lecture4 - ENERQV DEMSITY , Enemy FLUX Aw: HbHEMTu-M...

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Unformatted text preview: ENERQV DEMSITY , Enemy FLUX Aw: HbHEMTu-M “FLUX OF SDRFAQE wAugs PUTENTIAL K 1 VET! a E «15254 ENE a“ Y AREA 5 t ,5 €() ‘S'LH "’ t 2 g: “‘5 ‘6 S (Jr/+3294? -“L*____..__._t t I SXLt) m =36 V 4a +-_,‘:Pj(g_Ha) OJHERE 30c) 13 FREE gamma ELEUA'T‘? mu. [GLUOKE "TERM Aéeg HZ WHICH REPRESEUTS THE PGTEMT/AL BUERGV OFTHE OCEAN AT 255?. THE REHAIMMG PERTURBA'T’ON COMPONENT 15‘ THE 9m 0F THE tamer/c + POTENTIAL. ENEBAV Cch’POMem’S g : 810:4 + {PUT —" 3cm t - l 1 a.“ — {.0 v24: , \/ = V¢~W —-H ' A A t ' ¢xz+ gm = :% 93 m7 mspoere Now” A3 AsPECIAL. CASE PLANE PROGRESS—NE wAVES DEFINED 37 THE VELOCITY PWAL ,U .9559 wA'TEE (Fm: S‘tHPuu'rr) f p “A K-'kx'é (je’flzqg—l—Ej—ezt +100; ‘ .t _.I . Chg: LET/A: E Lc'x +1205} _ W; . : Am’fweka—ka—Hwé} CF kwemgoilox—Amé} kE—ikx+fw’5} v.— LET: mafia“; 2%649 W {18 a”; {my t {Au—3(8Ct) = 5’: {Ref/Q [8*E 0,.— W=gg<5 +5 )(¢f+¢:)clz Do 0 t Z 2 v“ w _ 'L 2. .- ‘L .. E) 4K ._ 493A , P02 2—w/3 __ z I 2 WT -.— Jim 36H = 4793A -—- HENCE —.— mm; 0? CHANGE or: E~5?avc%wswy “5(6) E NERC‘! FLU x 2. (Pee? = A gm , €05): (gems—z}: I At m) 3;; , . A S “ C on ‘ W3 *7 . 1 25+ 3*} q \, V0,? *‘w-wuj‘ VN'Wd—M 00 BESS) clay + (Q ecemndg N: sle) A gfl) : i ace) Av: (if? (At \rét) 3“? 1E- 13. {Levvlmagri a?“ q, V49) Bt’ Wc Z M Wm): 01 ECU: (3 v.[‘%}tv¢) (In; (it \I’Lt) '1. His). (—L—AI +32) U» <13 Ste) lm/oxcma THE ScALAQ FoRH OF GAUSSJS THH IN THE FHZST TERM , we OBTAIN! 'b'n Au ALTERNATIVELFORM FOR THE ENErem/ FLUX We) ckassmc THE cLagEo QMROL S‘UBFAQE Ste) [5 bgTAmED 31 mvorma Seeuovuz's EcovA‘Trcm/ IN THE SECOND TERM“ RECALL THLAT! 47' AM? FDHJT m+ mmwwwo P be DUI-IAIN AND ON 130 mu 9/4215 HERE we DH) ALLow qu': ATMOSPHERIC P25311195: TO BE NON~2€R0 FOR ‘TH-t? SAKE OF PHYSICAL— cLAEtT‘I. (Jme S‘uBSTIT—J’now W ?(+) we OBTAIN TrHE ALTERNA‘TNE F6 R M? '(PC‘E)=€ ash EAS“€<§ (Pfl—eEé—DBUHQIS bi;th ‘9 So THE Ewéfa‘v FLUX ACROSS SM) IS GIVEN BY THE TERMS UNDER THE INTEGRAL. smw. may CAN BE CDLLECTED IN THE MORE coM PA c'r FORM ': a (Pee): 6}? 