JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 92, NO. C9, PAGES 9487-9493, AUGUST 15, 1987

Edge Waves on the SydneyCoast

JASON H. •[IDDI.ETON AND MADELEINE L. CAmLL

Schoolof Mathematics,University oJ'New South Wales, Kensington, Australia

WILLIAM W. HSIEH

Departmentof Oceanography,University of British Columbia,Vancouver, Canada

Pressureand currentoscillations at periodsof 40 s to 17 min observedduring stormconditions at two locationsseparated by 560 m in thealongshore direction in thecoastal ocean near Sydney, Australia, indicate the existenceof infragravity waves having amplitudes of -20 cmand velocities of -10 cms -1. Theobserved infragravitywaves appearto be locally forcedby the wind wave envelopethrough radiation stress, yet the observedalongshore phase differences of the infragravitywaves are consistentwith thosepredicted from free edgewave theoryfor low-modeedge waves travelling northward and the relationshipof pressureto velocityat eachlocation is alsoconsistent with freeedge wave theory. As a functionof time, the infragravitywave spectral energygrows and decays in stepwith thelonger-period wind waves, suggesting a continuoustransfer of energy. The infragravitywaves appear to containenergy in both directlyforced and freely propagating(edge wave) oscillations.The edgewaves may be generatedeither by radiationstress as outlinedabove, by a resonanttriad mechanism,or by a combinationof the two.

1. INTRODUCTION having periodsperhaps a few minutes or less. For somewhat Edgewaves are surface gravity waves which are trapped along longer period waves, Greenspan [1956], Buchwald andde Szoeke shorelines by theshoaling topography. They generally have [1973], Viera and Buchwald [1982] and Worthy [1984] found periodssomewhat longer than those of windwaves and are theoreticalsolutions for edgewaves driven by travelling believedtoplay an important role in coastal sedimentation and atmospheric events. surfbeat [Bowen and Inman, 1971; Huntley and Bowen, 1975; Thework reported here was prompted by suggestions by Guzaand Thornton, 1985; Holman and Sallenger, 1986]. The Buchwaldand de Szoeke[1973] that the 3-min-period earliesttheory ofedge waves appears tobe due to Stokes [1846], oscillations ofsea level, observed inPort Kembla harbor (70 km whofound wavelike solutions to the barotropic equations of south of Sydney)during storms, were due to storm-generated motionappropriate forshallow water on a beachof constantedge waves travelling northward along the coast. Our experiment slope.Subsequently, thesetheories were extended byEckart was designed asa pilotstudy to observethe magnitude of [1951],Ursell [1952], and Reid [1958], who identified the oscillationswithperiods of0.5 -17 min in the coastal ocean south discretemodal structure. Thedynamics ofedge wave propagation ofSydney and to determine if the observed propagation ratesare arenow well understood inprinciple [LeBlond andMysak, 1978], consistent withedge wave theory. Since edge waves propagate asis the general relationship ofedge waves tothe wider class of becauseof refraction by shoaling topography, a section of coastaltrapped waves. relativelystraight coastline with steep cliffs and few energy Observationsof2- to 30-min-period oscillations insea level off absorbinginlets was chosen, thisoccurring offthe Royal National theCalifornia coast led Munk et al. [1956]to propose that a Park-25 km south of Sydneyand-45 km north of Port Kembla "wake"ofedge waves of 10-to 30-min period was produced by (Figure 1). theimpulsive forcing ofa moving atmospheric front,while higher Thispaper isorganized asfollows. Section 2 outlines edge frequencywaves of2- to 5-min period were due to surf beat. An wavetheory and experiment design while section 3 describes the extensivealongshore arrayof pressure gauges was later used on experimentalmethod and the observations. A comparison of thesame beach by Munk et al. [1964] to obtain wave number- observation withtheory isundertaken insection 4,while section 5 frequencyrelations ofoscillations withperiods of 1 minto 10 concludeswitha discussion. hours, andwavelength of 1.5 to 30 km. They concludedthat the 2. EDGE WAVE TttEORY AND DESIGN OF EXPERIMENT observedoscillations were predominantly caused by discreteedge We choose a Cartesian coordinate system with the x axis wave modes,and that little energy was associatedwith leaky pointing offshore and the y axis alongshore.The sea level waves.More recently,Huntley et al. [1981]used alongshore and displacementrl is assumedto havea travellingwave form, with offshorearrays of currentmeters to showthat 1- to 4-min-period oscillationsoff Scrippsbeach in Californiahave both structures rI = F (x)ei(•y-•) (1) anddispersion curves consistent with thosepredicted from edge From the unforcedshallow water equations,the coastaltrapped wave theory. Whilethe propagation ofedge waves iswell understood, theirwave equation forlinear waves ina barotropic oceanis derived by generationisnot. Gallagher [1971], Guza and Davis [1974], LeBlond and Mysak [1978, equation (25.7)]. Neglecting the Bowenand Guza [1978] and Symonds etal. [1982] argue that Earth's rotation, wecan rewrite their equation as nonlinearresonant interactions between incoming surface gravity F"-k2F+H-I(H 'F' + to2g-iF)= 0 (2) waves are the main mechanismsfor the generationof waves where prime denotesdifferentiation with respectto x, H = H (x) Copyright1987 by the American Geophysical Union. denotesthe depth,and g is the gravitationconstant. The Papernumber 7C0393. eigenvaluesof (2), whichdetermine the dispersionrelation 0148-0227/87/007C-0393505.00 to= to(k), and the eigenfunctionsF (x) were found numerically

