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R. SILVESTER *

BEACH PROFILES AND LITTORAL DRIFT ASSESSMENT

Typical or standard profiles if established Shoreline slabilily. for a given climate and sediment charaete­ If a theoretical or empirical relationship could ristic, couId prove useful as a yard stick of sta­ be developed for a given wave climate and sediment bili,ty. The balance of vohllnes in a storm and characteristic, in terms of a stahle undenvater pro­ profile wonld permit the assessment of immi­ file, a measuring stick would be availahle with nent beach degradation. The many formulae deriv­ which to gauge any shoreline. Should a beach sec­ ed for li ttoral and littoral drift need atten­ tion be significantly steeper than the "standard," tion, as also the many praetical variables involved reasons for erosion should be sought and necessary in their measurement. Greater cognisance should remedial measures taken. Should the profile be be taken of sediment transport offshore from the flatter than normal, transient accretion mav be . indicated, such as humps traversing the " [1 J. For oceanic mal"gins the wave climate in this respect is closely associated to the persistent swell, but in enelosed storm are the sole source Beach profiles of wave energy. In the latter case the profile beyond the permanent offshore har must be related to a wide'ly varying spectral width. Some relation­ ship may be derivable which employs average In order to assess the probable movement of energy pel' unit area of , logether ,vith mean sediment it is necessary to compute the amplitude sediment characteristics [2J. and velocity of water parüCile motion near the bed. '1'0 do this the depth of water must he lmown. Hydrographie charts supply a reasonably aecurate Sweil 10 storm profile. profile of the deeper zones of1', which change One of the major concerns of the coastal engineer imperceptibly over a number of decades. For is the prohable loss of beach in a future storm depths less than 10 fathoms, however, CUITent sur­ sequence and the depth ta which the eroded sur­ vey data are required. face may fall. If this kno,vledge were availahle he Before detailing attempts to define beach pro­ could advise on the safe limit for beach encroach­ files in terms of wave and sediment charaeteristics ment for commercial purposes and the depth to it is pertinent to question the need for such infor­ which pipelines and cables must he laid through mation. The answers should provide a lead for the heach zone. Most heaches are subjeet lo storm future research inln lhis malter. waves at some lime, generally on a wintel' summer sequence. These may be accompanied by higher than nonnal water levels, which must be allowed • Pr'ofessol' Coasta! Engineering, Asian Institute of Techno­ for in any forecasting procedure. Heference [aJ logy. 13anglwl{, Thailnnd. details the long tcnn effects in the erosion process, 615

Article published by SHF and available at http://www.shf-lhb.org or http://dx.doi.org/10.1051/lhb/1969049 R. SILVESTER whereas the present discussion refers to anv spe- cified swell-built beach profile. . _--...,Swell buUt profile ....1' Profil créé par /a houle A typical transposition from sweIl to stol'ln-wave rectangular profile is depicLed in Figure 1 A, in 'which the se­ equivolent ta Storm seo level storm wave ", Niveau de tempête 1 condary undulations can be smoothed to straicrht profile tJ rectangle Hnes as. indicated, whilst preserving equal areas of équivalant au profil de houle the val'lOUs sections. If the swell profile can be de tempête :~~::t;~:~~. defined, up to the average beach level R *, plus the storm wave beach depth d s and the overall width Z, then manipulation of the profile can be carried out to give equal volumes of beach erosion and submarine accretion (See Figure 1 B). As seen, a probable elevation of the normal water level d' duri'Ilg the storm cycle can be seen to displace the beach Hne back an amount Z'.

Theorelical analyses. 1/ Swell and storm-wave beach profiles showing : A. Equi­ Sitarz [.4, ?] has developed equations, based upon va1ent rectanguhu' sectioll. B. Degree of recessioll hy e.nergy pnnclples, for the profile beyond the breaker halancing volumes. :hne to the limit of bed disturbance. He has also Pro/ils de plage cOl'respondant à des houles ordinaires et determined the width of the sweH and storm-wave de tempête. En A : section rectan{Julaire équivalente. En surf zones, and the cross-sectional area of the water B : de{Jl'é de ré{Jression exprimé pal' le bilan des volumes. in the surf zone.

