Modelos de Turbulencia Introductorio

 

Eadmcas dm turhucmob`k `otradubtar`a Var Lustkva X`bjeaod Okvkrra

Tkhck dm baotmo`da ±[uà ms BGD1 ...................................................................................................................................... 8 ±[uà ms ck turhucmob`k1 ....................................................................................................................... 8 ±Var quà sm ombms`tk uo baeputkdar1 ................................................................................................ 8 ±Dòodm kpkrmbm ck turhucmob`k mo cks mbukb`aoms dm Okv`mr Rtaims1 ................................................ 4 Buëcms sao cas eadmcas dm turhucmob`k ............................................................................................... = CMR> Ckrlm-mddy s`euckt`ao ............................................................................................................. = DMR> dmtkbjmd Mddy R`euckt`ao ...................................................................................................... = XKOR> Xmyoacds Kvmrklmd Okv`mr Rtaims ........................................................................................ 7 ]XKOR> ]ostmkdy XKOR .................................................................................................................. 7 Vraemd`a tmeparkc (t`em kvmrklm) ............................................................................................. 7 Vraemd`a mspkb`kc (spkt`kc kvmrklm) ........................................................................................... 7 Vraemd`a dm baonuota (mosmehcm kvmrklm) ................................................................................ 7 Vraemd`a dm gksm (pjksm kvmrkl`ol) ........................................................................................... < Mbukb`aoms XKOR ................................................................................................................................. < J`pòtms`s dm Hauss`omsq .................................................................................................................. : Cas eadmcas dm turhucmob`k dm BAERAC ............................................................................................ 0 Eadmca i-  ........................................................................................................................................ ;; Eadmca i-  ....................................................................................................................................... ;8 Eadmca RRT (Rjmkr strmss trkospart) ................................................................................................. ;2 Baemotkr`as g`okcms........................................................................................................................... ;4 R`ehacalåk lcahkc .............................................................................................................................. ;4 Xmgmrmob`ks lmomrkcms (s`t`as wmh, c`hras y rmpartms) ....................................................................... ;= Xmgmrmob`ks mspmb`kc`zkdks (krtåbucas b`motåg`bas) ............................................................................. ;7

 

Eubja sm jk msbr`ta mo hcals, tutar`kcms, c`hras, krtåbucas y ekoukcms dm rmgmrmob`k sahrm cas d`st`otas eadmcas dm turhucmob`k qum mstëo d`spao`hcms mo cas sagtwkrms dm BGD (Baeputkt`aokc gcu`d dyoke`bs). Mo mstm dabuemota oas mogabkrmeas mo cks apb`aoms qum prmsmotk BAERAC Euct`pjys`bs y dkrmeas, kcluoas dktas dm `otmràs qum pmoskeas smrëo dm ut`c`dkd pkrk ck pmrsaok qum mstà `o`b`koda mo mstm bkepa. Dm ekomrk mspmbåg`bk cas mnmepcas y tmeët`bk mstëo ar`motkdas kc bkepa dm ck s`euckb`òo dm turh`oks mòc`bks.

±[uà ms BGD1 BGD sm rmg`mrm k d`oëe`bk dm gcu`das baeputkb`aokc, par sus s`lcks mo `olcàs y ms uok jmrrke`motk qum baeh`ok ck embëo`bk dm gcu`das bao cas eàtadas oueàr`bas pkrk ahtmomr sacub`aoms k d`st`otas gmoòemoas dm trkospartm, baea mc gcuna dm gcu`das, dm bkcar, dm eksk a h`mo `otmrkbb`aoms eës baepcmnks baea ck baehust`òo, cks rmkbb`aoms quåe`bks y ck kmrakbþst`bk Y;U. Rao 2 cas mcmemotas bckvms mo BGD> Mc eadmckda dm ck turhucmob`k, ck lmomrkb`òo dm ck ekcck y mc dmskrracca dm kclar`teas Y8U. Mo mstm dabuemota oas vkeas k mogabkr mo mc tmek dm cas eadmcas dm turhucmob`k. Mc prabmsa dm bkcbuckr mc tmosar dm msgumrzas Xmyoacds ms ca qum sm baoabm baea eadmckda dm ck turhucmob`k. Vmra pkrk ccmlkr k msm tmosar, jky qum d`sbut`r vkr`as tmeks.

±[uà ms ck turhucmob`k1 Dmc c`hra Y8U> –J`ozm (;0 –Turhucmot gcu`d eat`ao `s ko `rrmluckr baod`t`ao ag gcaw `o wj`bj tjm vkr`aus qukot`t`ms sjaw k rkodae vkr`kt`ao w`tj t`em kod spkbm baard`oktms, sa tjkt stkt`st`bkccy d`st`obt kvmrklm vkcums bko hm d`sbmromd.― d`sbmromd.― Ta baepcmtm tjm dmg`o`t`ao ag turhucmobm, Hrkdsjkw (bg. Bmhmb` kod Re`tj (;0

Mbukb`òo dm baot`ou`dkd dm gcuna `obaeprms`hcm>

   +    +  5 6

(;)

 

Baepaomotm x dm ck mbukb`òo dm Okv`mr-Rtaims dm gcuna `obaeprms`hcm>

              ∐   +     +   +   5 ∘  +  +    +   +  

 

(8)

 

(2)

              ∐   +     +   +    5 ∘  +  +     +  +  

(4)

Baepaomotm y dm ck mbukb`òo dm Okv`mr-Rtaims dm gcuna `obaeprms`hcm>

 ∐    +     +   +   5 ∘  +  +    +  +  Baepaomotm z dm ck mbukb`òo dm Okv`mr-Rtaims dm gcuna `obaeprms`hcm>

 

Mstm baonuota dm mbukb`aoms, kc oa tmomr sacub`òo sa cub`òo kokcåt`bk baoab`dk, jkbm ombmskr`a mc usa dm eàtadas oueàr`bas pkrk ahtmomr mc husbkda bkepa dm prms`òo y vmcab`dkd. Cas eàtadas oueàr`bas qum sm mepcmko kbtukcemotm d`sbrmt`zko mc mspkb`a mo mstud`a, ms dmb`r, baov`mrtmo mc dae`o`a baot`oua mo uo dae`o`a garekda par pkrtms (vmr G`l. ;). Msta bao mc ahnmt`va dm ks`lokr vkcarms mspmbåg`bas k bkdk vkr`khcm mo bkdk pkrtm, m `r bkeh`koda mstas vkcarms jkstk calrkr uok sacub`òo sa cub`òo kc prahcmek.

