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Földi Áramlások Fizikája I És II FÖLDI ÁRAMLÁSOK FIZIKÁJA Dr. Galsa Attila Eötvös Loránd Tudományegyetem Természettudományi Kar Geofizikai és Űrtudományi Tanszék Budapest, 2018. TARTALOMJEGYZÉK 1. Áramlás porózus közegben .............................................................................................. 4 1.1. Bevezetés ..................................................................................................................... 4 1.2. Alapfogalmak .............................................................................................................. 5 1.2.1. Porozitás ............................................................................................................... 5 1.2.2. A felszín alatti vizek mélysége és eredete ............................................................ 6 1.2.3. A Darcy-törvény és a permeabilitás fogalma ....................................................... 7 1.2.4. Egy permeábilis kőzet modellje ............................................................................. 12 1.3. Hidraulikus vezetőképesség. Homogén, izotróp vagy inhomogén, anizotróp közeg? .. ................................................................................................................................... 15 1.3.1. A Darcy-törvény különböző alakjai ................................................................... 15 1.3.2. Üledékes medencék vízvezető-képesség anizotrópiája ...................................... 17 1.3.3. Analógia a vízvezető-képesség és az elektromos vezetőképesség között .......... 20 1.3.4. Hidrogeológiai alapszituációk ............................................................................ 21 1.4. Vízáramlás szabad tükrű víztározóban ...................................................................... 25 1.4.1. A modell leírása ................................................................................................. 25 1.4.2. A felszínalatti vízáramlást leíró alapegyenletek és határfeltételek .................... 26 1.4.3. A probléma megoldása ....................................................................................... 27 1.4.4. A megoldás diszkussziója .................................................................................. 29 1.4.5. Homogén, anizotróp tározó ................................................................................ 32 1.5. A Dupuit-féle közelítés és alkalmazása egyszerű kúthidraulikai problémák esetén ..... 34 1.5.1. Stacionárius áramlás alapegyenlete .................................................................... 34 1.5.2. Fedett és fedetlen víztározó egyenlete.................................................................... 35 1.5.3. Kúthidraulika fedett és fedetlen tározóban ......................................................... 37 1.6. A felszínalatti vízáramlás alapegyenlete stacionárius és időfüggő esetben............... 44 1.6.1. Stacionárius áramlás egyenlete .......................................................................... 44 1.6.2. Nem stacionárius áramlás egyenlete .................................................................. 45 1.6.3. Tározási tényezők ............................................................................................... 49 1.7. Termikus konvekció porózus közegben .................................................................... 50 1.7.1. Porózus közegben zajló termikus konvekció alapegyenletei ............................. 50 1.7.2. A perturbációs egyenletrendszer ........................................................................ 51 1.7.3. A perturbációs egyenletrendszer megoldása ...................................................... 53 1.8. Tömeg- és hőtranszport felszín alatti vizekben ......................................................... 60 1.8.1. Tömegtranszport ................................................................................................. 60 1.8.2. Hőtranszport egyenlet ........................................................................................ 65 2. Áramlás a földköpenyben .............................................................................................. 70 2.1. Bevezetés ................................................................................................................... 70 1 2.2. Lemeztektonika — a földköpeny-konvekció szemszögéből ..................................... 75 2.2.1. Óceánközépi hátság, mint akkréciós lemezszegély ............................................ 75 2.2.2. Óceáni litoszféra ................................................................................................. 75 2.2.3. Mélytengeri árok, mint konvergens lemezszegély ............................................. 77 2.2.4. Forrófoltok, köpenyoszlopok ............................................................................. 82 2.3. A lemeztektonika motorja és időbelisége .................................................................. 85 2.3.1. A lemeztektonika hajtóerői ................................................................................ 85 2.3.2. Mi hajtja a lemeztektonikát? .............................................................................. 85 2.3.3. A Wilson-ciklus .................................................................................................. 89 2.3.4. Bizonyíték és magyarázat a Wilson-ciklus létezésére ........................................ 91 2.4. A Föld belső szerkezete ............................................................................................. 93 2.4.1. A Föld radiális szerkezete .................................................................................. 93 2.4.2. Kéreg .................................................................................................................. 97 2.4.3. Köpeny ............................................................................................................... 98 2.4.4. Mag ................................................................................................................... 102 2.4.5. A köpeny háromdimenziós szerkezete ............................................................. 103 2.5. Ásványtani fázisátalakulások a köpenyben ............................................................. 112 2.5.1. Az ásványtani fázisátmenet kvalitatív ismertetése ........................................... 112 2.5.2. A 410 és a 660 km-es ásványtani fázisátmenet kvalitatív hatása a köpenyáramlásokra ......................................................................................................... 115 2.5.3. A 410 km-es ásványtani fázisátmenet kvantitatív hatása a lebukó lemezre..... 117 2.5.4. A 660 km-es ásványtani fázisátmenet kvantitatív hatása a lebukó lemezre..... 121 2.5.5. Az átmeneti zóna vastagsága ............................................................................ 121 2.6. Jégkorszak utáni felszínemelkedés .......................................................................... 124 2.7. A köpeny viszkozitása ............................................................................................. 132 2.7.1. A köpenyviszkozitás meghatározásának módszerei......................................... 132 2.7.2. Radiális hőmérsékleteloszlás a köpenyben ...................................................... 135 2.7.3. Radiális viszkozitásprofil a köpenyben ............................................................ 137 2.7.4. Földköpeny, mint viszkoelasztikus közeg ........................................................ 139 2.7.5. A creep folyás, mint viszkózus deformáció ..................................................... 141 2.8. Termikus köpenykonvekció alapegyenletei ............................................................ 146 2.8.1. Kontinuitási egyenlet — tömegmegmaradás ................................................... 146 2.8.2. Navier–Stokes-egyenlet — impulzusmegmaradás ........................................... 148 2.8.3. Hőtranszport egyenlet — energiamegmaradás ................................................ 151 2.8.4. Az állapotegyenlet ............................................................................................ 154 2.8.5. A szubsztanciális időderivált ............................................................................ 155 2.9. Az alapegyenletektől a közelítő egyenletekig ......................................................... 157 2 2.9.1. Alapegyenletek ................................................................................................. 157 2.9.2. Referenciaállapot .............................................................................................. 158 2.9.3. Dimenziótlan egyenletek .................................................................................. 160 2.9.4. Boussinesq-approximáció ................................................................................ 163 2.10. Rayleigh–Bénard-probléma ................................................................................. 165 2.10.1. Lineáris stabilitási elmélet ............................................................................ 165 2.10.2. A kritikus Rayleigh-szám meghatározása .................................................... 168 2.10.3. Az áramlási szerkezet változása a Rayleigh-szám hatására ......................... 176 3. Áramlás a külső magban ............................................................................................. 179 3.1. A termomágneses konvekció alapegyenletei ........................................................... 179 3.1.1. A Boussinesq-approximáció
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