COASTAL ENGINEERING Chapter 2

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1 CASTAL ENGINEERING Chapter 2 GENERALIZED WAVE DIFFRACTIN DIAGRAMS J. W. Jhnsn Assciate Prfessr f Mechanical Engineering University f Califrnia Berkeley, Califrnia INTRDUCTIN Wave diffractin is the phenmenn in which water waves are prpagated int a sheltered regin frmed by a breakwater r similar barrier which interrupts a prtin f a regular wave train (Fig. 1). The principles f diffractin have cnsiderable practical applicatin in cnnectin with the design f breakwaters as discussed by Dunham (1951) at the Lng Beach Cnference. The phenmenn is analgus t the diffractin f light, sund, and electrmagnetic waves. Tw general types f diffractin prblems usually are encuntered: ne, the passage f waves arund the end f a semi-infinite impermeable breakwater (Putnam and Arthur, 1948), and, secnd, the passage f waves thrugh a gap in a breakwater (Blue and Jhnsn, 1949t Carr and Stelzriede, 1951). In general, the theretical slutins have been fund t apply with cnservative results, that is, the predicted wave heights in the lee f a breakwater are fund t be slightly larger than the height f waves that may be expected under actual cnditins. The use f the diffractin thery in breakwater design is made cnvenient when summarized in the frm f diagrams with curves f equal values f diffractin cefficients n a crdinate system in which the rigin f the Bystem is at the tip f a single breakwater (Figs. 2a-2b, and 3) r at the center f a gap (Figs. 2c, and 4-6). The diffractin cefficient in this instance is defined as the rati f the diffracted wave height t the incident wave height and usually is designated by the symbl K». The prcedure in preparing diffractin diagrams appears elsewhere (Jhnsn, 1950). The purpse f this paper is t present diffractin diagrams t supplement the material f Dunham (1951). Fr cmplete details n the applicatin f diffractin diagrams t typical harbr prblems the reader is referred t this latter paper. Semi-infinite breakwater - The generalized diffractin diagram shwn in frtg. 3 can be applied t a particular breakwater prblem nce the characteristics f the design wave have been selected - that is, the height, perid and directin f the incident wave frm which prtectin is t be prvided. The design wave is selected either frm recrded wave data as described by Sndgrass (1951) r by applicatin f the hindcesting prcedure utlined by Arthur (1951). As an illustratin

2 GENERALIZED WAVE DIFFRACTIN DIAGRAMS 1 BREAKWATER "^ ' INCIDENT WAVES ' ft DIFFRACTED WAVESJ rm. BREAKWATER- ** *, Fig. 1 Diffractin f waves at a breakwater

3 CASTAL ENGINEERING (0 y P ai fl H P Q N ai 5* <W b<m i-4 'H <^ a a> P. V ] T a) E-t

$GENERALIZED WAVE DIFFRACTIN DIAGRAMS f the use f a diffractin diagram, Fig.$

4 GENERALIZED WAVE DIFFRACTIN DIAGRAMS f the use f a diffractin diagram, Fig. 2a shws a map f a harbr fr which prtectin is desired fr a specified reach f the shreline with waves appraching frm the directin frm which the maximum height waves ccur. Fr a given wave perid (r length) a diagram similar t Fig. 3 is pltted n transparent paper t the same length scale as the map f the harbr area. This transparent verlay then is mved ver the map (keeping the gemetric shadw parallel t the directin f travel) until the desired degree f prtectin fr the selected reach f the shreline is btained. The lcatin f the tip f the breakwater thus is btained as illustrated by the final lcatin f the verlay shwn in Fig. 2a. It shuld be nted that the diffractin diagram shwn in Fig. S is the same diagram as discussed by Dunham (1951) but applied t bth semi-infinite breakwaters and breakwater gaps. The material summarized belw presents diffractin diagrams als fr gaps and permits refinement t the slutin f sme f the prblems discussed by Dunham (1951). Diffractin at a Breakwater Gap - The treatment f diffractin prblems, as discussed in the abve paragraph is cncerned with waves mving past a breakwater tip with an infinite expanse f water existing away frm the tip. In many harbrs, hwever, waves mve thrugh a relatively narrw gap in a break.vater (Fig. 2c); hence, diffractin ccurs at the tw sides f the gap and changes in wave height in the lee f the breakwater will be different than if a single tip existed. Theries fr this cnditin als have been develped. Experimental studies have verified the general frm f the theretical expressins fr breakwater gap penings as small as a half wave length. As lng as the water depth in the lee f the structure remains cnstant the diffractin pattern is independent f the actual depth. In natural harbrs, hwever, this cnditin f unifrm depth may nt always ccur. Instead a shaling bttm usually exists - in which case the waves are nt nly diffracted, but refractin als results as the waves mve further t the lee f the structure. At a cnsiderable distance frm the breakwater, it is prbable that the refractin effects predminate ver the diffractin effects. Figs. 4-6 shw generalized diagrams which give diffractin cefficients t the lee f breakwater gaps f varius widths but with nrmal apprach f the waves. The methd f making the necessary cmputatins f these diffractin cefficients as well as the cmputatins fr the psitin f the wave frnts (shwn nly in Fig. 5a) is presented elsewhere (Jhnsn, 1950; Carr and Stelzriede, 1951). These generalized diagrams, when used as transparent verlays, can be mved ver a map f an area t btain the mst desirable prtectin, similar t the prcedure illustrated in Figs. 2a-2b fr a single breakwater.