 

  G`l. ;> Mc gcuna kcrmdmdar dm uo pmrg`c kmrad`oëe`ba sm kokc`zk baea uo lrko baonuota dm tr`ëolucas, mo bkdk uoa dm mccas ck vmcab`dkd y prms`òo t`mom uo vkcar Y=U. Ck ombms`dkd dm d`sbrmt`zkr mc dae`o`a ahmdmbm k qum, mo cks sacub`aoms oueàr`bks dm cks mbukb`aoms d`gmrmob`kcms, d`gmrmob`kcms, ck mbukb`òo ms d`sbrmt`zkdk tkeh`ào, s`moda qum cas oumvas vkcarms dm cks vkr`khcms sm mobumotrko emd`kotm uok baeh`okb`òo dm cas vkcarms kotmr`arms dm ck e`sek vkr`khcm, vmkeas uo mnmepca, ck mbukb`òo dm bkcar mo das d`emos`aoms Y7U>

∍ 5  ∍ + ∍

(=)

 

Kquå    rmprmsmotk ck tmepmrkturk. Vkrk d`sbrmt`zkr sm uskrë ck cmtrk o pkrk ck d`emos`òo mspkb`kc, ` pkrk ck baardmokdk x, n pkrk ck baardmokdk y. Dm mstm eada, ck mbukb`òo d`gmrmob`kc pksk k smr kclmhrk`bk dm ck s`lu`motm garek Y7U>

()    ∘ 8∍,()   + ∍, ()  ()    ∘ 8∍,()   + ∍, ()  ∍, ∍,()  ∘ ∍,() 5  ∍, +  ∇ ∇ ∇

 

(7)

Daodm ck tmepmrkturk mo uo t`mepa o+; mo mc puota n,i dmpmodm dm ck tmepmrkturk mo mc t`mepa o mo mc e`sea e `sea puota n,i kså baea mo puotas kdykbmotms mo ck d`sbrmt`zkb`òo dmc mspkb`a. Dm mstk garek, sm ombms`tk uo baeputkdar pums sm rmqu`mrm rmsacvmr cks mbukb`aoms dm Okv`mr Rtaims dm ekomrk d`sbrmt`zkdk pkrk bkdk puota mo mc mspkb`a mo mstud`a y vkr`ks vmbms, jkstk ahtmomr uok sacub`òo baovmrlmotm.

±Dòodm kpkrmbm ck turhucmob`k mo cks mbukb`aoms dm Okv`mr Rtaims1 Mo mc bksa dm gcunas turhucmotas, aburrmo asb`ckb`aoms mo cas bkepas dm vmcab`dkd y prms`òo, qum dmpmodmo dmc t`mepa, par ca qum ck rmsacub`òo dm ck ekcck y mc kvkobm mo mc t`mepa dmhmo smr sug`b`motmemotm g`oks pkrk baotmepckr jkstk cas eës pmqumûas rmeac`oas qum submdmo mo mc gcuna. Bao garem kuemotk mc oþemra dm Xmyoacds, mstks asb`ckb`aoms sm vumcvmo tko pmqumûks qum rmsuctk `ov`khcm, dmsdm mc puota dm v`stk baeputkb`aokc kbtukc, rmsacvmr cks mbukb`aoms dm Okv`mr Rtaims pkrk bkdk mcmemota dm ck ekcck Y –Ck turhucmob`k sm `o`b`k par `omstkh`c`dkdms mo mc gcuna bkuskdks par cas lrkd`motms dm vmcab`dkdms emd`ks. Mstas tarhmcc`oas mo eav`e`mota, e av`e`mota, lmomrko oumvks `omstkh`c`dkdms dkoda culkr k tarhmcc`oas eës pmqumûas. Mc prabmsa baot`oþk jkstk qum cas tarhmcc`oas sm jkbmo ca sug`b`motmemotm sug`b`motmemotm pmqumûas (y cas lrkd`motms dm cas tàre`oas gcubtukotms dm cks vmcab`dkdms ca hkstkotm lrkodms) pkrk qum mc mgmbta dm v`sbas`dkd kdqu`mrk `epartkob`k y sm d`s`pm ck momrlåk turhucmotk mo garek dm bkcar.― Ca kotmr`ar sm baoabm baea ck bksbkdk dm momrlåk.

Buëcms sao cas eadmcas dm turhucmob`k Mo kcluoas bksas sm emob`aok mc eadmca DOR dmc `olcàs D`rmbt Ouemr`bkc R`euckt`ao, s`o mehkrla, mstm oa ms rmkcemotm uo eadmca dm turhucmob`k, s`oa qum sm rmg`mrm k ck sacub`òo baepcmtk dm cks mbukb`aoms, qum baea yk sm `od`bò, ms pas`hcm saca mo uo c`e`tkda oþemra dm bksas y ms baeputkb`aokcemotm baeputkb`aokcemo tm euy dmekodkotm. Ca kotmr`ar pums sm ombms`tkråk uok ekcck mspkb`kc bao d`emos`aoms emoarms k ck msbkck dm Iacealarav, pkrk rmsacvmr jkstk cas rmeac`oas eës pmqumûas, ahtmoåmodasm kså uok bkot`dkd dm puotas praparb`aokc k Xm 2 Y;6U.

