lecture21 - NOML! HEAR EFFECTS §OME OF THE MOST IMPORTANT...

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Unformatted text preview: NOML! HEAR EFFECTS §OME OF THE MOST IMPORTANT NONLINEAR EFFECTS ARISING IN CONNECTIMJ OOI'TH NAVE’JSOP?’ ‘N‘TEFACTIONS‘ kZE O DRIFT FORCES - THEYDRE'FHE MEAN FORCES Excmso ow FwATIMG OR SOBHEI’ZGED BODIES 8v AMBIEM'TIAJAI/ES“ HAV BE TREATED vc—zev WELL 5“! PEETUQBA'FIGN T145067 @ SLA H’Mzuc. "Mes: A25 HIG HLY NONLINEAR EFFECTS AEIS'INC AJHEN A S‘HIP SECTION (HACTS uPow ’THE OOATEK S‘oeFAcE oa OOHEIU A STEEP OR SIZEA Irma wAIIE IHPINGES UPaN A FLo/I'Tma STRUCTURE. MAY BE MGOGLED BY FULLY ofz PART(ALLY IUDN'LINE AR ?CVTE’MTIAL FLOW) HOPELS OF ANAvI‘TICAL me NUMERICAL NATU'IEE 0 Fozces DUE. ‘TO vzscws new §EPAKATIGN Akbpmo FUA'T‘INQ S,TEOCTUE€S A100 THEIR S‘u BSYSTEHS', EC. RISERS,Hoo Rwa LINES ETC. VORTEX INDUCED VIBRATION? (UN) (5 AuIMPon‘mW E YAHPVLE. 90 CH EFFECTS CA N BE "FREA 7‘50 EXPEfétMEM‘TA LLV Auo C1014 PUTATzomALLV BY Sowch THE NAUtera—STGKES Eczuprnch 0' N016 LINEAR SH 1P Ma-ncms m 3755;: WAVES THESE EFFECTS ARE MOSTLY OF PWE—WAb 5:er “147'er AND M25 {35mg TREATED Bf/ NONLrNEAQ RANKIME, pANa METHooszHE Pen MARY NON LINEA RwTy 13 THE VARIABLE wETMESSOF‘THE SHIP HULL > THE NONLINEARFCY OFTHE CINEHfl'T/CS 01> AMBIENTOJA v53 AND THE NU‘HEQICAL Sour—17m OF THE EcQuflTlmuS oFH ISTImu IN THE TM 5 Dev AfN O woman/£14K QESPONS'ES OF DEEP LuHTER OF‘F-S‘HO {as PLATFOQ—HS (N CERTAIN FLsxutzm. MODES OF THEIR TETHERS. THEJ‘E EFFECTS ARE unaww A3’3P‘EINGtN6 X 61m G’HVG AND A25 Trc GATE—D BY A CQ’MBINJQ'TIG‘IU 0F PERTOLBATtoN AUO NONLINEAR METHo D5 AM) EXPERIMEAFTS‘.~ DEWT FORCES a mar—‘7 FOEQES’ CUM—L F—HZS‘T BE CONSIDERED w REQULAK OJA «res. THE MAIN Reruun thL THEN BE EXTENDED w FAMDOLL ’wmej o out: VERY IMPORTANT PROPERTY oF Dian-‘7‘ ON THE; LWEMZ So Lu‘ncw .4, HfiAU DELFT Foam; on A VERTLCAL wALL, A Z (2..) NCAIW I K ,- - -..