The offshore profile is given by: 10

0.8 x= ay2 and: 0.6

(1) 0.5 where: 04 o x is distance seawards from the breaker line; (mm) 0.3 f···················· y is depth below SWL; S is ratio: density of sediment to (:2.6); • 0.2 D is median sediment diameter at some appro­ priate depth (mm); H is just offshore from breaker zone (metres). O. 1 L-.L:-_L-~ -'---_-'---'--_-'---'--'--'---'._~. __...l.__-'-- 0.01 0.02 0.03 0.04 0.06 0.08 0.1 0.2 Beach slope m Pente de /a plage From equation Cl) it can be seen that the milder slopes ~ccur with lm'ger values of (a), which in turn 2/ Natural slopes for with various sizes and result trom finer sediment or smaller waves. The exposures to waves. u.sual,value of S = 2.65 is applicable to most sand Penles naturel/es de plages en fonction de la grarllliomé­ sItuatIons. trie du sable et de lelll' exposition rI la houle. It appears strange that wave period does not enter. this n~lationship, since on this depends the amplüude of water particle oscillation, as much as ficant height (HI/a), [6, 7], which is defined as the ':av,~ h~ig~1t. Similarly the mass transport "velo­ average of the third highest vmves in the spectrum cIty wIthm the boundary layer also is dependent [8]. The diameter of sediment D (mm) would be ~trOl~gly on the period. In the overall picture it that at the beach face and hence ,vould dift'er from IS tins factor that determines the refraction pattern D in equation Cl). and hence the proportion of the deep-water wave The cross-sectional area of water in the surf zone height occuring near the breaker zone. is given by: The width of the surf zone Z is given by: 3.4 gl/2H2T A-··················- (S "':_-ITii2Dl/2 (3) 2 r BH-31 Z = ------.--- (2) where: (S -- 1)l/2DI/2 H is signifieant wave height (metres); T is signifieant period [8] (seconds); where H and D are of dimensions similar to those in equat~~n (~). Factor B = 4:1.5 for a swell pro­ D is median sediment diameter (mm); file ~md la.O 101' a storm profile. In the latter case g is n.81 metres/see2 ; the height H eou]d weil be represented by the signi- S is sediment to seawater density ratio. Division of equation (3) hy (2) gives the mean • Symbols used aI'e listed nt the end of the paper. depth of the surf zone (d" in Figure 1). This could 616 LA HOUILLE BLANCHE / N° 6-1969 be compared to the depth of Hl/a which approxi­ lengthy period of swell. Also the wave c1imale mates the mean depth as suggested by BrulIn [6]. shollid be expressed in average conditions over the The slope of the swell built beach face is best part of the year when this swell incidence occurs. taken from prototype measurements [\), 10] which Any criteria should he derived for both oceanic are summarised in Figure 2 for three conditions of and enclosed conditions, since the latter will exposure. The slope in a face is of experiencc mainly storm type waves rather than little consequence compared to the other relevant sweU. dimensions (See Figure l). The lleight of the beach above S\VL should be measured where possible, since the calculation from wave and sediment cha­ raeteristics involves too many variables ta serve any Littoral drift practical purpose. Other workers [11, 12, 13] have attempted to relate the offshore bed profile to ,vave climate, but much more wave data are needed on before Vvaves arnvlng obliquely to a shoreline are re­ specific equations can be quoted. The arder of fracted as they traverse the , thus differences that exists between such relationships tending to move more nearly normal ta the bed can be gauged by that for the formulae by Sitarz contours. However, on breaking, the crests are still [4, 5] equation (l) and hy Larras [12] as follows: angled slighUy to the beachline, so that a component of their energy is directed a'long the shore. This produces a littoral current which, together with (4) the suspension of sediment due to the present, effects a transport of material known as where: "littoral drift". Ho Dl / 2 -~ Since the water momentum generating this Cllr­ K = + O.03\) (S-=-l)lI;) rent can he assessed from knowledge of the wave and: energy, and its longshore component, it is possible to relate deep-water wave charaeteristics to both the current and the volume of sediment carried. There are factors such as energy dissipation, bottolll where: perco'lation and wave reflection which are difIicult ru is the heach slope; to account for, hut information is heing accumulat­ Ho is the deep-water wave lleight [9]; ed which indicates general values. But as indicat­ ed by Sonu 'et al. [14] the several formulae they L o is the deep-water wave length, and other va­ riables as before. examined [15, 1H, 17, 18, l\), 20, 21, 22] did not agree with the measurements made over some 6 The constants refer to Ho and Lo in metres and months. They concluded: "Under natural condi­ D in mms. tions, the nearshore topography participates in the Substituting D = 1 mm, '1' = 12 sec, and H = 1 longshore CUITent mechanism as a dynamic varia­ metre inequations (1) and (4) results in x = 0.75 y2 ble, not only redistributing the hreaker influx into (Sitarz) and x = 0.025 yU (Larras). different positions along the shore but also itself un­ The former is much more uniform from the dergoing displacements and transformation due to x = 0 at the breaker line, whereas the latter proba­ the waves and the currents thus afl'ected." Any hly refers more to the zone some distance from this meaSllrements taken during a transition period origin. The anomalies indicate the need for fur­ from the storm-wave profile to that of the swell ther data on these profiles, so that standards could profile is certain to be a failllre, even though the be derived to test for heach stability. deep-water wave characteristics may be steady and One difIiculty in using such measurements, which weU defined. include a wave height and wave length (or as noted Further formulae have become avaiIable, the above a wave steepness) is that these vary from theoretical aspects of which disagree amongst them­ hour to hour. \Vith each change the sand ripples selves and previous papers [23, 24, 25, 26, 27, 28, associated therewith are aHered and so, in given 29, 30, 31, 32]. These differences arise from using time, is the profile. During these transition periods either momentum or energy fluxes of the breaking the sediment in transit 1S at a maximum. Thus an wave and employing theo1'Y for thes1nusoidal, equilibrium profile would take some days to esta­ cnoidal or solitarv waves in the transition and shal­ blish itself even with a steady input of wave energy low water zone. v Most workers have based their with uniform characterislics. computations on a single sinusoidal wave which Adding to the above dynamics of the beach pro­ cOllld well represent the persistent swell situation file, is the seasonal winter and summer sequences on an oceanic margin, if its characteristics are of storm and swell. The storm waves transfer suitably chosen. Bruun [6, 7] has specifically portions of the beach offshore to form a bar. Sub­ dealt with the storm beach profile, but the transient sequent swell returns this to the beach, but this condition in respect to wave height, period and di­ task may take several weeks or even months. Dur­ rection makes application in this case extremely ing this time the profile recorded would not be in subjective. equilibrium, since material is being transmitted The step l'rom littoral Cllrrent to littoral drift through it to the beach. involves empirical factors, provided ei,ther from Thus, ta obtain a "standardised" prome for any models or prototype data. In order to indicate the given wave climate and sediment characteristic, variables involved the obtained by Cas­ measurements should be taken at the end of a tanho [:30] will he outlined, since this is the result 617 R. SILVESTER