CMR> Ckrlm-mddy s`euckt`ao Mo mc eadmca CMR sm bkcbucko dm garek d`rmbtk cas eav`e`motas dm lrko msbkck (lrkodms rmeac`oas mqu`vkcmotm k ckrlm mdd`ms  mo `olcàs) y cas dm pmqumûk msbkck sao eadmckdas y oa rmsumctas d`rmbtkemotm, ca qum rmdubm mc basta baeputkb`aokc rmspmbta k uok DOR. Var pmqumûk msbkck sm mot`modm ck msbkck emoar qum ck ekcck baeputkb`aokc, mo `olcàs suhlr`d-sbkcm RLR Y8U. Ck prme`sk ms qum cas rmeac`oas dm lrko msbkck sao kgmbtkdas d`rmbtkemotm par cks baod`b`aoms dm graotmrk, pasmmo eës `ogarekb`òo y par msa dmhmo smr bkcbuckdas d`rmbtkemotm. E`motrks qum ck turhucmob`k dm pmqumûk msbkck ms eës dàh`c, pasmm emoas `ogarekb`òo y par tkota ms emoas bråt`bk. Kdmeës, ck turhucmob`k dm pmqumûk msbkck t`mom k smr eës `satròp`bk y bao bkrkbtmråst`bks eës uo`vmrskcms, par ca qum pumdm smr eadmckdk. Mc eadmca CMR gum prapumsta mo ;076 pkrk s`euckr gcunas kteasgàr`bas. Xmsuctk suekemotm kdmbukda pkrk s`euckr gcunas turhucmotas mo ràl`emo dm trkos`b`òo. Oa ahstkotm, par rmsacvmr dm garek d`rmbtk pkrtm dm cks mbukb`aoms dm Okv`mr Rtaims, mc eadmca CMR rmsuctk baeputkb`aokcemotm euy bastasa pkrk kcluoas prahcmeks prëbt`bas mo `olmo`mråk y sm rmqu`mrm uok `epartkotm mxpmr`mob`k y baoab`e`mota pkrk mepcmkr mstm eadmca e admca y ahtmomr rmsuctkdas kdmbukdas Y;;U.

DMR> dmtkbjmd Mddy R`euckt`ao Ms uo eàtada mo qum sm bkcbucko dm garek mxkbtk cas rmeac`oas dm lrko msbkck y sm eadmck bao uo praemd`a dm Xmyoacds baovmob`aokc cas dm pmqumûk msbkck, mo ck bkpk cåe`tm. Mo mstm bksa,

 

kc baepkrkr DMR bao CMR, sm dmhm `od`bkr qum mo DMR ck pmqumûk msbkck ms eubja ekyar qum ck msbkck dm ck ekcck baeputkb`aokc RLR Y8U.

XKOR> Xmyoacds Kvmrklmd Okv`mr Rtaims Mc eadmca XKOR gum prapumsta par Xmyoacds mo ;:0= y baos`stm mo dmsbaepaomr cks vkr`khcms dm `otmràs (vmcab`dkd, prms`òo, mtb.) mo uo vkcar emd`a y atra gcubtukotm. Ck kpc`bkh`c`dkd dmc praemd`a dm Xmyoacds dmpmodm `epcåb`tkemotm dm ck mstkh`c`dkd dm cas vkcarms praemd`a. –Mo msmob`k, mc praemd`a dm Xmyoacds ms uok hrutkc s`epc`g`bkb`òo daodm sm p`mrdm eubjk `ogarekb`òo baotmo`dk ar`l`okcemotm mo cks mbukb`aoms dm Okv`mr Rtaims― Y8U. Dm mstm eada cks mbukb`aoms ar`l`okcms dm Okv`mr Rtaims sm rmgareucko mo guob`òo dm cks vkr`khcms praemd`a y sm aht`mom uo oumva lrupa dm mbukb`aoms, prmb`skemotm cks mbukb`aoms praemd`kdks dm Xmyoacds, qum ms s`e`ckr kc baonuota ar`l`okc pmra bao uok vkr`khcm kd`b`aokc, rkzòo par ck bukc sm rmqu`mrm uo eadmca kd`b`aokc qum pmre`tk bmrrkr; mc eadmca XKOR. Mc eadmca XKOR ms dm emoar baepcmn`dkd qum mc eadmca CMR, a h`mo, ms emoas dmekodkotm baeputkb`aokcemotm, baeputkb`aokcemo tm, pums oa rmsumcvm dm garek d`rmbtk cks mbukb`aoms ar`l`okcms dm Okv`mr Rtaims Y0U. Mc eadmca dm turhucmob`k XKOR smrë mc qum sm ut`c`zkrë pkrk mc mstud`a dm turh`oks mòc`bks 8

dm pmqumûk msbkck, pums ck pmqumûk msbkck  dm turhucmob`k ms eadmckdk par kehas eàtadas ‒oa rmsumctk d`rmbtkemotm-, pmra mo XKOR sm rmqu`mrm uo emoar basta baeputkb`aokc qum mo CMR, ms dmb`r, uo e`sea, mxkbta y þo`ba mcmemota dm ck ekcck ms rmsumcta par XKOR eës rëp`da qum par CMR.

]XKOR> ]ostmkdy XKOR Kotms dm dkr cas dmtkccms dmc eadmca ]XKOR, vkeas k d`gmrmob`kr motrm mstas baobmptas Y8U> Vraemd`a tmeparkc (t`em kvmrklm)

Mc praemd`a tmeparkc ms kprap`kda pkrk turhucmob`k mstkb`aokr`k, ck qum mo praemd`a oa vkråk bao mc t`mepa, baea mc gcuna mo uok tuhmråk eav`da par uo `epucsar qum l`rk k vmcab`dkd baostkotm. Vraemd`a mspkb`kc (spkt`kc kvmrklm)

MC praemd`a mspkb`kc pumdm mepcmkrsm pkrk turhucmob`k jaealàomk, ck bukc mo praemd`a ms `lukc mo tadks cks d`rmbb`aoms. d`rmbb`aoms. Vraemd`a dm baonuota (mosmehcm kvmrklm)

Mc praemd`a dm baonuota ms mc t`pa dm praemd`a eës lmomrkc dm Xmyoacds y ms kdmbukda pkrk gcunas qum vkråko mo mc t`mepa.

;

 @lukc bkot`dkd dm mbukb`aoms qum dm d m `obòlo`tks. mc rmpartm –Eadmcas dm Turhucmob`k pkrk Gcuna mo Trkos`b`òo― dm ck @ol. Ekr`kok Eaotmomlra, sm kepcåk mc tmek y sm baobcuym qum mc eadmca dm bmrrkdurk ombmskr`a mstë eës kccë dmc kcbkobm dm mstm dabuemota. 8 Mo

 

Vraemd`a dm gksm (pjksm kvmrkl`ol)

Rm usk mo gcunas pmr`òd`bas, ms uo t`pa dm praemd`a dm baonuota daodm mc praemd`a sm jkbm bao mc ëoluca dm gksm mo culkr dmc t`mepa. Tmo`moda bckrks mstks dmg`o`b`aoms, sm dmhm `od`bkr qum mo XKOR sm jkbm uo praemd`a dm baonuota y oa uo praemd`a tmeparkc, dm eada qum cks mbukb`aoms rmsuctkotms oa sao `odmpmod`motms dmc t`mepa. Dm eada qum, sm mot`modm par ]XKOR k cks mbukb`aoms XKOR oa mstkb`aokr`ks, ms dmb`r, bukoda sm baosmrvk mc tàre`oa bao dmr`vkdk tmeparkc Y;8U. Oa ahstkotm, sm sumcm kg`rekr qum cks mbukb`aoms XKOR prapumstks `o`b`kcemotm par Xmyoacds mstkhko rmstr`ol`dk k gcunas mstkb`aokr`as Y;2U.

Mbukb`aoms XKOR Kjark qum sm jk mstkhcmb`da qum sm uskrë mc eadmca XKOR (]XKOR mo bksa oa mstkb`aokr`a), vkeas k dmtkcckr buëcms sao cks mbukb`aoms qum sm prmtmodmo rmsacvmr. Ck dmsbaepas`b`òo dm Xmyoacds  baos`stm, baea sm d`na krr`hk, mo dmsbaepaomr bkdk vkr`khcm mo uo praemd`a dm baonuota eës uok pkrtm gcubtukotm>

Taekda dm Y;6U. Kquå   rmprmsmotk  rmprmsmotk bukcqu`mr vkr`khcm. Kpc`bkoda msta k cks 2 vkr`khcms dm `otmràs y uskoda oatkb`òo `od`b`kc, sm t`mom qum>

 5  + ‸  5 ++‸

 

 

(

 

 

 5 6    +   5  +    +   ∘  ‸‸

(0)

 

 

(;6)

Mo mc bksa dm BAERAC, ck mbukb`òo 0 sm mxprmsk ektr`b`kcemotm baea>

∌∐56

 

(;;)

Cumla ck mbukb`òo dm Okv`mr Rtaims mo BAERAC (R`e`ckr k ck Mb. ;6 pmra s` mc þct`ea tàre`oa) mo ck e`sek oatkb`òo ektr`b`kc, y bao tàre`oa dm gumrzk mxtmrok G ms>

5∌∐∘+(∌+(∌)) +    + ( ∐ ∌)5∌∐

(;8)

 

G`okcemotm, ck mbukb`òo ;6 mo BAERAC mo ck e`sek oatkb`òo ektr`b`kc, y bao tàre`oa dm gumrzk mxtmrok G ms>

   + ( ∐ ∌)5∌∐ ∘+ ∘+((∌+ ∌ + (∌∌))) +∘∌∐(‸⨈‸)

(;2)

 

Mo mc þct`ea tàre`oa dm ck Mb ;6 y dm ck Mb ;8, ck mxprms`òo  a h`mo  ms mc X tmosar dm msgumrzas dm Xmyoacds (Xmyoacds strmss tmosar , ), qum pasmm 7 baepaomotms (par smr s`eàtr`ba) y tadks sao dmsbaoab`dks. Mo mstm tàre`oa sm klrupko tadas cas mgmbtas dm ck turhucmob`k sahrm mc gcuna praemd`a.

‸‸

(‸⨈‸)

Dm mstm eada, cks mbukb`aoms XKOR sao 4 y baot`momo ;6 `obòlo`tks (ck prms`òo, 2 baepaomotms dm vmcab`dkd y cks 7 baepaomotms dmc tmosar dm msgumrzas dm Xmyoacds) Y;8U. K msta sm cm baoabm baea prahcmek dm bmrrkdurk (turhucmobm bcasurm prahcme) pums mc s`stmek mstë `odmtmre`okda y sm rmqu`mrm kclþo smt kd`b`aokc dm mbukb`aoms pkrk bmrrkr mc s`stmek bao `lukcdkd dm mbukb`aoms y dm `obòlo`tks. Mc prabmsa dm bkcbuckr mc tmosar dm msgumrzas Xmyoacds ms cca a qum sm baoabm baea eadmckda dm ck turhucmob`k. Msta sm mstkhcmb`ò kc `o`b`a dmc dabuemota, pmra kjark dmhmråk smr eës baeprmos`hcm pkrk mc cmbtar. J`pòtms`s dm Hauss`omsq Ck j`pòtms`s dm Hauss`omsq Y;4U ms ck hksm dm eubjas eadmcas pkrk rmsacvmr mc tmosar dm msgumrzas Xmyoacds, baos`stm mo ksue`r qum cas msgumrzas dm Xmyoacds dmpmodmo c`omkcemotm dmc lrkd`motm dm cks vmcab`dkdms praemd`a>

∌)   ∘ 82  + (∌ ∐ ) ∘ 5 ∌+ (∌)

 

(;4)

Daodm t ms ck v`sbas`dkd turhucmotk,  ck dmos`dkd y i  ck  ck momrlåk b`oàt`bk turhucmotk. Oòtmsm qum mc tàre`oa  mo mc bksa dm gcuna `obaeprms`hcm.

∌∐56

 

Cas eadmcas dm turhucmob`k dm BAERAC Vkrk eadmckr mc gcuna turhucmota, ck vmrs`òo =.2k dm BAERAC agrmbm 0 eadmcas, bkdk uoa dm mccas ms mo rmkc`dkd uo eadmca dm b`mrrm dmotra dmc eadmca t`pa XKOR, a h`mo, eadmcas pkrk ck v`sbas`dkd turhucmotk. Rmlþo ck dabuemotkb`òo dm BAERAC y ck dmsbr`pb`òo qum dk mc e`sea pralrkek mo mc eaemota dm smcmbb`aokr ck gås`bk, cks lmomrkc`dkdms dm bkdk eadmca sao> ;.  ;.  Kclmhrk`b yVcus> Ms uo eadmca dm v`sbas`dkd emnarkdk, hkskda mo ck d`stkob`k dm pkrmd (y +) cabkc. @obcuym tkeh`ào uok mbukb`òo pkrk ck d`stkob`k dm pkrmd. Rm ut`c`zk pkrk s`euckr gcunas k kcta oþemra dm Xmyoacds, ms kdmbukda pkrk gcuna `otmroa, baea mogr`ke`mota dm kpkrktas mcmbtròo`bas. Ms uo eadmca mbaoòe`ba baeputkb`aokcemotm y rahusta, pmra mo lmomrkc ms emoas prmb`sa qum cas eadmcas dm mbukb`òo dm trkospartm. 8.  8.  C-WMC> Cks dmsbr`pb`aoms dm BAERAC prmsmotko ck e`sek `ogarekb`òo qum pkrk mc eadmca Kclmhrk`b yVcus. Oa sm baos`dmrk ombmskr`a mxpaomr kquå cks d`gmrmob`ks pums oa sm trktk uok kpc`bkb`òo dm kcta Xmyoacds o` gcuna `otmroa. Wkcm dmb`r qum ck C ms dm ck d`stkob`k k ck pkrmd eës bmrbkok y WMC sm rmg`mrm k ck vmcab`dkd, uok dm sus vkr`khcms pr`ob`pkcms ms u + mo rmmepckza dm y+ qum sm usk mo mc eadmca Kclmhrk`b yVcus. 2.  i-ԛ> Ms mc eadmca dm turhucmob`k eës baeþo y ms uskda bao grmbumob`k mo kpc`bkb`aoms `odustr`kcms par su rahustmz y par su hkna basta baeputkb`aokc Y;4U. K pmskr qum oa sm dmsmepmûk h`mo mo bksas dm gumrtms lrkd`motms dm prms`òo kdvmrsk. Baos`stm mo rmsacvmr das mbukb`aoms kd`b`aokcms> pkrk mc trkospartm dm momrlåk b`oàt`bk turhucmotk i (qum dmtmre`ok ck momrlåk mo ck turhucmob`k) y pkrk ck tksk dm d`s`pkb`òo dm ck momrlåk b`oàt`bk turhucmotk ԛ  (qum dmtmre`ok ck msbkck dm ck turhucmob`k). Msta cm pmre`tm baos`dmrkr mgmbtas mo ck j`star`k dmc gcuna baea baovmbb`òo y d`gus`òo dm ck momrlåk turhucmotk Y;=U. Rm usk pkrk gcunas k kcta oþemra dm Xmyoacds, smk mo ràl`emo `obaeprms`hcm a baeprms`hcm bao Ek 3 6.2. Mc gcuna bmrbk dm cks pkrmdms ms eadmckda uskoda guob`aoms dm pkrmd, par tkota, oa ms s`euckda. Vumdm smr kpc`bkda mo mstud`as mstkb`aokr`as a dmpmod`motms dmc t`mepa. 4.  Xmkc`zkhcm i-ԛ> Ms s`e`ckr kc kotmr`ar, pmra baotmepck emnarks pkrk b`mrtas gcunas, baea bjarras turhucmotas. =.  =.  i- > Ms uo eadmca s`e`ckr kc i-ԛ, pmra mo mstm mstm bksa sm rmsumcvm rmsumcvm pkrk , ck tksk mspmbåg`bk mspmbåg`bk dm dm d`s`pkb`òo dm momrlåk b`oàt`bk. Ms uo eadmca dm hkna oþemra dm Xmyoacds y sm pumdm uskr baeh`okda bao guob`aoms dm pkrmd. Dm kbumrda bao ck dabuemotkb`òo dm BAERAC, ms uo eadmca pkrk gcunas bao kcta oþemra dm Xmyoacds, pmra tkeh`ào ms baoab`da baea uo eadmca dm hkna oþemra dm Xmyoacds pums pumdm rmsacvmr tada mc gcuna jkstk cks pkrmdms, s`o uskr guob`aoms dm pkrmd. Mstm eadmca ms eks oa-c`omkc y par tkota su baovmrlmob`k ms eës dmskg`kotm qum mo mc eadmca i-ԛ. Kdmeës, ms eës smos`hcm kc vkcar `o`b`kc supumsta pkrk ck sacub`òo. Var tkota, ms emoas rahusta.

 

]sukcemotm dk emnarms rmsuctkdas y ms eës kdmbukda qum mc i-ԛ mo rml`aoms bao rmb`rbuckb`òo, bmrbk dm pkrmdms sòc`dks, pkrk gcunas `otmroas, gcunas bao eubjk burvkturk, smpkrkb`òo dm gcuna y bjarras. 7.  7.  RRT> Rus s`lcks dmc `olcàs Rjmkr Rtrmss Trkospar, ms uo eadmca qum baeh`ok ck rahustmz dmc i-ԛ  bao ck mxkbt`tud dmc eadmca i- , ca qum ca jkbm kpc`bkhcm k uok kepc`k lkek dm gcunas. Mepcmk i-ԛ  mo cks zaoks dm barr`motm c`hrm y i-  mo cks rml`aoms bmrbkoks k cks pkrmdms, pmra su gareuckb`òo mc`e`ok kcluoks dmh`c`dkdms dm mstas das eadmcas. Dm kbumrda bao ck dabuemotkb`òo dm BAERAC, ms uo eadmca pkrk gcunas bao kcta oþemra dm Xmyoacds, pmra tkeh`ào ms baoab`da baea uo eadmca dm hkna oþemra dm Xmyoacds pums pumdm rmsacvmr tada mc gcuna jkstk cks pkrmdms, s`o uskr guob`aoms dm pkrmd. R`o mehkrla, mc eadmca dmpmodm dm ck d`stkob`k k ck pkrmd eës bmrbkok, par ca tkota, sm `obcuym uok mbukb`òo pkrk ck d`stkob`k jkb`k ck pkrmd. Ck rmsacub`òo dm ekcck rmqumr`dk ms s`e`ckr k ck dm cas eadmcas i-  y Caw Xm i-ԛ. Ms uo eadmca d`smûkda ar`l`okcemotm pkrk kpc`bkb`aoms kmrad`oëe`bks, baea gcuna kcrmdmdar dm pmrg`cms kmrad`oëe`bas. Ck mxpmr`mob`k eumstrk qum oa s`euck kdmbukdkemotm ck smpkrkb`òo dm gcuna, s`o mehkrla, ms mstkhcm y agrmbm humok baovmrlmob`k. Ms uo eadmca dm saca ; mbukb`òo. Mc eadmca dmpmodm dm ck d`stkob`k k ck pkrmd eës bmrbkok, par ca tkota, sm `obcuym uok mbukb`òo pkrk ck d`stkob`k jkb`k ck pkrmd. 0.  0.  W8-g > Ms uo eadmca kdmbukda pkrk dmsbr`h`r ck ko`satrapåk dm ck `otmos`dkd dm turhucmob`k mo ck bkpk cåe`tm, sm rmbae`modk pkrk gcunas bmrrkdas sahrm supmrg`b`ms burvks, par mnmepca, b`bcaoms. Kokc`zkoda cks dmsbr`pb`aoms hr`odkdks dm ekomrk lmomrkc. Rm baobcuym qum sao eadmcas dm `otmràs pkrk mc bksa dm mstud`a i-ԛ, i- , RRT y Caw Xm i-ԛ. Vkrk uo dmtkccm dm bkdk eadmca, sm rmbae`modk kbud`r k ck dabuemotkb`òo dm BAERAC, s`lu`moda ck rutk qum sm eumstrk k baot`oukb`òo>

 

  Kc rmv`skr ck c`tmrkturk mspmbåg`bk mo mc tmek, dmstkbko vkr`as mstud`as qum mepcmko mc eadmca RRT (Emomlazza, Dkc Eaotm, Hmo`o`, & Hmokta, 86;:), (Tueekck, Wmckekt`, R`ojk, @odrknk, & Ir`sjok, 86;7), (Xabjk, Xabjk, Bkrom`ra, dk R`cvk, & dm Kodrkdm, 86;7), (\mimsk, \kol, & \m`, 86;7), (Xabjk, Xabjk, Bkrom`ra, W`m`rk dk R`cvk, & Humoa, 86;4) y (R`olj, Kjemd, ^ucckj, & Cmm, 86;8). Var ca kotmr`ar, sm mstkhcmbmrë mc eadmca RRT pkrk cks s`euckb`aoms qum sm rmkc`zkrëo mo BAERAC. (Mo kdmckotm, tadk mbukb`òo oa rmgmrmob`kdk ms parqum gum taekdk dm ck dabuemotkb`òo dm BAERAC) 

Eadmca i-  Baea sm `od`bò kotmr`aremotm, sm rmqu`mrm rmsacvmr mc þct`ea tàre`oa dm ck dmrmbjk dm ck mbukb`òo ;6 a ;8, qum ms mc pradubta dm kpc`bkr ck dmsbaepas`b`òo a praemd`a dm Xmyoacds. Rm `otradubmo das vkr`khcms dmpmod`motms> ck momrlåk b`oàt`bk turhucmotk i  y  y ck tksk dm d`s`pkb`òo dm turhucmob`k . Vkrk bkdk uok dm mccks sm klrmlk uok mbukb`òo dm trkospartm. Mo mstm eadmca ck v`sbas`dkd turhucmotk sm bkcbuck emd`kotm ck mxprms`òo uok baostkotm. Ck mbukb`òo dm trkospartm pkrk ck momrlåk b`oàt`bk turhucmotk ms>

 5  

 daodm B ms

 

∌ +  ∘    + ( ∐ ∌) 5 ∌∐∌∐+  ∌

 

(;=)

 

Ck tksk dm pradubb`òo sm bkcbuck baea>

∌u)) ∘ 82 (∌∐) ∘ 82 ∌∐  5  ∌>∌>((∌ + (∌u) ∌∐56.         + ( ∐ ∌) 5 ∌∐∌∐+   ∌ν∌ν +    ∘  

(;7)

 

Rm rmbkcbk uok vmz eës qum pkrk mc bksa `obaeprms`hcm mc tàre`oa   Cumla, ck mbukb`òo dm trkospartm pkrk ck tksk dm d`s`pkb`òo dm turhucmob`k ms>

(;

Tksk dm bkeh`a + Trkospartm par baovmbb`òo 5 Trkospartm par d`gus`òo + tksk dm pradubb`òo ‒ ck tksk dm d`s`pkb`òo.

 56.60  5;.44  5;.08  5 ;  5;. 2

Mo mstm eadmca cks baostkotms sao , , , , . Wkcm dmstkbkr qum cks mbukb`aoms ;= y ;< oa sm pumdmo `epcmemotkr d`rmbtkemotm, par rkzaoms baea qum oa jky lkrkotåk dm oa tmomr mo kcluoas bksas d`v`s`òo motrm bmra. Ck `epcmemotkb`òo rmqu`mrm dm baos`dmrkb`aoms mspmb`kcms dmtkcckdks mo (Iuze`o, E`mrik, & Turmi, 866

  + ( ∐ ∌)5∌∐ ∘+(+)(∌+(∌)) + 

(;:)

 

Cumla, mx`stm ck vkr`kotm XOL (dmc `olcàs Xm-Oarekc`skt`ao Lraup) daodm trktko cks mbukb`aoms dm Okv`mr Rtaims pkrk taekr mo bumotk cas mgmbtas dm msbkcks eës pmqumûks dm eav`e`mota. Mo mc eadmca mstëodkr ck v`sbas`dkd turhucmotk sm dmtmre`ok bao uok þo`bk msbkck dm caol`tud, mo mc XOL sm ead`g`bk mc tàre`oa tà re`oa dm pradubb`òo pkrk baos`dmrkr d`gmrmotms msbkcks dm eav`e`mota.

Eadmca i-  Mo mc eadmca i-  sm baos`dmrk ck e`sek momrlåk b`oàt`bk turhucmotk qum mo mc bksa kotmr`ar, pmra kjark ck tksk dm d`s`pkb`òo dm turhucmob`k  sm rmmepckzk par ck tksk mspmbåg`bk dm d`s`pkb`òo dm turhucmob`k, . Mo mstm eadmca ck v`sbas`dkd turhucmotk sm bkcbuck emd`kotm ck mxprms`òo

 5  

 

Ck mbukb`òo dm trkospartm pkrk ck momrlåk b`oàt`bk turhucmotk ms>

  + ( ∐ ∌) 5  ∘ ∜+∌∐ ( + ∜)∌  

 

Ck tksk dm pradubb`òo

sm bkcbuck dmc e`sea eada qum mo mc eadmca kotmr`ar.

(;0)

 

Cumla, ck mbukb`òo dm trkospartm pkrk ck tksk dm d`s`pkb`òo mspmbåg`bk ms>

  + ( ∐ ∌) 5 ∌∐∌∐( + )∌∌ +    ∘     5   ∜ 5 ∜ ∜  5   ∜ 5   5       (86)

Mo mstm eadmca cks baostkotms y cas pkrëemtras sao

,

,

,

,

,

 , , ∜  ∜ , ; ,  5 s`    3 6  5    5    5∜ 5(  )  ;   s`    ? 6    5   (∌∐∌π)      Daodm Π  ms mc tmosar dm tksk dm ratkb`òo praemd`a Π 5   ∘  y R  ms mc tmosar dm tksk       praemd`a dm dmgarekb`òo R 5   +       Kquå sm barr`l`ò ca qum pkrmbm smr uo pmqumûa mrrar mo ck dabuemotkb`òo dm BAERAC, pums pkrk  ∜   mo ck dabuemotkb`òo mstë ck mxprms`òo  ∜ 5 ∜  , pmra kquå sm jk bacabkda  ∜ 5 ∜ ∜ . Msta parqum mo ck e`sek dabuemotkb`òo mx`stm uok mxprms`òo pkrk   ∜  ck bukc smråk `oombmskr`k dm oa mx`st`r msm tàre`oa mo cas pkrëemtras kotmr`arms.

Eadmca RRT (Rjmkr strmss trkospart) Mc eadmca dm trkospartm dm msgumrza bartkotm (RRT) baeh`ok cks vmotknks dm cas das eadmcas kotmr`arms. Ms dmc t`pa hkna oþemra dm Xmyoacds pums oa ut`c`zk guob`òo dm pkrmd, s`oa qum rmsumcvm mc gcuna mo cks rml`aoms bmrbkoks k cks pkrmdms. Mo mstm eadmca ck v`sbas`dkd turhucmotk sm bkcbuck emd`kotm ck mxprms`òo

 5  ((, )  5  8R8RR

daodm R ms ck eklo`tud bkrkbtmråst`bk dmc praemd`a dm lrkd`motms dm vmcab`dkd,

 

 

Tkeh`ào ms baoab`da baea RRT i-  pums cks das mbukb`aoms dmc eadmca mstëo mo tàre`oas dm i y , y sao>  

∜ + ∌∐∌∐( +  )∌    +  ∐ ∐∌ ∌ i 5  ∘ ∘  ∌    + ∐∐ 5   ∘  +  ∐ ( + ) +8(;∘)  ∐ 5e`o((,;6∜) 5e`o   ,  , , ) 

Daodm mc eadmca kotmr`ar.

, cumla ck tksk dm pradubb`òo

(8;) (88)

sm bkcbuck dmc e`sea eada qum mo sm

Cks baostkotms dmc eadmca (  sm dmg`omo emd`kotm `otmrpackb`òo, cks mxprms`aoms pkrk msta (d`spao`hcms mo ck dabuemotkb`òo dm BAERAC), `obcuymo k  qum sm rmg`mrm k ck d`stkob`k k ck pkrmd eës bmrbkok.



Vkrk rmsacvmr



 sm rmkc`zk uo mstud`a prmv`a, baoab`da baea –\kcc d`stkobm `o`t`kc`zkt`ao―.

 

Baemotkr`as g`okcms Ck barrmbtk y baepcmtk baeprmos`òo dm cas eadmcas dm turhucmob`k kquå mxpumstas, rmqu`mrm dm uok kepc`k garekb`òo mo ektmeët`bks (kc o`vmc dm apmrkb`aoms tmosar`kcms), embëo`bk dm gcu`das y eàtadas oueàr`bas. Var ca kotmr`ar, mstm dabuemota mspmrk baotr`hu`r bao uok baeprmos`òo hës`bk y lmomrkc, mspmb`kcemotm pkrk mstud`kotms qum `o`b`ko bao mc usa dm pralrkeks baea BAERAC, dm eada qum pumdko baeprmodmr dm ekomrk lmomrkc mc guob`aoke`mota `otmroa dmc pralrkek. Emd`kotm prëbt`bk bao mc usa dmc pralrkek y ck baepkrkb`òo dm rmsuctkdas bao dktas mxpmr`emotkcms9 y cumla dm vkr`as `otmotas dm calrkr s`euckr ck rmkc`dkd dm ekomrk skt`sgkbtar`k, mc usukr`a pumdm baeprmodmr emnar ck okturkcmzk dm bkdk eadmca y pumdm ccmlkr k knustkr kcluoas pkrëemtras a bkc`hrkr mc eadmca, pkrk qum sm knustm k cks baod`b`aoms pkrt`buckrms dm mstud`a. Vkrk bmrrkr, sm b`tk kc VjD. Krom Wko Lkrrmc, qu`mo mo uok baeuo`bkb`òo pr`vkdk mxprmsò>

–Tjm rmsmkrbj ao XkOR turhucmobm eadmcs `s oat 'smttcmd' kod  prahkhcy omvmr w`cc. Xmsmkrbjmrs krm caai`ol `ota CMR eadmcs ta rmeavm saem ag tjm prahcmes tjkt surrauod tjm Xmyoacdskvmrklmd wky ag caai`ol kt turhucmobm. Tjkt sk`d, tjm burrmot bjkep`ao `o tjm w`od momrly warcd `s tjm i-aemlk RRT eadmc w`tj mxtmos`ao ag tjm Ckoltry-Emotmr cke`okr-turhucmot c ke`okr-turhucmot trkos`t`ao eadmc. (Gar w`od turh`om kmradyoke`bs ko kbburktm prmd`bt`ao ag tjm trkos`t`ao cabkt`ao `s vmry `epartkot.)―

R`ehacalåk lcahkc 

,  ,  ,  ,   ‸  

 

 

Mnms bkrtms`koas  

Baepaomotms dm ck vmcab`dkd mo

,  , 

 

 

Baepaomotm dm ck vmcab`dkd, praemd`a, mo mc mnm   Baepaomotm dm ck vmcab`dkd, gcubtukotm, mo mc mnm  

 

dmos`dkd

V

Vrms`òo

l

Kbmcmrkb`òo dm ck lrkvmdkd

 

v`sbas`dkd d`oëe`bk

t

T`mepa

i

Momrlåk b`oàt`bk turhucmotk, par uo`dkd dm eksk, sm dmg`om baea ms ck e`tkd dm ck trkzk dmc tmosar dm msgumrzas dm Xmyoacds

 

ԛ

Tksk dm d`s`pkb`òo (momrlåk baovmrt`dk mo momrlåk tàre`bk `otmrok) dm ck momrlåk b`oàt`bk turhucmotk Ͻ 5 -di/dt

 

Tksk dm d`s`pkb`òo mspmbåg`bk.