---,__ \M ’ x ' IL,%-—~ka+ Co“? : 4);: 02,0; fl 8 t E E w (J, H :00 Ki+£k5¢+zwt CPD: “2'9 g ‘0': } Lb: ¢z+c1>b (131:0) x20 (VETBIFY) o Mouuuauz HYDRODYNAL—HC Pizess‘uvzez _ 2d) 4m. —§> (:54 .ZLV¢.V<{> +323 0 NONLINEAR Homzou—rm (:ch5 ON THE WALL! 3 F“=‘S ’P‘Ji; =‘-~L§:t +0042) 0 we:— NEED “to EUALDATE F; coeeecr Tn CDC/43) MUTWC THAT'I'HE MEAN “('(ME VALUE OF E FFECTS OF OCA)VWH(LCH M25 LHULSAra, (g 2590. ASSUME A PEP—TURBA'TICDM EXPANSION For: 4» (MHERE THE Pmswmz, DERIVED aauerzm THE LINEAR TEBM DENOTED ABOVE 3y ck, . c [U EVALUATING: THE LEADING otz DER EFFECT INTHE MEAN HORI'Z/OAJTAL FORCE £05 DECNF‘TEEHS wth-L ZErco HEAMVA L053 012 OF OprR A3 AMI) HIGHER. we IUdTE ouc'THmrr‘ Page”? THA—T b 492(6) '=;© THE "TOTAL HG‘BIZOUTAL szce: Fx ALSO ACCEPTS "THE EXPANSION: Fx.= F-l +F2 +;3+‘1'- W \rvv OCA) omz) 0M3) , a 0 4 . 3 ° F1: X’P,A%=-Ej gcli=O€AJ -00 ‘00 4: F1“) :0 (VERIFY) 0-: 'S o F2: 3191ch +3134; =®ufl ’00 O I ’F 30(E’i’i+-‘2~v¢,-vc{>,)cia ‘34: “Q S§(D—4fl+gz>clz + OLA3> o 'at tux-m mamas 0FocA33, THE LAST HJTEGPAL HA4 BE APP ROXIHATED BY TAYLMZ EX PAL/DING ABOUT %=O THE REST TEEN AUO 8'7 DIRECT IN‘TEGZATIONOFTHE SECLbuD. YT FO‘LLWS'THAT: 3+. 3 , _ s 03+?sz a?» + 153% 0 3t Em, ‘ ‘ / 2. Z '- ~331+é33 = “1233’ v- COLLECTING TERMS: o 9 F = -— 21473 e S 3t AZ —oo ‘ D -2 3° V¢,-V4>,cl% +J£f>g Eczt) + C3043) .6 "THE MEAN. True VALUE OF (ENE/gt =0 FOR ANY STATImMAray SgGMAL. (1‘22 05), So THESEchD— CHLOE-(l PCSTEMTIAL Does NOT Confirm BVTE 773 THE MEAN DmF‘T Fofice AS‘ STATED ABOVE] ,— oF THE BEHAtNING Two TERMS THIS QuADPA‘r/c BERNOULL! TERM COUTEIBUTES A S‘U CTloN FOKCE GJHICH 13 “PULLWG” THE wALL (UTO'THE wme CCouN'CERIWUlTH/E BUT T205!) wHILe THE— LAST TEEM (3 41.4924 ‘13 POSITIVE PUSH—(HUG THE 00A LLIN “THE DvfiEc'rrow 0? .‘THE ouAuE A: EXVECR'EO UPON SUB$TlTuTto~ OF THE LHJEAR VELOCITY @eJTEMTML. DEewE—D ABOVE AM: use of “THE FAqu@ IDENTITY \Re(A.e‘°°t)fiZe(AzeM) = J2: Elf/1&5} IT Is EAS‘I TO VERIFY: a : §93A2+ 0043) 5:) THE MEAN H0) EIZDIUTAL FothE 5N A VE'KTIQALWALL 0F rUFHwTe DRAFT 137A 1:94.05 Ffioazygsgme NAVE HAS A mes MEAN VALUE N A7. H: «THE PLANE REGULAR wAue (S mane—Mr A‘l’ AN ANGLE 1741? MEAN HottZoM‘TAL FofaCE— HAY Be SHouuN To TAKE THE VALUE: a: £ A?“ Z 7!— Fx___2:98 C09X3,__ .— C VEE1‘F‘l)... [u SPITE 0F THEME SmPucz'Tv THE: ABOVE RESULTS HAUC: A NUMBER OF USEFULAPPMCATMNS w PYACTICE wHeu wAVES' THAT ARE SUFFICISM’TLY SHORT IUTEEACT WITH FUDATINQ S‘Tfiurrurzcsn $0M; EXAMPLES FOLLouJ‘: ~--a-- —- I PE NETR ATM“ D a P TH 9~/z 3/147 => 9(T/2 1 3m? born: wALL SIDED GEOHETRY ACTS LIKE A MALL. 0 FOR A BARCe LIKE S‘H~(P wz'ru LENGTH L. THE MEAN gwAv DfaiFT Emacs m BEASGNABLY 9140a? wAuss IS APPROXIMATELY aweru 8v: ——— F7 2. EXTEND THE ABovE RES‘ULT 00 HEN THE SHIP HULL $Ecfio~ HAS FLARE wITH swPE— o< . e aesAZL e 3 NWT wxwes INCIDENT uPou A 311%” AT AM ANGLE ARE LOCALLY REFLECTED A: 1F THEY ENcou WEK. A cow-rmuuH 0F VERTICAL wALLs Iucuweo AT3VAIZY1NG ANGLES, we Um THUS APPLY THE ZESUUT‘ DERIVED A‘BOUE. 0 <9va PART OF THE $Hu> myreeume DUN—L E—Ncaom'EE WAVES. THIS [256mm :3 BOLDFACED ABeuE AND CAN Be DETEEMIMED 8v A S1HPL€ GEOMETEICA-L ARGUMEUT. DENJTE THL’S‘ PorZTzow OF THE st-HP GUATEfiLIME 5% W. \T IS EAsv To $1406» ‘ITIATTHE MEAN mam-T Foace— w Tue (x,y) omecnoms IS GIVEN BY 2. {31(5" = g—w" 3 1313:} N9 ,. P F5 CVE‘ZIFV) W18 KESULTIS Known) As RM THEoev... 4—. CONSIDEP A VERTICAL CUZCULAQ CYLUUDEQ PlERClNC THE- FREE SURFACE 4N0 SHoeT WAVES moot—m’ WM 11’: “N A rCrx- USE THE RESULT ‘F—fiGM 92M THEOQ‘! STATED ABove 1135mm THAT THE MEAN DiziFT Fol/Zea In THE \x-DHZECT10N [S GWEN 87.- M PX: 5. \‘T [3?“mb To EXTEND 2%“! THEORY wm—z LITTE ADDI’HOMAL COHPLSX'IT‘Y 10 THE CASE NH 625 THE VESSEL A DVAIUCE§ thH A HODEKATE Foeweo SPEED. (32:; cup) (AA) Ark» ‘1)?va FOECES‘ BY P26530625 tweakATzoM' W 9 [U THE MORE GEMEPAL CASE OF 50£FACE OJAvES (WEEAC'TIMC LUl'TH FwA'Twa BODIES Oscwmrcwa Due To THEAMBzemwAuEs, A Hoke GENERAL EXPQES’SHDN MAW BE DEENE‘D B‘I Dmecnv INTEGRATING THE. P2539025 owe—:2 THE INSTA WANEOJS POSITION 0? THE N16395:, wET'rE-p SURFACE Am> LmEAKIawa 480$ {TS MEAN PO‘EaiTiaM KEEPIMQ CONSISTEYxf/Ly TERMS 0F 0 (AZ). THE ExPeess‘zoN IS NWGMJEM «* - HERE FORSIHLICI’TY.\ . I ____,__-_M,,_ .13" s HE-AN STATM N Vosmow 0F , S‘I-HP HULL DEWT Foeces 8v H‘OHEM’TUH CoN§€2vATm>M 0 IT [3 Posscaua TO DEIZWEAU EKPRE$StOM F02 THE MEAN DEIFT FORCE BY APPLYING THE HoHEMTuM CON SERVATHDN Pelmc-PLE DERIVED EARLIE2.THIS APPROACH mepeskw EXPRESSION FOR THE DRIFT FORCE 1N TERMS OF THE WAVE SYSTEMS (u THE FM? FIELD Am; CAN BE SHowu TO Pwoouce THEO?ETI(ALLV Au lDEW’ICALjQES‘UL/‘F TD THAT org-rmwso Fraoq THE CDNSIQERAeLY News EMBOEATE TASK 0,: gym; Maire—HELD PRESSURE (WEGEATION 9 THE FULL, THKEE ‘BIHENS‘IOMAL RESULT thL too-T BE PRES’E WED HERE , AS FOP THE Pit ESTU tee 'IUicGRA‘er, AMD CAN BE Foo ND IN THE EEFEEENCES CtTED nu OMF AUD N‘EL. (T 13 NUTEDTHAT )7 IS NUMERICALLY SUPEEIGR TO ‘PiLES‘S‘oRE HUTECRATIGN Apr) 13 OFTEN PREFEKED (N PRACTICE 9 BELDvJ we Ptoue emu FHZST PRINCIPLES‘ THE RESULT IN Two DIMENSIONS leCH (3 [TSELF 02»th USEFUL Lu PgAcTuE Aw EDUCATIBNAL.._ ‘ HEAL) DRIFT Foecs ON A FLGAT/NG 20 [3007 o AMBIEUT zea’uuuz waves 00er AMPLITUDE/A A—RE wCiDEMTCDN A FLDATING Beoy we 20 WHICH (S ALLoooED To OSCILLATE FQEELY Mu HEAUE, Sm Av Auo EGLL . A: A IZESvu‘roF THE DtFFféALTzom AND EADmT/ON (DAME DNTDKBAMCES) A REFLECTED PLANE PROGQESSNE wAvE OOITH CoHPLEX AMPLITUDE A" A‘P?5AES AT X: ~04 (wee A ComtzaLSuréFAce $“ AND A BADtATEO/DIFFEACTEO ooAvE wITH A—HPUTUOE A+ APPEAQS AT x=+oo owe—(a 3+ 0 APPLYHUG THE HauEfUToM couSeeuflTmN Patwclpbe IN THE X~DIQECTIOM (UlTHfN THE \fDLUHE \rtt) BOUNOED/ B‘l S++S'+ SFa) 4%10 we OBTAIN! [)5 FX : —— [43; +€<3/(Vn~Un3]<19 s": s ’ UHEEE THE Mwuemuu CousEEvA‘Twm PEHUCJPLE Dazweo EARLIER HAS BEEN APPLIED. HEflN VALUES 1N TIME ARE “TAKEN LEAD/Na TO A VAN73H1NC MEAN VALUE FOR THE HGHaUTuM RATE 0? (HA—Mae wwuw THE vo LU‘HE \I'Lt) , F0?— Fixer: Si“. _ 0 THE MEAN Hagen—rm Fun; ACROSS S}:(+) :3 25% 9 THE MEAN HoeIZOUI-AL 'HGHEIUTUH FLUX ACEOSS ———+, THE 500v SedTloN IS THE DetFTFoece (DEFX © THERE PENA—HUS TO EuALuATE THE INTEGRALS @152 Si comm: ARESUEFACES FIXED nu SPACE AND THEREFOQE J on :0 cm Si. RECALLTHA'T F.) f V: Vcb 13 THETQIrAL FLUID wacn'y AND 43 I3 Cwew 13‘! THE Beewouu: spew-1me 0 THE DEFIMTION OFTHE PLANE; szocuzesgwg WAVE FoRHS DEFINED 580m; (mu. BE WTIEODULED AND" AN EXPRESSMN mu, 85 Deraweo Foe. D” [M‘TEKHS 0F A,A+,A". THE RESULT I3 1\IWLDLY Sveeetsmal DEFHVE THE VELocn-v FUT'EkS—T—I/JCLS FOR THE PLANE Pfioaeesszue wAUES‘ Desuauseo ABOVE: [3A .t%—ka+3w1’: ._ e . 