9487 9488 MIDDLETON ET AL.: EDGE WAVES IN I) iii/ 0'15T--mode ROYAL if' / NATIONAL/•/'. // w (s-•)

34ø06'S

o1• I 0 0.00,5 0.010 J•.•'•/// PACIFICOCEAN k (m -'• ) •-• • _•o•/ // / Fig. 2b. The dispersioncurves for the first threeedge wave modes J•Oø-/?'i lkmI •/ calculatedfrom the theory using the actual depth profile. / / / I / where 151 ø10'E phase speed c is confined to Cm•< c Cmax,(2)Cmin < C < cnm,and (3) recordersusedinthis study. C< cx•. In case 1the waves generated arenot coastally trapped, [Holmanand Bowen, 1979] using F'/F =-{k2-co2/[gH (L)]]• whilein case 3,except forsome transients, nowavelike motions whereH'(L )=0 inthe deep ocean x =L. Sincethe coastline at are generated. Only in case2 areedge waves with c = C x =0 is composedof cliffs, we also used H(0)= 10 m and resonantlyexcited. For depth profiles with H = 0 atthe coast, F'(0)= 0. Cmi•= 0, andcase 3 doesnot arise. With H(0) = 10m andH (L) Thedepth profile H(x) in our experimental areatogether with = 5000 m, we have Cmi• = 10 m s -• andCm• =220 m s -x. thepredicted offshore dependence ofthe modal structure for1.3- Fromour dispersion diagram (Figure 2b), the zeroth mode edge and3.3-min waves are shownin Figure2a while themode 0, 1, wave with c matchingthe fastestfrontal speedC of about23 m and2edge wave dispersion curvesare shown inFigure 2b. s-• have aperiod ofaround 8min and awavelength of12 km. On FromLeBlond and Mysak [1978, equation (25.3) with f = 0], theother hand, the zeroth mode wave with a 1-minperiod has a onecan easily show that the edge wave velocity components obeywavelength of1 km and a phasespeed ofc = 17m s -•. These spatial and time scales basically determinedthe instrument u= g CO-•F' exp[i(ky - cot - •)] (3) locationsand the sampling rates. 3. Tim EXPERIMENT AND Tim OBSERVATIONS v = gkco-lFexp [i (ky- cot)] (4) For this experimentwe were able to obtain two Seadata635- andthe pressure perturbation p obeys 12S instrumentscapable of measuringboth wavepressures and p = pgF exp [i (ky - tot)] (5) currentsat wind wave periodsand longer. Thesewere deployed on bottom-mountedtripods so that the sensorswere 1.5 m off the wherep is the waterdensity and (5) followsfrom p = pgTI. bottom. To resolve wavelengthsof-1 km or longer the Hence v and p arein phase,each leading u by 90ø. instrumentswere deployed560 m apart and 100 m from the Theatmospherically forced problem was studied by Buchwald coastal cliffs in 21 m of water.The sampling strategy was to andde Szoeke [1973] and Viera and Buchwald [1982]. As their simultaneouslyburst sample 512 samplesat 2-sintervals (for a depthprofiles have a verticalwall at thecoast, the edge wave durationof 17min and 4 s) withbursts occurring each 30 min. Wave periods(<4 s) unresolvedby the measurementswere not x(km) 0 2 4 6 expectedto seriouslyalias the data as a resultof the depth attenuationof shorter-periodwaves. During the experimental 50•_.• • I I I I I•- observationperiod, only one significantstorm occurred, and this storm developedgradually rather than arriving as an easily H(m)J identifiable front. A typicalburst of stormdata comprisingpressure p, offshore velocity u , and alongshorevelocity v componentsis shownin Figure 3. Superimposedon the raw time seriesare low-pass- filteredtime seriescalculated using a discreteFourier transform filter with frequencydomain tapering and a half-powerperiod of 40 s. Wind waveamplitudes are clearly considerable (-1 m) with significantorbital currents for waveswith periodsof-8-20 s. The low-passeddata show the existenceof persistentlonger-period

1 T = 1 28 m•n (-2-20 min) oscillationsof muchsmaller amplitude (-20 cm) and P 4 6 current(--10 cm s-x). Suchlow-frequency oscillations are often referredto as infragravitywaves. Similar plots were obtained for many other burstsduring the storm,and in all casesthese lower- frequencyoscillations existed. Before the storm, amplitudes were Fig.2a. Theoffshore depth profile together withthe offshore structure of negligible, and as the storm gradually developed, theamplitudes thepressure (sea level) field for the zeroth and first mode edge waves of of the lower-frequencyoscillations increased at aboutthe same period1.28 min and3.33 min foundfrom the theory. rate as did the wind waves. MIDDLETON ET AL.: EDGE WAVES 9489

- f: 0 073 s -1

_ / '1'1 _ - /1'x'J// .5- ...... -.--T/X•/'• ' 0'02...... ' _/ ',___- ...... _-- .... - •0.0 (] '__ 12 24 12 24 /• 12 24 12 5- - 00 - /15x•x 10uJZ

12 24 12 24 12 24 12 24 DAY 2 DAY 3 DAY 4 DAY 5

Fig. 5. Spectralestimates (b(/') of windwave, edge wave and envelope seriesplotted in theform f •(f ) asa functionof timefor selectedbands centeredaround the indicatedcyclic frequencies f Wind wavespectra are plottedon the upperaxes, while infragravity(solid line) and envelope TIME (MINS) (dashedline) spectraare shownon the lower axes. Eachestimate has 120 Fig. 3. Time seriesof pressurep, offshorevelocity u andalongshore degrees of freedomand is plotted using six consecutive bursts of data. velocityv for a singleburst of 512 samplesat 2 secondintervals. Overlaid onthe raw data are low-passed timeseries obtained fromthe raw data infragravity current and pressure fluctuations in the time series, usinga frequencydomain filter with a cosineshaped taper centered at a frequencyof0.025 Hz. thespectral estimates rise once more. Although the time series used were not strictly stationary,the spectraldistributions of To examinethe energy contributions in the frequency domain, Figure4 aretypical of thosefound for individualbursts, although spectralestimates for p, u andv werecalculated for eachburst. To theburst spectra were of coursesubstantially noisier. maximiseresolution, while maintaining good statistical reliability, To investigatethe growth of thespectral energies, calculations thespectral estimates at eachfrequency were ensemble averaged of spectralestimates as a functionof timewere made for selected with thosefrom all otherbursts on the sameday, giving96 frequencybands. In eachcase, spectral estimates were obtained degreesof freedom.Figure 4 showsspectral estimates from the by ensembleaveraging over 6 bursts(covering 3 hours),and band southernlocation for theday of maximumwind wave energy. It averagingover 10 adjacentestimates in the frequencydomain is clearthat in eachcase, there is significantenergy at periods of givingan effective cyclic bandwidth of -0.01 s-a. Theestimates 5-15 s (windwaves) and that a spectralgap exists at periodsof for eachconsecutive 3-hour period are plotted for theentire storm 2040 s. At periodslonger than -40 s wherewe observethe for the northernSeadata in Figure5. For the wind wavebands centeredon cyclicfrequencies of 0.073 s -a, 0.083s -• and0.102 s-a, thespectrum for thehighest frequency rises first, followed by