 T , t 

W`sbas`dkd dm rmeac`oa a v`sbas`dkd turhucmotk, mo `olcàs turhucmot mddy v`sbas`ty  

 

X

⨈

 

Tmosar dm msgumrzas dm Xmyoacds Vradubta vmbtar`kc mxtmroa, a pradubta tmosar`kc

Xmgmrmob`ks lmomrkcms (s`t`as wmh, c`hras y rmpartms) Y;U MRRR, «D@OËE@BK DM GC]@DAR BAEV]TKB@AOKC> BAEV]TKB@AOKC> ±[]M MR1,¹ Imsscmr, E., 84 Nuo`a 86;7. YMo cåomkU. Kvk`ckhcm> jttps>//www.msss.ba/hcal/ms/d`o jttps>//www.msss.ba/hcal/ms/d`oke`bk-dm-gcu`d ke`bk-dm-gcu`das-baeputkb`aokc-q as-baeputkb`aokc-qum-ms/. um-ms/. Y8U D. B. \`cbax, Turhucmobm Eadmc`ol gar BGD, 8667. Y2U Bcky Ektjmekt`bs @ost`tutm, «Okv`mr-Rtaims Mqukt`ao,¹ YMo cåomkU. Kvk`ckhcm> jttp>//www.bckyektj.arl/e`ccmoo`ue-p jttp>//www.bckyektj.a rl/e`ccmoo`ue-prahcmes/okv`mr%M8% rahcmes/okv`mr%M8%:6%02staims-mqukt`ao. :6%02staims-mqukt`ao. Y4U P. K. &. B. N. E. Ìmolmc, Embëo`bk dm gcu`das> guodkemotas y kpc`bkb`aoms, Eàx`ba> Eàx`ba> EbLrkwJ`cc., 8667. Y=U E. Ekrt`o, M. Kodrms y B. &. V. G. Bkrrmrks, «Racv`ol tjm Mucmr Mqukt`aos gar ]ostrubturmd Lr`ds ao Lrkpj`bkc Vrabmssar ]o`ts,¹ D`b`mehrm 8660. Y7U \. Bkcdmròo, Kpuotms bursa bursa eàtadas oueàr`bas, Rkot`kla> ]o`vmrs`dkd dm Bj`cm, 86;2. Y//www.BAERAC.bae/hcals/wj`bjjttps>//www.BAERAC.bae/hcals/wj`bjturhucmobm-eadmc-sjaucd-bjaas turhucmobm-eadmcsjaucd-bjaasm-bgd-kppc`bkt` m-bgd-kppc`bkt`ao/. ao/. Y:U Iacealarav, «@otradubb`òo kc Eav`e`mota Turhucmota,¹ YMo cåomkU. Kvk`ckhcm> jttp>//wmhsmrvmr.det.upe.ms/zapm/DE jttp>//wmhsmrvmr.d et.upe.ms/zapm/DET/dabmob`k/ T/dabmob`k/embko`bk-dm-g embko`bk-dm-gcu`dascu`das``/ektmr`kc/`otrturh.pdg. Y0U H`h`ol, «Mbukb`aoms dm Okv`mr-Rtaims. Gmoòemoas Turhucmotas,¹ YMo cåomkU. Kvk`ckhcm> jttp>//h`h`ol.us.ms/praymbtas/khr jttp>//h`h`ol.us .ms/praymbtas/khrmpray/2 jttp>//www.tgd.bjkcemrs.sm/~ckd jttp>//www.tgd.bjkcemrs.sm/~ckdk/pastsbr`ptQg`cm k/pastsbr`ptQg`cms/tjms`sQvklms s/tjms`sQvklmsj.pdg. j.pdg. Y;2U T. Cmaokrd, «Rtmkdy/]ostmkdy «Rtmkdy/]ostmkdy XmyoacdsKvmrklmd,¹ Naurokc ag Turhaekbj`omry, Turhaekbj`omry, o¾ jttps>//bmrgkbs.gr/wp-baotmot/upca jttps>//bmrgkbs.gr /wp-baotmot/upcakds/86; jttps>//www.bgd-aoc`om.b jttps>//www.bgd-aoc`om.bae/\`i`/Iae/\`i`/Imps`caoQeadmcs.

Xmgmrmob`ks mspmb`kc`zkdks (krtåbucas b`motåg`bas) Iuze`o, D., E`mrik, A., & Turmi, R. (866 K ouemr`bkc study gar kmradyoke`b pmrgarekobm kssmssemot uodmr lust baod`t`aos. Xmomwkhcm Momrly . jttps>//da`.arl/;6.;6;7/n.rmomom.86;//da`.arl/;6.;6;7/n.momrly.86;=.;8.6:; Xabjk, V. K. B., Xabjk, J. J. H., Bkrom`ra, G. A. E., W`m`rk dk R`cvk, E. M., & Humoa, K. W. (86;4). I-π RRT (sjmkr strmss trkospart) turhucmobm eadmc bkc`hrkt`ao> K bksm study ao k sekcc sbkcm jar`zaotkc kx`s w`od turh`om. Momrly , 7=, 4;8‒4;:. jttps>//da`.arl/;6.;6;7/n.momrly.86;2.;;.6=6 R`olj, X. I., Kjemd, E. X., ^ucckj, E. K., & Cmm, P.-J. (86;8). Dms`lo ag k caw Xmyoacds ouehmr k`rga`c gar sekcc jar`zaotkc kx`s w`od turh`oms. Xmomwkhcm Momrly . jttps>//da`.arl/;6.;6;7/n.rmomom.86;;.60.6;4 Tueekck, K., Wmckekt`, X. I., R`ojk, D. I., @odrknk, W., & Ir`sjok, W. J. (86;7). K rmv`mw ao sekcc sbkcm w`od turh`oms. Xmomwkhcm kod Rustk`okhcm Momrly Xmv`mws . jttps>//da`.arl/;6.;6;7/n.rsmr.86;=.;8.68< \mimsk, D. \., \kol, B., & \m`, P. (86;7). Mep`r`bkc kod ouemr`bkc kokcys`s ag sekcc w`od turh`om kmradyoke`b pmrgarekobm kt k pcktmku tmrrk`o `o Imoyk. Xmomwkhcm Momrly . jttps>//da`.arl/;6.;6;7/n.rmomom.86;7.6;.664