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6 GENERALIZED WAVE DIFFRACTIN DIAGRAMS GENERALIZED DIAGRAMS Fr semi-infinite breakwaters the single diagram shwn in Fig. 3 is sufficient fr all such breakwaters with waves appraching frm any directin within the limits indicated (als see universal diagram f Dunham, 1951), In the case f breakwater gaps, hwever, a different diagram is required fr each cmbinatin f gap width and directin f wave apprach. A number f representative generalized diagrams fr gaps are shwn in Figs. 4-6, inclusive. These diagrams pertain t gaps which range in width frm t 5 wave lengths with the directin f wave apprach being nrmal t the gap. These diagrams cver a wide range f gap penings with a sufficiently small spacing f values such that ne f the diagrams can be selected and applied with reasnable accuracy t a specific prblem. Fr sme specific gap width it may be desirable t btain the diffractin pattern by interplatin between tw diagrams; hwever, the accuracy with -which the design wave data are knwn usually des nt justify such a refinement. In the event thugh that interplatin is desired, Figs are prvided which shw values f diffractin cefficients fr varius gap widths at varius XL distances frm the gap center line and at varius yl distances t the lee f the gap. These curves have been smthed smewhat t eliminate the unimprtant lbes which result frm the theretical slutins as shwn in Figs It is t be nted that in Figs. 4-6, inclusive, the diffractin diagrams have been terminated arbitrarily at a distance f 'i0 wave lengths in the lee f a gap. It is believed that in mst applicatins the effects f refractin, as discussed abve, wuld predminate by the time the waves had traveled a distance f 20 wave lengths beynd a breakwater; therefre, the extensin f the diffractin patterns t greater distances is unnecessary. When a gap width is in excess f abut five wave lengths, the diffractin patterns at each side f the pening are mre r less independent f each ther (cmpare Figs. 3 and 6b). In such cases the pattern given by Fig. 3 fr a semi-infinite breakwater can be used t estimate the height and directin f waves n the leeward side as discussed by Dunham (1951) and illustrated in Fig. 2b. Fr these relatively large gap penings the directin f the incident waves with respect t the breakwater alignment can lie anywhere within the zne indicated in Fig. 3 withut the diffractin pattern being appreciably affected. Fr relatively narrw gaps (gap penings f abut 3 wave lengths and less) the diffractin pattern can be cmputed easily by the methd f Carr and Stelzriede (1951) fr varius values f the angle between the incident wave and the breakwater. As an example, Figs shw diffractin patterns fr waves appraching a breakwater gap with a width f ne wave length frm varius directins. 11

7 CASTAL ENGINEERING -BREAKWATER Fig. 5 Generalized diagrams fr diffractin at breakwater gaps f tw and apprximately three wave lengths in width (90 degree apprach). 12

8 GENERALIZED WAVE DIFFRACTIN DIAGRAMS.BREAKWATER yl IS 20. BREAKWATER 0 2 IS IS 20 Fig. 6 Generalized diagrams fr diffractin at breakwater gaps f five and apprximately fur wave lengths in width (90 degree apprach}, 13

9 CASTAL ENGINEERING JD Xft j 22--^ Gf* ^ 7 1 i -^""'" 0 % ID fl s 0 u <H <M m Pn s) U) fc 0) -p S A (XI <l> ^ N JH ^ r 05 6* h a. (D P. ID as rh P ID,0 s" P is s ID H JH V) M> p «rt x( H a 0 s.r) 0 +> rl T) t» S3 p H a) 01 5 p -p a W) <0 a H a> a r-«h «H ID <H <s> $ 0 B 0 ID d t> 0 H H ^ 0 cs -P u <H *H <H r-4.h at ^J fa 14

10 GENERALIZED WAVE DIFFRACTIN DIAGRAMS JCl 00 ^fy ' &S^1 ^ ^ n^^ 0> a IT) rl 15

11 CASTAL ENGINEERING in.j. -J -j$2 2^ c v^ 0J f 1 G> ^ r ^ 1 c J c > 0 ) a ) h- u > ir > < t V > c J in in l a 4-4 m ti at w *H -p 1 «0).* ^ fc ^5 & at *-> t* Vn (D a. «cd rh a> <l> >,c p fl t rl CD I-. t bfl -p a> El Tt H a ^ * A P. H TJ u at > * 3 P H as Rl 0> X! +5 P a bl) a H <D a H rl «H a> «H >» P CD a > H rl <1-1 4» CD P U <H <^ <*-! l-l 3 b 16