93(33—00’W’PMUnEc‘S S (H mm; THAT (PM) MEASUEES‘ THE [fr/EBAY aux (We THE VOLUME \I'Lé) ova THE {EA—TE 0P c;th OF THE ENERfiv DENS‘W’Y §L{)__ we ARE i25on NW‘TO A.va THE/ABOVE WHUME TO THE SOZFflCE NIH/E onfnm‘rzm PQDBLEH. BREAK 3m INTO (T3 Commwews AND DEren/g SPEC‘AL’ZEO FORMS OF (he) Paa'r‘mem'ro EflCHV‘ e 3; : Nomuuae Powwow oP'me Frees SUKFA—CE (E? : Uh ‘5 NOKHAL Row VELOClTY E NORMAL 7"” r VEwu—rr ocrrzaaswzFAcc; ' 13001004be SKIUEHA-TILCU'NP. at): ,Pak g FLUID PQESJ‘UQE EATHOSPHEIQIC THEREFORE ova? SF ; (POE) 20 A3 EXPECTED. NO EN 5120‘! CAN FLow INTO THE AW 03 P H E261 o S?) : NON~HOWNG 301,10 BOUNDARY L)" - o) 34’ _ Uh 5 NED—NORMAL ‘3'“ FLUX CONDITION 9 S“: ; FLUID BOUNPAQIES FRED INSPACE ZELATNE '11) AM EARTH FRAME . ‘ '34» Uta-:07 fi?‘50 9 So : FLUIV‘BOUMDARIES MMING W~VEL0C1Tr P; L) RELATWE To An earn: FRAME .3 UV): U’m) 3;?) o THts CASE thL 85 0F (WEREST LATER IN THE COURSE WHEN buECcmlS‘tDEf? SH1PS MOUMIG Gal‘TH CON§TANT VELOCITY U . _. THE Fokuumeosezveyo ABOVE ARE “VERY GENERAL Foe Farm/4L Pumas szH A FREE SuezFAceAuQ ewe Bouprrewes 9 0oz; ARE Nowf KEADV TO Mime THEM '71) PLANE Pea GVESSJVE 00:30:53,. ' ENEECV FLUX ACROSS A VERTICAL FLUID BOUMDA Ev FIXED m S?AQ5 HEAu EquQaq FLUX FOR A PLANE PROCRe—Zsswfi NAUE For.st 09m; SOBSTITUTIO'N OF THE REGULAR cums ngocrw PdTEMTIAz, AMP TAKING MEAN VALUES: 4: _ , 3d? Bd> - 1. (LE (‘3‘ PS: ayxdi " 293A 20)) W W '— \/ 5 5 0‘2 1 7‘3: E VS V%;CROUFVELOC\7} ) _I [’1‘ FOwas FROM TIME EXERCISE THAT THE MEAN ENERRV FLU'X OF A ?LAN£ PfOG?ESSWE WAVE (5 THE PRGDUCT 0F [73 MEAN ENEPGY DENSFW TlHES‘ A VELOCITY wmm EQUALS ii THE; PHASE vewary w DEEP OUATEIZ ODE CALL THIS THE Cram/p VELOQTY 0F DEEP wA‘Tee wAves MID IT 13 DEFINED A5: 3 ~ : l .I vs: A Hate FoKHAL PQooF THAT THIS is 7H5 Vii—LE)ch wrrH w FHCH THE ENEKGY Fwy 0F ‘FLAME PKoaVESSI VE bum/53 PBGPAGA'TES 15' TO ASK THE FOLLOwIUC (QUESTION: "4 comm mews TD <55 THE H0 er 2o mm, VELOC‘A‘T‘I’ Una) OFA Fume BOUNDARY SO'THAT ‘THE MEAN ENEQG’V FLUX ACEQSS LT VANI§HES ?- “rt—HS CAN BE FOUND FRGH "(745301.127on OF THE FOLLowa/a EcQUlQTION.‘ ~— 0 _ 8 ‘MH PC-é),—®,I§J-m__ég;4% __ t O 94> ,. UR: (2+fiBJz ~63 COHEN; TERMS oF om?) HAVE BEEN Newer-r50. NCSTE THAT wLTHrM LINEAR THEO (EV , ENERQY DENSITY AND WEIPGV FLUX ARE COUAM‘T’ITIES 0F OLA?) «(IF HiGHER-CNEDER 752m: AKE K61” THEN wE N550 TO CONSIDER THE TKEA‘FHEMT 0F SECONO'OEOEE SURFACE WAVE T1450 gay) AT LEAST. (see MEI),_~ Souvsz THE ABOVE EcQUfiTIG'N FOR U DOE OBTAIN: t o 2) mp U 9 .3“ 3L4? 4* - ‘ o h F 32” g (403942 UPON 50537276170“) 6)? THE PLANE Pfiado‘u-ES‘SIUE :0wa VEwaTv PUTEIUTIAL A‘MD DEF7w1'T/ow a? Paessoae Few Bemoum's Eco 04—17mm m5 OBTAIN: .LEJK? UEV‘S” ZE'EV? Meme THA'T USA/6 ('3‘! DEQMTIOW. (F'THE ABOVE EXEQCIZE )5 [250624759 w WATER 0F FXNlZTE DEPTH THE SQLU'T'ION‘ Fog: U AFTER $O’HE ALCEBRA 13'. U:V%=(_;:4 [ct—t >21? Sink ZKH w Com-l /K 002:6 k +aw‘nKH ._ rr MM 85 §Hcvww THAT THE Glam)? VELOQT)’ \La 13 czvau :94 firms OF w 411131 174.; RELATION v r. €12? 