Koriolis kuchi - Coriolis force - Wikipedia

Inersial mos yozuvlar tizimida (rasmning yuqori qismida) qora shar to'g'ri chiziq bo'ylab harakatlanadi. Shu bilan birga, aylanadigan / inersial bo'lmagan mos yozuvlar tizimida (rasmning pastki qismida) turgan kuzatuvchi (qizil nuqta) ob'ektni ushbu freymda mavjud bo'lgan Coriolis va markazdan qochiruvchi kuchlar tufayli egri yo'ldan yurgan deb biladi.

Yilda fizika, Koriolis kuchi bu harakatsiz yoki xayoliy kuch^[1] a ichida harakatlanadigan narsalarga ta'sir qiladi ma'lumotnoma doirasi inersial ramkaga nisbatan aylanadigan. Bilan mos yozuvlar ramkasida soat yo'nalishi bo'yicha aylanish, kuch ob'ekt harakatining chap tomoniga ta'sir qiladi. Soat yo'nalishi bo'yicha teskari (yoki teskari) aylanadigan kuchda kuch o'ng tomonga harakat qiladi. Burilish Koriolis kuchi ta'siridagi narsaning Coriolis ta'siri. Ilgari boshqalar tomonidan tan olingan bo'lsa-da, Coriolis kuchining matematik ifodasi frantsuz olimi tomonidan 1835 yilda nashr etilgan Gaspard-Gustav de Koriolis, nazariyasi bilan bog'liq holda suv g'ildiraklari.^[2] 20-asrning boshlarida bu atama Koriolis kuchi bilan bog'liq holda ishlatila boshlandi meteorologiya.

Nyuton harakat qonunlari ob'ektning harakatini an inersial (tezlashtirmaydigan) mos yozuvlar tizimi. Nyuton qonunlari aylanadigan mos yozuvlar tizimiga aylantirilganda, Coriolis va markazdan qochiruvchi tezlashishlar paydo bo'ladi. Massiv narsalarga qo'llanganda tegishli kuchlar ga mutanosib bo'ladi ommaviy ulardan. Koriolis kuchi aylanish tezligiga, markazdan qochirma kuch esa aylanish tezligining kvadratiga mutanosibdir. Coriolis kuchi aylanish o'qiga va aylanadigan ramkada tananing tezligiga perpendikulyar yo'nalishda harakat qiladi va aylanayotgan kadrdagi ob'ektning tezligiga mutanosib (aniqrog'i, uning tezligi o'qiga perpendikulyar bo'lgan qismiga mutanosib). aylanish). Santrifüj kuch radiusli yo'nalishda tashqi tomonga ta'sir qiladi va tananing aylanadigan ramka o'qidan masofasiga mutanosibdir. Ushbu qo'shimcha kuchlar atalet kuchlari deb nomlanadi, uydirma kuchlar yoki psevdo kuchlari.^[3] Ushbu xayoliy kuchlarning qo'shilishi bilan aylanishni hisobga olgan holda Nyuton harakat qonunlari aylanma tizimga xuddi inertsional tizim singari qo'llanilishi mumkin. Ular aylanmaydigan tizimda talab qilinmaydigan tuzatish omillari.^[4]

"Coriolis effect" atamasining mashhur (texnik bo'lmagan) ishlatilishida aylanadigan mos yozuvlar tizimi deyarli har doim Yer. Yer aylanayotganligi sababli, Yerga bog'langan kuzatuvchilar ob'ektlarning harakatini to'g'ri tahlil qilish uchun Coriolis kuchini hisobga olishlari kerak. Yer har bir kun / tun tsikli uchun bitta aylanishni yakunlaydi, shuning uchun kundalik narsalar harakati uchun Coriolis kuchi boshqa kuchlarga nisbatan odatda juda kichik; uning ta'siri odatda katta masofalar va uzoq vaqt davomida sodir bo'ladigan harakatlar, masalan, atmosferada havo yoki okeandagi suvning katta miqyosdagi harakati uchun seziladi; yoki uzoq aniqlikdagi artilleriya yoki raketa traektoriyalari kabi yuqori aniqlik muhim bo'lgan joyda. Bunday harakatlar Yer yuzi tomonidan cheklangan, shuning uchun faqat Koriolis kuchining faqat gorizontal komponenti muhimdir. Ushbu kuch Yer yuzidagi harakatlanuvchi jismlarni o'ng tomonga (harakat yo'nalishi bo'yicha) burilishga olib keladi. Shimoliy yarim shar va chap tomonda Janubiy yarim shar. Gorizontal burilish effekti yaqinida katta qutblar, chunki mahalliy vertikal o'q atrofida samarali aylanish tezligi u erda eng katta va nolga kamayadi ekvator.^[5] To'g'ridan-to'g'ri aylanadigan tizimda bo'lgani kabi, yuqori bosimli joylardan past bosimga o'tishdan ko'ra, shamollar va oqimlar ushbu yo'nalishning o'ng tomoniga shimolga qarab oqadi. ekvator (soat sohasi farqli o'laroq) va undan chap tomonda (soat yo'nalishi bo'yicha). Ushbu ta'sir aylanish va shu bilan shakllanish uchun javobgardir tsiklonlar (qarang Meteorologiyada koriolis effektlari ).

Koriolis kuchining kelib chiqishini intuitiv tushuntirish uchun Yer yuziga ergashishga majbur bo'lgan va shimoliy yarim sharda shimolga qarab harakatlanadigan ob'ektni ko'rib chiqing. Kosmik kosmosdan ko'rilgan narsa shimolga qarab ketmaydi, lekin sharqqa qarab harakatlanadi (u Yer yuzi bilan birga o'ng tomonga aylanadi). U shimolni qanchalik uzoqlashtirsa, "uning parallelligi diametri" shunchalik kichik bo'ladi (sirt nuqtasidan aylanish o'qiga minimal masofa, u o'qga to'g'ri burchakli tekislikda bo'ladi) va shuning uchun uning yuzasining sharqqa harakati sekinroq bo'ladi . Ob'ekt shimolga, yuqori kengliklarga qarab harakatlanayotganda, u boshlagan sharqiy tezlikni saqlab qolish tendentsiyasiga ega (Yer yuzidagi mahalliy narsalarning pasaygan sharqiy tezligiga mos kelish uchun sekinlashgandan ko'ra), shuning uchun u sharqqa (ya'ni uning dastlabki harakatining huquqi).^[6][7]

Shimolga qarab harakatlanishni ko'rib chiqadigan ushbu misoldan ko'rinmasa ham, gorizontal burilish sharqqa yoki g'arbga (yoki boshqa yo'nalishda) harakatlanadigan narsalar uchun teng ravishda sodir bo'ladi.^[8] Biroq, effekt drenaj suvining odatdagi kattalikdagi vannada, lavaboda yoki hojatxonada aylanishini belgilaydi degan nazariya zamonaviy olimlar tomonidan bir necha bor rad etilgan; kuch aylanishdagi boshqa ko'plab ta'sirlarga nisbatan ahamiyatsiz kichikdir.^[9][10][11]

Tarix

Rasm Cursus seu Mundus Mathematicus (1674) ning C.F.M. To'pponcha aylanayotgan Yerda qanday qilib o'z nishonidan o'ng tomonga burilib ketishi kerakligini ko'rsatib turibdi, chunki to'pning o'ngga burilishi minoraga qaraganda tezroq.

Rasm Cursus seu Mundus Mathematicus (1674) ning C.F.M. To'p aylanayotgan Yerdagi minoradan qanday tushishi kerakligini ko'rsatib beradi. To'p bo'shatildi F. Minora tepasi uning asosidan tezroq harakat qiladi, shuning uchun to'p yiqilayotganda minora tagligi tomon harakatlanadi Men, lekin minora tepaligining sharqqa tomon tezligiga ega bo'lgan to'p minora poydevoridan oshib ketadi va sharqqa yana L.

Italiyalik olim Jovanni Battista Rikcioli va uning yordamchisi Franchesko Mariya Grimaldi ta'sirini artilleriya bilan bog'liq holda 1651 yilda tasvirlab bergan Almagestum Novum, Yerning aylanishi shimolga otilgan to'p sharqqa burilishiga olib kelishi kerak deb yozgan.^[12] 1674 yilda Klod François Milliet Dechales unda tasvirlangan Cursus seu Mundus Mathematicus Yerning aylanishi sayyora qutblaridan biriga yo'naltirilgan ham tushayotgan jismlarning, ham snaryadlarning traektoriyalarida burilishni keltirib chiqarishi kerak. Rikcioli, Grimaldi va Dechales bu ta'sirni Kopernikning geliosentrik tizimiga qarshi bahsning bir qismi sifatida tasvirlashdi. Boshqacha qilib aytganda, ular Yerning aylanishi effekt yaratishi kerak, shuning uchun ta'sirni aniqlay olmaganlik harakatsiz Yer uchun dalil edi.^[13] Coriolis tezlanish tenglamasi 1749 yilda Eyler tomonidan chiqarilgan,^[14][15] va effekt gelgit tenglamalari ning Per-Simon Laplas 1778 yilda.^[16]

Gaspard-Gustav Koriolis kabi aylanadigan qismlarga ega mashinalarning energiya samaradorligi to'g'risida 1835 yilda maqola nashr etdi suv g'ildiraklari.^[17] Ushbu maqolada aylanuvchi mos yozuvlar tizimida aniqlanadigan qo'shimcha kuchlar ko'rib chiqildi. Coriolis ushbu qo'shimcha kuchlarni ikki toifaga ajratdi. Ikkinchi toifaga kelib chiqadigan kuch mavjud edi o'zaro faoliyat mahsulot ning burchak tezligi a koordinatalar tizimi va zarrachaning proektsiyasi tezlik samolyotga perpendikulyar tizimga aylanish o'qi. Koriolis bu o'xshashlikni "bilan o'xshash markazlashtiruvchi kuch" deb atagan markazdan qochiradigan kuch allaqachon birinchi toifada ko'rib chiqilgan.^[18][19] Effekt 20-asrning boshlarida "nomi bilan tanilgantezlashtirish Coriolis ",^[20] 1920 yilga kelib esa "Koriolis kuchi" sifatida.^[21]

1856 yilda, Uilyam Ferrel mavjudligini taklif qildi qon aylanish hujayrasi yaratish uchun Coriolis kuchi tomonidan havo o'zgarib ketadigan o'rta kengliklarda g'arbiy shamollar hukmron.^[22]

Erning aylanishi havo oqimiga qanday ta'sir ko'rsatishi haqidagi kinematikani tushunish dastlab qisman edi.^[23] 19-asr oxiri, ning keng ko'lamli o'zaro ta'sirining to'liq darajasi bosim gradyanli kuch va oxir-oqibat havo massalari bo'ylab harakatlanishiga olib keladigan kuchni qaytaruvchi izobarlar tushunilgan.^[24]

Formula

Yilda Nyuton mexanikasi, inersial mos yozuvlar tizimidagi ob'ekt uchun harakat tenglamasi

${ displaystyle { boldsymbol {F}} = m { boldsymbol {a}}}$

qayerda ${ displaystyle { boldsymbol {F}}}$ - ob'ektga ta'sir qiluvchi jismoniy kuchlarning vektor yig'indisi, ${ displaystyle m}$ bu ob'ektning massasi va ${ displaystyle { boldsymbol {a}}}$ ob'ektning inersial mos yozuvlar tizimiga nisbatan tezlashishi.

Ushbu tenglamani boshlang'ich orqali sobit o'q atrofida aylanadigan mos yozuvlar tizimiga o'tkazish burchak tezligi ${ displaystyle { boldsymbol { omega}}}$ o'zgaruvchan aylanish tezligiga ega bo'lib, tenglama shaklni oladi

${ displaystyle { boldsymbol {F}} - m { frac { operatorname {d} { boldsymbol { omega}}} { operatorname {d} t}} times { boldsymbol {r '}} - 2m { boldsymbol { omega}} times { boldsymbol {v '}} - m { boldsymbol { omega}} times ({ boldsymbol { omega}} times { boldsymbol {r'}} )}$ ${ displaystyle = m { boldsymbol {a '}}}$

qayerda

${ displaystyle { boldsymbol {F}}}$ - ob'ektga ta'sir qiluvchi jismoniy kuchlarning vektor yig'indisi