t000 the spectrumfor the next highestfrequency. The spectrafor the 9 9 % longer-periodwind wavesrise later,but to largervalues. Energy p :too, is thus fed to longer and longer period waves as the storm develops,with the high frequency waves (0.102 s -a) approaching 1oi some "steady state" value quite early in day 2. The spectral estimatesfor the infragravitywave band centred at 0.005 s-a include contributions from -0.001 s-a to 0.010 s-a and thus are essentiallyestimates of the entire observedinfragravity wave spectral energy. Of interest here is the similar shape of the lower-frequencywind wave bandand the infragravitywave band; both bandsrise and fall in proportion.It thereforeseems likely that it is the wind wavesof longerperiod that are feedingenergy into the infragravitywaves. This linear dependencebetween the incident longer-period wind wave energy level and the t infragravity energy level has been observedby others [e.g., Tucker, 1950; Guza et al., 1984], althoughthe data are usually u presentedby meansof significantwave height estimateswhich mask any frequency dependence. The present spectral .01 calculationsshow clearly that the infragravity (---200-speriod) waves grow linearly only with the longer-period(11-14 s) wind 0.0 .05 .t0 .t5 .20 waves,but not with the shorterperiod (---10 s) waves. FRF.OUENC¾ (CPS) Tofurther investigate therelationship between wind waves and Fig.4. Spectralestimates ofpressure p0cP_a2/.cps), Offshorevelocity u infragravity waves, the pressure time series were band passed to Seadata.(m2s-2/cps) Each andestimate alongshore was calculatedvelocityvby(m ensemble 2s-2/cps) averagingfrom the oversouthern the retaincyclic frequencies between0.065 and 0.095 s-z ' Envelope spectraland cross-spectral estimates for48 consecutive bursts, giving 96 timeseries for theband-passed data were then found using the degreesof freedom. methodoutlined by Bracewell[1978] andMelville [1983]. Figure 9490 Mn)DLETON ET ^L.: EDOE WAV•

./envelope N

00.50 25 (M) -1 • bond-pos$filtered 10'

IV V v- 1800 2000 2200 2400 • -•J •ow-passfiltered vV 19 JUN 1984 Fig. 8. Time seriesof sealevel found from thepressures recorded by two ...... ' , Aanderaapressure gauges separated by 10 km in the alongshoredirection. TINE (NINS) The characteristicoscillations beginning at -1900 LT in the southem(S) data and -1920 LT in the northem (N) data are associatedwith the H•. 6. • •ad-p•s•ad(0.•5 infragravity wave pressure time series of waveshaving large amplitudes have a highradiation stress for the sameburst is shownon the lower set of axes. The wind which causes an expulsionof fluid below, thus leading to a waveenvelope has significant low-frequency energy, and there is reducedmean sea level. High wave envelopes are therefore rcout somevisual correlation between the envelope and the infragravity of phasewith variations in themean sea level. This feature is wavetime series. Similar calculations of the spectral energy of clearlyevident in thepresent data, indicating that a substantial theenvelope time series were made as a functionof timefor a amountof energyin theobserved low-frequency oscillations is frequencyband centered on f = 0.005s -] andthese are presented locally forced by the wind wave envelope. in thelower section of Figure5 for directcomparison with the Asexplained earlier, for theparticular storm observed with the infragravitywave results. The envelopespectra (dashed line) Seadams,the wind stressgrew gradually, thus preventing any growsimultaneously with boththe longer-periodwind wave studyof the impulsivegeneration mechanism. Some weeks spectraand the infragravity wave spectra (solid line), indicating earlier, however, two Aanderaa pressure gauges were deployed in thatwind wave energy is transferredto theinfragravity wave thesame region with a 10-kmseparation during the passage of a frequenciesthrough the wind wave envelopes. This conclusion is strongfront. Thisfront arrived in theSydney region at about reinforcedby calculationssummarized by Figure7, whichshows 2000LT onJune 19. Calculationsof the speed of thefront from spectralenergies, coherences, gain and phase lag betweentime Bureauof Meteorologymean sea level atmospheric pressure data seriesof windwave envelopes and the observed time series at suggestanaverage front speed of -8 m s-]. Timeseries of sea infragravitywave frequencies. Here spectral and cross-spectral level data are shown in Figure8. Oscillationslooking remarkably estimateshave been ensemble averaged over the 48 burstsof day like the Cauchy-Poissonoscillations depicted by Lamb[1932, 4. Spectralenergies for theenvelope series are larger than those article238], and observed by Munket al. [1956]are evident at for theinfragravity wave time series by a factorof 20;however, -1900 LT (southerngauge) and-1920 LT (northerngauge). The asis shownby thegain (wherein only the coherent contributions time lag betweenthe oscillations suggests an apparentspeed of arecompared), there is approximately10% as much coherent propagation of-8 m s-•, consistentwith the speed of thefront, energyin the infragravitywave spectrum as in the envelopeand it thereforeseems likely that the oscillationsare indeed specmun.Coherences are significantover much of theplotted Cauchy-Poissonoscillations caused by the impulsedue to the moving front. Calculation of the phase speedsof lower-modeedge waves •000/ 100• .50 showstheir speed (>17 m s-•) to be muchlarger than the front speed. Thus it is unlikely that the resonantmechanisms proposed • 5oo• o• • by Buchwald and de Szoeke[1973] and Viera and Buchwald [1982] would be effectivein thiscase. "' o/ , , • o.o , , *• 4. COMPARISON OF OBSERVATIONS WITH EDGE-WAVE THEORY o.o .5• .• o.o .5• .& One methodof comparingthe infragravitydata with theoriesof edge wave propagation is to measure coherenceand phase betweentime seriesof observationsseparated along the direction _ **+, tj j of propagation. Values of coherencesquared and phasewere (uz 1.i 360 calculatedfor day 4 of the storm (June 30), this particularday -.r-o o o o o ø o Do I being chosenbecause the stormand the infragravitywave spectra t,_) o Doo I ...... •oe,, 95 • were largest. The spectral and cross-spectralestimates for O0 oo.... o ..• 0 0.0 .01 .02 0 o .d• .d• pressureand velocity time serieswere ensembleaveraged over all FI IEflUENCY (CPS) FRE•UENCY (CPS) bursts taken on the day, and values of coherencesquared and Fig.7. Spectralandcross-spectral quantitiesof the pressure envelope phase are shown inFigure 9. Allvalues ofcoherence squared are timeseries (E) and the observed time series (R) at infragravity frequencies, plotted, while plotting of phaseswas restricted to thosepoints ensembleaveraged over 48 bursts. where the coherencesquared exceeded the 95% confidencelimit MIDDLETON ETA!..: EDop. WAVF.S 9491

t.0 P

0 0 .0! .02 0.0 .0! .02 0.0 .0! .02 270, .. • 27ø/ , ø•1x2/

,,, 90 9o ,l' 90 ••

-90 ,• -90 -90 0.0 .0! .02 0.0 .01 .02 0.0 .0! .02 FFIE9UENCY (CPS) FFIEOUENCY FRE9UENCY (CPS)