12 GENERALIZED WAVE DIFFRACTIN DIAGRAMS. < > < 2 < 2 S3AVM 1N3QI0NI d Niiiauia H i i,a <#y 1 l ' "H 1 i - 17

13 CASTAL ENGINEERING »--' c B'lL ^ K'- 80 ^ K'-070 < K' v-v K' *1& & xl 6 8 «^ ' ^J 9^-^,0 c X; 0 4 i y L r 1^ K'-0 8 ^ K'-.. B "" "v. ' 05 ^s y K i&v 6 e X; K'-0 2 -^ 0 I yl Pig. 12 Generalized diagrams fr diffractin at a breakwater gap f ne wave length width {$ - 0 and 15 degrees). b 18

14 GENERALIZED WAVE DIFFRACTIN DIAGRAMS 30* K 1-7^ r vn^k' 2 <i0 *y l_k-0 6^^. E^ _K'-07 t-, "<^03»L V e ^^<i0? s! B IC i I 1 t 1 5 1» Fig. 13 Generalized diagrams fr diffractin at a breakwater gap f ne wave length width (jb = S and 45 degrees). N b 19

15 CASTAL ENGINEERING Fig. 14 Generalized diagrams fr diffractin at a breakwater gap f ne wave length width (p 60 and 75 degrees). 20

16 GENERALIZED WAVE DIFFRACTIN DIAGRAMS 02 K'= 0 2 e Gap width f 2 L, and <f> = 45 (slutin f Carr S Stelznede) Breakwater Scale f xl and yl Imaginary gap with a width f I 41 L, and <>=90 (slutin f Blue & Jhnsn ) Fig. 15 Generalized diffractin diagram fr a gap f tw wave lengths and a 45 degree apprach cmpared with that fr a gap f width IT wave lengths with a 90 degree apprach. 21

17 CASTAL ENGINEERING Fr wider gap penings, where blique appraches make cmputatins f diffractin patterns relatively difficult, useful apprximatins can be made by drawling a line thrugh the gap center and nrmal t the incident wave directin, and then cmputing diffractin cefficients as thugh the breakwater were alng this line the end f the imaginary fap being at the prjectins n this line f the true gap ends (Fig. 11). hat this apprximatin gives acceptable results is demnstrated in Fig. 15 where the diffractin diagrams cmputed fr a gap pening f 2 wave lengths with a wave apprach f 45 degrees is cmpared with a diagram which has been cmputed fr a 90 degree apprach t a gap whse width f pening is 1.41 wave lengths. Fr a given gap pening with an blique wave apprach the width f an imaginary gap fr 90 degree apprach undubtedly will be an uneven value. The preparatin f a diffractin diagram fr such a gap pening is easily accmplished by interplatin frm the diagrams shwn in Figs. 7-10, inclusive. SUMMARY The material summarized in this paper presents generalized diffractin diagrams t be used in the rapid slutin f wave diffractin prblems which ccur in breakwater design. The diagrams are t be used in cnjunctin with the techniques f applicatin previusly described by Dunham (1951). REFERENCES Arthur, R.S. (1951). Wave frecasting and hindcastingt Prc. First Cnference n Castal Engineering, Cuncil n Wave Research. Blue, F.L., Jr. and Jhnsn, J.W. (1949). Diffractin f water waves passing thrugh a breakwater gaps Trans. Amer. Gephys. Unin, vl. 30, pp Carr, J.H., and Stelzriede, M.E. (1951). Diffractin f water waves by breakwaters: Presented at sympsium n gravity waves, Natinal Bureau f Standards, Washingtn, D.C., June 18-20,

18 GENERALIZED WAVE DIFFRACTIN DIAGRAMS Dunham, J. H. (1951). Refractin and diffractin diagrams: Prc. First Cnference n Castal Engineering, Cuncil n Wave Research. Jhnsn, J. W. (1950). Engineering aspects f diffractin and refractin: Prceedings Separate N. 122, Am. Sc. Civil Engrs., vl. 77, Putnam, J. A. and Arthur, R. S. (1948). Diffractin f water waves bybreakwaters: Trans. Amer. Gephys. Unin, vl. 29, pp Sndgrass, P. E. (1951). Wave recrders: Prc. First Cnference n Castal Engineering, Cuncil n Wave Research. 23

Interference is when two (or more) sets of waves meet and combine to produce a new pattern.

Interference is when two (or more) sets of waves meet and combine to produce a new pattern. Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme