
guruthwaakarshana tharamgam

draavaka chalanathmakathayil, guruthwaakarshana shaktiyo kuthichuchaattamo santhulithaavastha punasthaapikkaan shramikkumbol oru draavaka maadhyamathilo rund maadyamangal thammilulla interfacilo srishtikkappedunna tharamgangalaanu guruthwaakarshana tharamgangal. atharamoru interfasinte oru udaaharanam anthareekshathinum samudrathinum edayilullathaanu, ithu kaatt thiramalakalkk kaaranamaakunnu.
santhulithaavasthayil ninnu draavakam sthaanabhramsham varuthumbol guruthwaakarshana tharamgam undaakunnu. draavakam santhulithaavasthayilekku punasthaapikkunnathu draavakathinte angotum ingottum oru chalanam srishtikkum, athine taranga bhramanapatham ennu vilikkunnu. samudrathinte vaayu-samudra interfacile guruthwaakarshana tharamgangale uparithala guruthwaakarshana tharamgangal (oru tharam uparithala tharamgam) ennum jalathinte pindamaya guruthwaakarshana tharamgangale (vyathyastha saandrathayude bhaagangalkkidayil polullava) "aantharika tharamgangal" ennum vilikkunnu. jala uparithalathil kaattil ninnu srishtikkappedunna thiramaalakal, athupole thanne sunaamikalum samudra veliyettangalum guruthwaakarshana tharamgangalude udaaharanangalaan.
bhoomiyile kulangal, thadakangal, kadalukal, samudrangal ennivayude swatantra uparithalathil kaattil ninnu srishtikkappedunna guruthwaakarshana tharamgangalude kaalayalav pradhaanamaayum 0.3 muthal 30 second vareyaanu (3 hearts muthal 30 megaherts vareyulla aavruthikalkku anusrithamaayi). hraswatharamgangale uparithala pirimurukkam baadikkukayum avaye "guruthwaakarshana-capillary tharamgangal" ennum (guruthwaakarshanam swaadheenikkunnillengil) "capillary tharamgangal" ennum vilikkukayum cheiyunnu. pakaramaayi, kaatt tharamgangalumaayulla subhermonic nonleeniyar taranga edapedal moolamundaakunna "infragravity tharamgangal" ennu vilikkappedunna avaykku kaatt srishtikkunna tharamgangalekkaal dairkhyamundu.
bhoomiyile anthareeksha chalanathmakatha.
bhoomiyude anthareekshathil, troposphere ninnu stratospherelake mesospherelekkum aakkam kaimaattam cheiyunna oru samvidaanamaanu guruthwaakarshana tharamgangal. troposphere guruthwaakarshana tharamgangal srishtikkunnathu frondall sistangaliloodeyo parvathangalkk mukaliloodeyulla vaayupravaahathiloodeyo aanu. thudakkathil, sharashari vegathayil ganyamaaya maattamillathe tharamgangal anthareekshathiloode vyaapikkunnu. ennaal uyarnna uyarathil tharamgangal kooduthal apoorvamaaya (nerttha) vaayuvil athumbol, avayude amplitude vardhikkukayum nonleeniyar efakttukal tharamgangale thakarkkukayum avayude aakkam sharashari ozhukkilekku maattukayum cheiyunnu. eee chalanaseshi kaimaattam anthareekshathinte niravadhi valia thothilulla chalanathmaka savisheshathakale nirbandhithamaakkunnathinna kaaranamaakunnu. udaaharanathinu, eee momentam transfer ardha-dwaivaarshika aandolanathinu bhaagikamaayi kaaranamaakunnu, mesospheres ithu ardha-vaarshika aandolanathinte pradhana prerakashakthiyaayi kanakkaakkappedunnu. athinaal, madhya anthareekshathinte chalanathmakathayil eee prakriya oru pradhana punk vahikkunnu.
meghangalile guruthwaakarshana tharamgangalude prabhavam altostraattas andulettas meghangal pole kaanapedaam, chilappol avayumaayi aashayakkuzhappathilaakume roopeekarana samvidaanam vyathyasthamaan.
alavilulla vivaranam.
aazhathilulla vellam.
tharamgasamkhya formula _ 2 ulla oru rekheeya guruthwaakarshana tharamgatthinte ghatta pravega formula _ 1 eee formula nalkunnu.
soothravaakyam _ 3
ivide "g" ennathu guruthwaakarshanam moolamulla thvaranamaanu. uparithala pirimurukkam pradhaanamaakumbol, ithu ingane parishkkarikkunnu
formula _ 4
ivide "σ" ennathu uparithala pirimurukkam gunakam, "ρ" saandrathayaanu.
guruthwaakarshana tharamgam vegathayillaatha oru nischalaavasthaykku chuttumulla oru aswasthathaye prathinidheekarikkunnu. athinaal, sisttathil avatharippicha perterbatione vivarikkunnath ananthamaaya cheria aamplityoodinte oru vegatha feeld aanu, formula _ 5 kaaranam draavakam amarcha cheyyaanaavillenn karuthappedunnu, eee vegatha feeldinu streamfuncion praathinidyamundu.
subscriptukal bhagika derivetteevukale soochippikkunna edangalil. eee derivationil, guruthwaakarshanam negatteevu "z"-dishayilekku pooyint cheiyunna rund alavukalulla formula _ 7 ll pravartthikkaan ithu mathiyakum. aduthathaayi, thudakkathil nischalamaaya amarthaanaavaatha draavakathil, vorttitti illa, draavakam itrotteshanal aayi thudarunnu, athinaal streamfuncion praathinidhyatthil formula _ 8, formula _ 9 aduthathaayi, "x"-dishayilulla sisttathinte translation invarians kaaranam, ansaats undakkaan kazhiyum.
ivide "k" oru speshyal tharamgasamkhyayaanu. angane, prashnam samavaakyam pariharikkunnathilekku kurayunnu.
nammal ananthamaaya aazhamulla oru kadalil pravartthikkunnu, athinaal athirthi vyavastha formula _ 12-laanu, aswasthathayillaatha uparithalam formula _ 13-laanu, koodaathe aswasthamaaya allengil alasamaaya uparithalam formula _ 14-laanu, avide formula _ 15 vyapthiyil cheruthaanu. thaazhe ninnu draavakam chornnolikkunnillenkil, namukk eee avastha undaayirikkanam.
athinaal, formula _ 18-leeii formula _ 17, avide "a" umm taranga vegatha "c" umm interfacile vyavasthakalil ninnu nirnnayikkenda sthiraankangalaanu.
"swatantra-uparithala avastha" swatantra uparithala soothravaakyathil _ 19, chalanathmaka avastha nilanilkkunnu
leaniorising, ithu lalithamaanu
normal-mode streamfuncion praathinidyangalum upayogichu velosity formula _ 22 uparithala formula _ 23 lake linearise cheyyumbol, eee avastha formula _ 24 aanu, ithu randaamathe interfasial avasthayaanu.
"interfasiludaneelamulla mardha bandham": uparithala pirimurukkatthinte kaaryatthil, formula _ 25 leeii interfasinmelulla mardha vyathyasam yuva-laplace samavaakyam nalkunnu
ivide "σ" ennathu uparithala pirimurukkavum "κ" ennathu interfasinte vakrathayumaan, ithu oru rekheeya ekadesharekhayil
athinaal,
ennirunnaalum, eee avastha motham marddathe (bays + aswasthatha) soochippikkunnu, athinaal
(pathivupole, aswasthamaaya alavukal uparithalathil "z = 0" aayi rekheeyamakkaam.) hydrostatic balance upayogichu, formula _ 30 roopathil
ithu maarunnu
prakshubdhamaaya marddangal stream functionukalude adisthaanathil vilayiruthunnu, prakshubdhathakalkkayi linearised euler samavaakyangalude thirashcheena momentam samavaakyam upayogikkunnu,
formula _ 33 nalkaan
eee avasana samavaakyavum jump avasthayum orumichu cherthu,
randaamathe interfasial avastha formula _ 35 pakaram vaykkukayum normal-mooad praathinidhyam upayogikkukayum cheythaal, eee bandham formula _ 36 aayi maarunnu.
parihara soothravaakyam _ 37 upayogichu, ithu nalkunnu
soothravaakyam _ 38
koneeya aavruthi soothravaakyam 40, tharamgasamkhya ennivayude adisthaanathil formula 39 ghatta vegathayaayathinaal, guruthwaakarshana taranga koneeya aavruthi ingane prakadippikkaam
soothravaakyam _ 41
oru tharamgatthinte koottavegam (athaayath, oru taranga paakkat sanjarikkunna vegatha)
soothravaakyam _ 42
angane oru guruthwaakarshana tharamgathinu,
formula _ 43
group vegatha ghatta vegathayude pakuthiyaanu. groupinteyum ghattathinteyum vegatha vyathyaasappedunna oru tharamgathe dispersive ennu vilikkunnu.
aazhamillaatha vellam.
aazhamillaatha vellathil sanjarikkunna guruthwaakarshana tharamgangal (tharamgadairkhyathekkaal valare kurravulla), avyakthamaann ghattavum koottatthilulla vegathayum samaanavum tharamgadairkhyathil ninnum aavruthiyilum ninnu swathanthravumaanu. jalathinte aazham "echu" aakumbol,
kaattil ninnu samudratharamgangalude uthpaadanam.
kaatt thiramaalakal, avayude peru soochippikkunnathu pole, anthareekshathil ninnu samudrathinte uparithalathilekku oorjjam kaimarunna kaattil ninnaan srishtikkappedunnathu, capillary-guruthwaakarshana tharamgangal eee phalatthil oru pradhana punk vahikkunnu. avayude vakthaakkalude peril vilikkappedunna rund vyathyastha samvidaanangalundu, phillips, mile.
philipsinte pravartthanatthil, samudra uparithalam thudakkathil parannathayi ("glassy") karuthappedunnu, koodaathe uparithalathinu mukaliloode prakshubdhamaaya kaatt veeshunnu. oru ozhukk prakshubdhamaakumbol, oru sharashari ozhukkine (draavaka chalanam kramappeduthukayum sugamamakkukayum cheiyunna oru laminar ozhukkinodu vipareethamaayi) kramarahithamayi ettakkurachilukal sambhavikkunna oru vegatha feeld nireekshikkunnu. ettakkurachilukalla vegatha feeld vaayu-jala interfacil pravartthikkunna ettakkurachilukalla sammarddangalkku (tangential, normal) kaaranamaakunnu. saadhaarana sammarddam allengil ettakkurachilukal oru nirbandhitha padamaayi pravartthikkunnu (oru swing thallunnathu pole oru nirbandhitha padam avatharippikkunnu). eee fozhsing padatthinte aavruthiyum tharamgasamkhya soothravaakyavum capillary-guruthwaakarshana tharamgatthinte vibration modumaayi (mukalil soochippichathupole) poruthappedunnuvenkil, oru anurananm undaakukayum tharamgam aamplityoodil valarukayum cheiyunnu. mattu anurananaafalangaleppole, eee tharamgatthinte amplitude kaalakramena rekheeyamaayi valarunnu.
capillary-gravity tharamgangal kaaranam vaayu-jala interface ippol uparithala parukkanthayaal sambannamaanu, koodaathe taranga valarchayude randaam ghattam nadakkunnu. mukalil vivarichathupole uparithalathil svayamprerithamaayi sthaapikkappetta oru tharamgam allengil laborattari saahacharyangalil, mailukal vivarikkunna reethiyil prakshubdhamaaya sharashari ozhukkumaayi samvadikkunnu. ithu critical-lair mechanism ennu vilikkappedunnu. tharangavegam "sii" sharashari prakshubdhamaaya ozhukk "yuu" nuu thulyamaaya uyarathil oru nirnaayaka paali roopappedunnu. ozhukk prakshubdhamayathinaal, athinte sharashari profile logarithamik aanu, athinaal athinte randaamathe derivative negatteevu aanu. nirnaayaka paaliyiloode interfacinu athinte oorjjam nalkaanulla sharashari ozhukkinulla vyavastha ithaanu. interfasilekkulla eee oorjja vitharanam asthirappeduthukayum interfacile tharamgatthinte vyaapthi samayabandhithamayi valaraan kaaranamaakukayum cheiyunnu. rekheeya asthirathayude mattu udaaharanangalilennapole, eee ghattatthile aswasthathayude valarchaa nirakk samayakramathil exponentialaanu.
eee mile-phillips mechanism prakriya oru santhulithaavasthayilethunna allengil kaatt tharamgangalilekku oorjjam kaimarunnathu nirthunnathuvare thudaraam (i.iii.avaye polikkuka) allengil avaa samudradooram theernnupokumbol, fetch length ennum ariyappedunnu.