Fig. 9. Coherencesquared and coherence phase plotted as a functionof frequencyfor the pressuretime series,the offshorevelocity time series,and the alongshorevelocty time series. The point estimatesare foundfrom the data, while the solid lines indicatephase lags predictedfor northwardpropagation of edgewaves by the theory. for the null hypothesis. The nonstationarynature of the time of the current signals being more easily affected by local seriesis less importantfor calculationsof phasewhich are not topographicirregularities. Phases are also somewhatnoisy but expectedto be dependenton theenergy levels. arereasonably consistent with thetheoretical predictions. There are severalnoteworthy features. Observedcoherences There appearto be no phaseestimates suggesting a southward betweenthe pressure time series are significant over most of the propagatingwave, so we concludethat the majorityof the rangeof periods(1-17 min). The observedphase lags (point observedlow frequencyenergy lies in northwardpropagating estimates)show a generalincrease with increasingfrequency, infragravity waves, with propagation rates being consistent with indicatinga northwardpropagation. Predicted phase lags (solid edgewave theory. lines)from the theory for the first three edge wave modes are also Anotherway of examiningthe properties of theoscillations is plottedfor comparison.The observationsare in general tocompare the relative amplitudes and phases of thepressure data agreementwith the theoryover most of the frequencyrange andthe onshore-offshore velocity field as a •anctionof frequency. plotted,although the scatterin the observationsprecludes a Thesecalculations were made from the datausing a frequency precisedetermination of which modes are responsible. responsetype of analysis,wherein only the coherent contributions Theoffshore and alongshore velocity coherence squared and at anyfrequency are considered. The results predicted by theory phasecalculations are somewhat different. Coherences arevery for thegain and phase (solid lines) are compared against the muchlower than those for the pressure series, probably asa resultestimates obtained from the data (point estimates) inFigure 10 for both the northem and southem Seadatas. In each case the observedphase lags are a little larger than the value of 90% predicted by edge wave theory and this may be due to the orientation chosen for the alongshore(and hence offshore) oaz t.0S t'04N direction. The orientation of the coastline was chosen to be •{D• .5 ,.,'",.,% .5 '"on n ILl 0 DOø 035øT, however as was outlined earlier, local small-scale f_•o ø o oø oø'"!3 ool 3 øo on topographicvariations might play an importantrole in "steering" 0.0[--_p-,-o -; ,,.,'",Y øø t 0.0 ko-oo.., o o. , ,-,,.,95, the currents. Estimates of the gain also show good general o.o .o• .o2 o.o .6• .6• quantitativeagreement with that predictedby edge wave theory, ß08 .06 althoughagain there appearsto be substantialnoise.

v mode In both the plots for the nonhem and southemdata, there are •_.03 .03 frequency bands where both the gain and the phase appear anomalous.These might be due to the relatedclass of "leaky" z ,-, 0 edge-waves or to reflected infragravity waves whose energy propagatesbut is not confined to the modal structure,nor to 0.0 0.0 .... o.o .6• .6a o.o .o• .oa propagatingalong the coastalwaveguide. 270 270 In general,however, thesepressure-velocity results show that the observed infragravity oscillationshave properties fully consistentwith unforcededge wave theory. ua90, 90 5. DISCUSSION Observationsof pressureand velocity made in the coastal -90 , , -90 , , oceanoff theRoyal National Park south of Sydney,Australia, -Jo.ot .6• .6• o.o+' ' .6• .62 show that infragravitywaves with heightof-20 cm and velocity of-10 cm s4 existat periodsof 40 s to 17 min duringstorm Fig. 10. Estimatesof coherencesquared, coherence phase, and gain for events. Theseinfragravity waves are apparentlylocally forcedby the pressureand offshorevelocity components for eachof the Seadata records.Solid lines in the phaseand gainplots are foundfrom the theory the radiation stress associated with the incident wind wave whilethe point estimates are found from thedata. envelope, yet the alongshore propagation speeds and the 9492 MIDDLETONET •a..: EDOmWAVES

P u v

0.0 .0• .02

', 0.0 .0! .02 FREI3UENCY(CPS) Fig. 11. Asfor Fig. 9, exceptthat calculations are made for the envelopes rather than the time series. pressure-velocityrelationships are consistent with those predicted where too is thecentral wind wave frequency and tx0 is theangle from unforcedlinear edge wave theory.These ideas seem of incidencein deep water. Knowing the angle of incidenceatthe somewhatcontradictory; however, from earlier calculations it was pointof observation,tx0may be foundby assumingconservation foundthat valuesof coherencesquared for the envelopeand of alongshorewave number as the windwaves shoal. For the infragravitytime series (Figure 7) aregenerally significant but presentcase where too -- 0.44-0.56s-] (correspondingto wave lessthan 0.5, as are valuesfor the southernand northern periods of 11-14s4), or0 .= 10ø-30 ø,and the range of speed of the infragravitytime series (Figure 10). Thusan explanation forthe forcingis = 17-64m s-], againquite consistent with the range of apparentcontradiction is that the observedinfragravity waves speedsfor the lower-mode edge waves. most probablycomprise of both locallyforced and freely Theedge wave spectral energies are observed to developand propagating(edge wave) oscillations. The separation of forced decay with time through a stormin stepwith the longer-period andfree infragravityoscillations and the identificationof the (-14 s) windwaves, suggesting a continuing energy transfer, forcingmechanisms have proved elusive in otherstudies even throughpossibly one or bothof theresonant mechanisms outlined wherethe instrument arrays are large, and we donot believe that above.The majority of energyappears to be transferredvia these theseissues can be properlyaddressed with the present data set. mechanismsrather than throughan impulsivegeneration Somediscussion of possibleforcing mechanisms is, however,mechanism, although this experiment was not a goodtest for the appropriate. impulsivegeneration theory or for Worthy's[1984] theory of Onepossible mechanism is a resonantmatching of alongshorewind-generated edge waves which is practicallyapplicable to propagationspeeds of envelopesand edge waves. To investigatewaves of periodlonger than 15 min. this mechanism,coherence and phase estimates were calculated Thereare severalimportant factors which need consideration, for envelopetime series from the southern and northern Seadatas, given that a relativelyenergetic infragravity wave signal exists in andthese are plotted as points in Figure11. Superimposed onthe theSydney coastal region. First, harbor resonance isliable to be a phasediagram are thepredicted phases for the firstthree edge continuingproblem for harborssuch as Port Kembla where the wavemodes (solid lines), and the general agreement confirms the firstmode seiching period (-3 min) occursat periodsfor which matchingof envelopeand edgewave speeds. Coherences are infragravitywaves are active. Second,standing edge waves generallylower thanfor the infragravitytime series calculations produced by reflectionfrom headlands may provide a generation (Figure9), addingfurther weight to the contentionthat some of mechanismor a transportmechanism for the large submerged theenergy resides in naturaloscillation (edge waves). Estimates sand beds which exist further north in the Sydneyarea [Gordon of envelopespeeds are readilyfound in the followingway. andHoffman, 1985]. These sand beds exist at 30- to40-m depth, Calculationsof the direction of the incident wind waves as correspondingto distancesoffshore of 1-3 km. As is indicatedin measuredby the instrumentsindicate that the wavespropagate Figure 2, theedge wave structure is suchthat for periodsof-3 basicallyfrom the south to southeastquadrant. Wave envelopes min or longer,significant edge wave currents will existas far as approachingthe coastline,which has an orientationof -035ø- 4.5 km offshore.At a 3-min periodthe mode0 wavelengthis 215øT,will propagatealong the coastline at a phase(and group) approximately3.2 km long,a lengthscale comparable with the velocityof c/sinct. Here c is the phasespeed of the shallow observedsand beds. water waves,and ot is the anglebetween the incidentwaves and thenormal to the coastline asmeasured bythe Seadatas. For the Acknowledgements.Thiswork was supported byMarine Sciences and Technologiesgrant 83/1176.We thankGreg Nippardand David presentcasewhere the coastal depth is-20 m, c -- 13 m s 4, ot= Griffinfortheir mooring expertise, Steedman Lidfor the provision ofone 5ø-20ø,and the apparent speed of propagationof the envelopes Seadata 635-12s andfor reading thedata tapes, and John Biddlecombe and alongthe coast is 35-150m s4, overlappingthe range of speedsDave Adams for the useof M.V. Laura-Eand M.V. Elizabeth, of freeedge waves of zerothmode (17-32 m s4), firstmode (29- respectively.BobGuza, Graham Symonds, andthe anonymous reviewers 68m s4), and second mode (38-192 ms 4) atperiods of3.3 to 17 providedhelpful comments onan earlier draft. min. Theconcept of forcingby resonant triads, proposed byBowen REFERENCES andGuza [1978] and supported by laboratory experiments, Bowen, A.J., and D. L. Inman, Edge waves and crescentic bars,J. predictsresonant forcing at a phasespeed of g(2co0sin or0) 4, Geophys.Res., 76, 8662-8671, 1971. MIDDLETON ET AL.: EDGE WAVES 9493

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