3 41¢ THIS RELATION FoLLows Fkau THE VERY ELEGANT "vewce" DvE “RD BAVLaléH comm APPLIES“ TO Am! some POEM: Co M 310.5% Two PLANE PfoafZESSw E WAVES OF NEAR—L“! EcQUAL FRECDUE‘NQES AND Haves wAVENUHBEES. THEM? 307W wAvE ELEVATION {S GWEN BY 3cm): A cos (om-m) + A (@236— W wHEKE THEAHPLJ‘TUOE IS ASSUHQD TO BE CD’HHON AND: '1wzzwl-J—Aw )IAw]<<w,JC«)L K7,: k; +1324 341d“ kulcz IDEMT/CALLY wHEQE F2<§ 1:20 COHEN .' {(Awt _ AkX) -——I 8 OR WHEN! Aw I; _. A1” = (2714-07?) n=a,;,2,._, $04.va Fetz x weoe'rA/w: M x = .L {aan +tAw§ .. XHfl Au Fog: VALVES OF ¢\’[‘E)C1UENAB&UE) KEG THESE ARE THE— MODES 0‘? THE Riv-CHPO HATIL wAuE WA!“ OJHE'IZE AT ALL TIME: "THE ELEJATIDN VANIS‘,HE§AMD HE'NCE THE @5125)! DENSITY '50 ,THE 0014065201)? HAS THE Foray XC—E ) xtt) Tue SPEED OF THE; IUD DES Is 3—: : £9.43 AIL elk AND THE EMEQGV. Tit/MOPED wl'fl-HN TwacousauT/u. NODES CANNOT EscA ()5 5‘0) IT HDS’T TPAUEL A‘T ng GROUPVELCDCITY,‘ Va 2 9.11 ._ +91 ( .7 dt dk a MUTE THA‘T RAVLEMH'S PROOF APPLIES EcQUALLV TD coAvE‘S w Fwwe DEPTH OQ_ DEEP unwise AND m Pizmcmus TO ANY “PaoPA CATde oumzs FORM ,‘ HS! FINITE DEPTH 1T CAM BE SHoouN AFTER SOME Pvt—CE BEA TH—ATfiSEEHHX GZAWIIcALLV, THE T’HAsE AND GkovP VELho/ej‘ MADE Naw’omemsvoum BY THE DEEP WATER =8/w TAKETHE FORM: PrP—AS‘E VELOCN’Y me THE Fozuume Foe THE ENEEGV FLUX DEEMED M30sz H26 Vazv amasme AND F0?— Pd'rEmJT/AL FLO‘W’ NONLINEAR sotzFAcE WAVES VTHLA‘T 42E NOT BEEAK'IUC CoNSTl‘TUTE Tm; ENEeav can/SERVA-WGN PEWQPLS- Euetzcv FLUX (P000512) INPUT m-ro THE FLUID DWAIN BY ANY MECHANISM ) wAvEH/mae comp (1N AC'ONSEIZVATIVE HANNEIC) , A SHtP cm: W FLOATING BODY HUS‘T 8E “za'rzaavep” yr sows QUTANCE AWAY." been/sz EXHZESS‘MNS OF‘THE EwEIEG‘V FLU)! RETREn/Ep AT "INFINITY" :3 A pow ERFUL HefHop F012 ES’UNATING THE WINE RESISTANCE 0F $HIPS (M M25 mv‘THts LATEflD, T445 cum/E DAMPINQ OF FLOATING BoDIES ETC. YET,T1+£ ONL‘I GENE—EAL Lo my GP EVALUATING wArvE FOECES ON FLOATING (500th (Hovtwa ’011 NOT) OR ON 501.11) $C>Ut\IOA—f21‘€325i 8V APPLY/MG THE: MON WW cause—emsz M PE 2 N CIPLE a .5 ...
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lecture4 - ENERQV DEMSITY , Enemy FLUX Aw: HbHEMTu-M...

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