking waves. J. Phys. Oceanogr., 26, 792± Test 7, Phase 2: Principal investigators' results. The Johns Hop- 807. kins University Applied Physics Laboratory Tech. Rep. STD-R- Thorpe, S. A., 1984: The effect of on the dis- 2258, F. T. Erskine and J. L. Hanson, Eds., 808 pp. tribution of submerged bubbles caused by breaking wind waves. Ogden, P. M., and F. T. Erskine, 1994: Surface and volume scattering J. Fluid Mech., 142, 151±170. measurements using broadband explosive charges in the Critical Toba, Y., K. Okada, and I. Jones, 1988: The response of wind±wave Sea Test 7 experiment. J. Acoust. Soc. Amer., 96 (5), 2908±2920. spectra to changing winds. Part I: Increasing winds. J. Phys. Phillips, O. M., 1958: The equilibrium range in the spectrum of wind- Oceanogr., 18, 1231±1240. generated waves. J. Fluid Mech., 4, 426±434. Tyler, G. D., 1992: The emergence of low-frequency active acoustics , 1977: Dynamics of the Upper Ocean. Cambridge University as a critical antisubmarine warfare technology. Johns Hopkins Press, 236 pp. APL Tech. Dig., 13 (1), 145±159. , 1985: Spectral and statistical properties of the equilibrium range Voorrips, A. C., V. K. Makin, and S. Hasselmann, 1997: Assimilation in wind-generated gravity waves. J. Fluid Mech., 156, 505±531. of wave spectra from pitch-and-roll buoys in a North Sea wave , 1988: Radar returns from the sea surfaceÐBragg scattering model. J. Geophys. Res., 102 (C3), 5829±5849. and breaking waves. J. Phys. Oceanogr., 18, 1065±1074. Wallace, D. W. R., and C. D. Wirick, 1992: Large air±sea gas ¯uxes , and M. L. Banner, 1974: Wave breaking in the presence of associated with breaking waves. Nature, 356, 694±696. wind drift and swell. J. Fluid Mech., 66 (Part 4), 625±640. Wenz, G. M., 1962: Acoustic ambient noise in the ocean: Spectra Pierson, W. J., and L. Moskowitz, 1964: A proposed spectral form and sources. J. Acoust. Soc. Amer., 34, 1936±1956. for fully developed wind seas based on the similarity theory of Wright, J. W., 1976: The wind drift and wave breaking. J. Phys. S. A. Kitaigorodskii. J. Geophys. Res., 69 (24), 5181±5190. Oceanogr., 6, 402±405. Plant, W. J., 1982: A relationship between wind stress and wave slope. Wu, J., 1992: Individual characteristics of whitecaps and volumetric J. Geophys. Res., 87 (C3), 1961±1967. description of bubbles. IEEE J. Oceanic Eng., 17 (1), 150±158.

Unauthenticated | Downloaded 09/25/21 08:45 AM UTC