3 a) CPI:HZ€{ C‘D'F: U22 k2,;loc +1.00‘Egy CF”: iiA‘ekg +210: +«'w£§ UPON soBs’nTQnow (mo THE HOMELqu FLUX Exveessqow DEFINED ABME Auo AFTER SOME fimPLE ALGEBQA’FHAT a—MS BEEN ILLUSTvm'z-gp EvMZLH-Z—rz7 VT FOLLowS TH AT: «D = E33: (At A”) — 925’- MHz—1ng DOE-1528 (x) DENOTES THE CGHPLEX co MUUGATE, Nu-re THAT A [9 REALM”) AiAQE COMPLEX (QUANTITIES. ALSO we‘re THAT THE DavFT FOQCE AS STATED Asove DOE.) NOTAPPE-AK w DEPENO ow A 3 lN’CE THE Amara“? wAvc-E APPEAQS AT BUTH lMFINlTlES4I'T'HE ABOVE EXPRESSION smmzmes A an rsv INVOKINGL amaze v ' CGNSEQUFYTIOM. 0 THE Fww AEGUND THE FLOATING [800V 15‘ CQNS‘EZVATNE IF Viscous EFFECTS 0’12 Brae?szer DUANE EFFECTS A25 LG‘NOQED, THE 1 FOEMER A625 OFTEN PRESENT WHE‘IU VOUZ'TICC-LS' A25 SHED Amme Coewees oF—THE BODY, BILOGE KEELS ET ._ INSU CH CASES THE EXPESSIONC BEww HAY BEA9P€OX1HATELV VALID 0? INVALID. o (N THE ABsENCEoFENEeRY Losses THE MEAN ENERGY FLUX Amaoss 3‘ Mug—(— BE [DE—UTICALJ‘O THAT Acfiass 3 + (4317'qu THE szvm'nows 0F LINEAR TH EOYZY ‘: .4 Ewavzav FLUX ACROSS 5””: [A11 [A171 |A+A+IZ = 'lA—«lfl» IAI1+IA+(Z+A(A:A+#) =9 A(A++A+*)=—(IA+IEHA’IZB.K 9 THIS BELA'TtoN (Karma—mom UPON THE LUAUE AMPuTuoES 19 THE (25qu 0F 6N5an Co MSEKVRT'ON‘ UPON SUBSTITUTION 1M 1D 2 TH 19 [mazes-(“ma (at:qu arm-r55 TWCT THE MEAN DchT F0203 ow A Two *DIHENS‘HDNAL. Boov FREED/ FwATING 1M AMBIEMTIZEGULAIZ UJAVES LTHATSHEDS NO onTzCES) IS \DE—MTICALW ECQUAL, ACCMZDIMG To LtMEAQ THEORY, ’1’?» THE: ABOVE EXPRESSION THAT DEPENOS oNLy 0N THE AMPLITO OE OF THE RELEETE‘D DUAUE. e 1: THE AMPLITUDE \A'Kzo THEN THE (BODY (mu. EXPERIENCE 2520 MEAN DEIF’T Faisch ‘ SUBHEPGED FIXED C—lE—CLE IT CAN BE SHowN THA‘T AS‘DBHEEGED F’IXED Cuzcu: 9063 New BELEC'TANV OFTHE AHl'SlENT WAVE DISTURBANCE. H ENCE gA—{éo => TD=O 0 THIS IS THE'on CASE we KNOUO m 24> 02 ° HE‘fiN DQtFT FORCEISZEZO. 3i) amaze THC SOTO HCDUE’THEN (D >0 VALID. 365 cm: Foe A 013cossm~ 0P V13cous EFFECT? AQopND BLUFF (300353.... ...
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lecture21 - NOML! HEAR EFFECTS §OME OF THE MOST IMPORTANT...

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