of a comprehensive study, but has not been report­ wriUen for the root-mean-square "mve height, cd ,videly. Using the solitary-wave them'y he ob­ which is the wave parameter most commonly mea­ tained: sured in the laboratory. However, the power com­ putation for the field data appears to be based on (5) and thus may be too high by a l'acter of 2. On the other hand, the practice where: of representing the entire power spectrum in terms G= of sediment moved pel' second of a single significant wave may result in the omis­ aeross a plane normal to the beach; sion of important energy contributions l'rom waves energy dissipated of difTerent frequency, causing the computations Er l()ùgsh 0 rèèllei'gY-Cüiili;()Iièiit to he too low. A rigorous evaluation of this rela­ tion is essential to beach planning." = SUl" a" l' [ :cc.~--"--mHb . hl tan ab Lb J In this respect the substantial difTerence between storm waves and the more prolonged swell condi­ where: tion should be kept in mind. 'Vith the former the concept of significant wave or energy of the spec­ m heaeh slope; trum is important, whereas with swell waves an Hb/Lb H,,/CbT - H,,/\/1.18 gd-~T H,JylTi8 g 1.:3 :H~)T

K' - roughness factor; P pel' unit length of shore; - 2.2 wHb:J sin ab cos ab/T wHo2Lo sin ab cos ao/16 '1' where w is the speci-fic weight of sea­ water;

equation (5) can be reduced to: 3/ Variation of 1':,. (Equation (i) with wave steepness and (6) obliquity. Yariation de 1\ (équation 6) en [onction de la raideur et de l'obliquité de la houle. The value of ab depends llpon ao and the wave steepness Ho/Lü [33, 34J, so that both Er = f (0.12/ tan ab) and siu ab cos ao have been graphed against Ho/L in Figures :3 & 4. Sinee equation (6) is o ~ sin ab cos <%0 dimensionally homogeneous any appropriate units 0.35 may be employed in solving for G. Inman and Frautschy [35J have derived an empi­ 03 rical relationship between immersed weight pel' second passing any point and wave power pel' unit 025 length of coast. In terms of equation (5) ihis is:

G = P/4 (l-l/S) (7)

and is graphed in Figure 5, together with data supplied l'rom references [:37, 38, 39, 40 J for labo­ ratory tests and references [41, 42, 43J from -field measurements. The hatched zone indicates the location of the bulk of the laboralory results. o1-0 -~;;;----:O"J,.O"'-o~.0"'15;---';0.!,;-.02;;---;Oc!;.oo.2,,---no"'03,---no.7;;o,,-,,--,o~.0>44--,~,,1i Awepting the value of tan

Conclusions Z: width of stonn-wave surf zone; Z': shoreward clisplacement of water lîne in storm wave heaeh profile at ahnormal SWL; 1. The profile of the beyond the breaker line might be related ta sediment and 'vave charac­ a" angle of waves to shore on hreaking; teristics, in arder that a measuring stick can be ao angle of waves to shore in deep-water; available ta test the stability of any given shoreline.

H : height of hreaking wave; [13J WELLS (D.H.). -- Beach équilibrium and second order b wave theory. ./. Geoph. Res., Î2 (196Î), p. 4!JÎ-504. Ho: deep-water wave height; [14] SONU (C.J.), ~lcCLOY (.I.M.) and McAl\THul\ (D.S.). ­ K: parameter in equation (4); Longshore cnrrents and nearshore topographies. Proc. 10Ul Conf. Coasta[ Eny., 1 (19(ii), p. 525-54\1. K' : roughness factor in equation (5); [15J pUT~IAN (.I.A.), MIJNK (W.H.) and Tl\AYLon (M.H.). - Lo deep-water wave length; The prediction of longshore currellts. Trans. A.ln. Lb : length of hreaking wave Geoph. Un., .10 (1949), p. :l:Ji-:J45. (= C"T = -vga;,. T); [Ui] lN~IAN (D.L.) and QUiNN (W.H.). - Currents in the surf nl : beach slope; zone. l'roc. 2nd Conf. Coasta[ Eng., (1951), p. 24-:16. p [nJ NAGAI (S.). -- On coastal groins. l'roc. 1st Conf. Coasta[ wave power pel' unit length of shoreline; Eny. in ./a[Jan, (1954). H: average heach height ahove S\VL; [18] BI\EBNEH (A.) and IÜ~[PHIIJS (.LW.I. -- ~lodel tests on S sediment to seawater density ratio; the relationship between decp-water wave characteris­ tics and longshore currents. Qlleens University, Ca­ T wave period; nada CE Hep. No. 1:1, (19G3). w: specifie weight of seawater; [HlJ GALVIN .Tr (C..I.) and EAGLESON (P.S.). -- Experimental x: horizontal distance t'rom hreaker line in stndy on longshol'c cnrrents on a plane heach. Coas/al heach profile equation (4); Eny. Res. Centre 'l'MIO, (19G5). [20J IN MAN (D.L.) and BAGNOLD (H.A.). - Beach and near­ y: depth to hed from S\VL in heach profile shore proeesses: littoral processes. The Sea (2) (Ed. equation (4); M.N. Hill), John Wiley, (19G3), p. 529-,'i5:3. 620 LA HOUILLE BLANCHE / N° 6-1969

[21] SHAIlHI:'; (l.F.). - Longshore ClllTents and cOInpensat­ [il4] LE l\lr\HAUTÉ (B.) and ROH (H.C.Y.). - On the breaking ing cUITents on the shallow eumulative heach. Trlldu, of waves arriving at an angle to the shore. .J. Hyd. Ocean. Comm. Ac. Sciences USSR, (Hl61). Res., 5 (l!Hi7), p. (i7-88. [22] BHlJlJN (P.). -- Longshore cUITents and longshore [il5] lN~IAN (D.L.) and FHAUTSCHY (.LD.). Littoral proces- troughs. J. Geoph. Res. 68, (1!Hiil), p. 1065-1078. ses and the development of shorelines. Proc. Santa Barbara Conf. Coas/al Eny., (19li6), p. 511-5il6. [2ilJ PVSHKIN (B.A.), l\IAKSDITCHOlJK (V.L.) and ZAITZ (E.S.). ­ The investigation of littoral sand transport in seas [;HiJ EAlrLESON (P.S.). - Growth of longshore eurrents and I·eservoil·s. Proc. tt/h Conf. IAHR, Leninyrad 5, downstream of a surf-zone harl'Ïer. Proc. San/a Barbara (1 !)(i5), p. 151-152. Conf. Coas/al Eny., (1 %6), p. 487-508. [24J I\AllAlJSHEY (A.V.), SUIlOLSI(V (A.S.) and SCHWAHZMAN [il7J I{r\iBlllEIN (W.C.). - Shore currents and sand movement (A ..!.). - Alongshore sediment transportation. Proc. on a model heach. Beach Erosion Board, Tech. MCI11. tt/h Conf. IAllR, Leninyrad 5, (1!Hi5), p. 1:l4-1il6. No. 7, (1!J44). [il8] SAVILLE .Jr. cr.). - Model study of sand transport along [25] BHIJl)N (P.). - Quantitative research on littoral drift an infinitely long straight heaeh. Trans. Am. Geopl!. in field and Jaboratory. Proc. 11/h Conf. IAllR Lenin­ Un., 81, No. 4, (1%0). Y1'lld 5, (1965), p. 211-215. [ilH J SHAV (KA.) and .J OHNSON (.LW.). - Model studies on the [21i] LAHHAs (.L) and BONNEFILLE (H.). - Quantités de sable movement of sand transported hy waye action along a chalTiées par la houle parallèlement àla côte. Proc. straight heach. UIl. of Cal. Berkeley 1ER, Issue 7, Sel'. tt/h Conf. !AllR Leninyrad 5, (1!Hi5), p. 2:1il-2illi. 14, (1\J51). [27] WV!\'rKi (1\.). - The balance of littoral transport in the [40J SAUVAGE (M.G.) and VINCENT (lILG.). - Transport litto­ surf :onc. Dell/che. Hyd. Zeit., li (Ul5;1), p. (i5-75. l'al; fonuation de tlèches et de tombo!os. Proc. 5/h Conf. Coas/al Eny., (1955), p. 296-:128. [28] ~lAsHIMA (Y.l. Study of littoral dl'Ïft and longshore CUrI'ent. Coas/a/ Eny. in Japan, 1 (1H58), p. 85-!Hi. [41J WATTS (G.M.). - Study of sand movement at south Lake \Vorth , Florida. Beach Erosion Board, Tech. [2!)j EAGLESON (p.S.).._- Theoretieal study of longshore cur­ Mem. No. 42, (1\)5il). l'el1ts on a plane beach. }[ass. lns/. Tech. Dept. Civil Enfl. Hep. No. 82, WHi5). [42] CALDWELL (.LM.). -- \Vave action and sand moyement near Anaheim bay, California. Beach Erosion Board, [:lOJ CASTANHO (.J.). - Breaking waves and littoral drift (in Tech. l\Iem. No. G8, (1!l51i). Portugese). Lab. Nac. de Enfl. Civil (Lisbon) Mem. [4:l] MOOHE CG.W.) and COLE (.J.Y.). - Coastal processes in No. 275, (19(j(i). the vieinity of Thompson, Alaska. V.S. GeaI. [:H] lWAGAKI (Y.) and SAWAHAGI Cl'.). - A new method for SlIl'I.leU Trace ElemeIlts lIlvesfiya/ioIls, Hep. No. 75il, estimation of the rate of littoral sand drift. Coas/al (H)(iO), p. 41-54. Eny. in Japon, ;j (1\Hi2), p. (i7-7!J. [H] SILVESTER (H.). - Stahilisation of sedimentary eoastli­ [il2] EIlELMAN CI'.). - Littoral transport in the hreaker zone nes. Na/lire, 188, No. 4H\J, (1!JGO), p. 4(i7-469. causes by oblique waves. Proc. 10/h Conf. lAllR, Lon­ [45J YASSO (W.E.). - Plan geoIl1etry of headland, hay don, 1 (1 !Hi il) , p. (i I -H8. beaches. .JI'. Geoloyu, 78 (1!Jli5), p. 702-714. [ilil] GHOEN (P.) and WEENINK (M.P.H.). - Two diagrams [4·G] HUGHS (E.p.C.). - The investigation and de·sign for for finding breaker eharaeteristies along astraight Portland Harbour, Victoria. .JI'. IIlstn. EIlyrs. Allst., 29 coast. Trans. Am. Geoph. Un., 81 (1!l50), p. il!J8-400. (1%7), p. 55-G8.

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