${ displaystyle { boldsymbol { omega}}}$ bo'ladi burchak tezligi, inersiya doirasiga nisbatan aylanadigan mos yozuvlar tizimining

${ displaystyle { boldsymbol {v '}}}$ aylanadigan mos yozuvlar tizimiga nisbatan tezlik

${ displaystyle { boldsymbol {r '}}}$ aylanayotgan mos yozuvlar tizimiga nisbatan ob'ektning pozitsiya vektori

${ displaystyle { boldsymbol {a '}}}$ aylanuvchi mos yozuvlar tizimiga nisbatan tezlanish

Xayoliy kuchlar, ular aylanadigan kadrda qabul qilinganidek, haqiqiy tashqi kuchlar singari aniq tezlashishga hissa qo'shadigan qo'shimcha kuchlar sifatida harakat qilishadi.^[25][26] Tenglamaning xayoliy kuch shartlari: chapdan o'ngga o'qish:^[27]

• Eyler kuchi ${ displaystyle -m { frac { operatorname {d} { boldsymbol { omega}}} { operatorname {d} t}} times { boldsymbol {r '}}}$
• Koriolis kuchi ${ displaystyle -2m ({ boldsymbol { omega}} times { boldsymbol {v '}})}$
• markazdan qochiradigan kuch ${ displaystyle -m { boldsymbol { omega}} times ({ boldsymbol { omega}} times { boldsymbol {r '}})}$

Euler va markazdan qochiruvchi kuchlar pozitsiya vektoriga bog'liqligiga e'tibor bering ${ displaystyle { boldsymbol {r '}}}$ ob'ektning, Coriolis kuchi esa ob'ektning tezligiga bog'liq ${ displaystyle { boldsymbol {v '}}}$ aylanadigan mos yozuvlar tizimida o'lchanganidek. Kutilganidek, aylanmaydigan uchun inersial mos yozuvlar tizimi ${ displaystyle ({ boldsymbol { omega}} = 0)}$ Coriolis kuchi va boshqa barcha xayoliy kuchlar yo'qoladi.^[28] Kuchlar nol massa uchun ham yo'qoladi ${ displaystyle (m = 0)}$.

Koriolis kuchi a ga mutanosib bo'lgani uchun o'zaro faoliyat mahsulot Ikkala vektordan ikkala vektorga perpendikulyar, bu holda ob'ektning tezligi va ramkaning aylanish vektori. Shuning uchun quyidagilar kelib chiqadi:

• agar tezlik aylanish o'qiga parallel bo'lsa, Koriolis kuchi nolga teng. (Masalan, Yerda, bu holat Yer yuziga nisbatan shimolga yoki janubga qarab harakatlanadigan ekvator tanasida sodir bo'ladi.)
• agar tezlik o'qga to'g'ri qarab to'g'ri keladigan bo'lsa, Koriolis kuchi mahalliy aylanish yo'nalishida bo'ladi. (Masalan, Yerda bu holat yuqoridagi Dechales illyustratsiyasida bo'lgani kabi ekvatorda pastga tushayotgan tanada sodir bo'ladi, u erda qulab tushayotgan shar minoraga qaraganda sharqqa qarab harakatlanadi).
• agar tezlik o'qdan to'g'ri tashqariga bo'lsa, Koriolis kuchi mahalliy aylanish yo'nalishiga qarshi. (Minora misolida yuqoriga ko'tarilgan to'p g'arbiy tomon siljiydi.)
• agar tezlik aylanish yo'nalishi bo'yicha bo'lsa, Coriolis kuchi o'qdan tashqariga chiqadi. (Masalan, Yerda bu holat ekvatorda Yer yuziga nisbatan sharq tomon siljigan jism uchun sodir bo'ladi. Bu narsa er yuzidagi kuzatuvchi ko'rganidek yuqoriga qarab siljiydi. Ushbu effekt (quyida Eötvos effektiga qarang) Galiley Galiley tomonidan muhokama qilingan. 1632 va 1651 yilda Rikcioli tomonidan.^[29])
• agar tezlik aylanish yo'nalishiga qarama-qarshi bo'lsa, Koriolis kuchi o'qga qarab yo'naladi. (Yerda bu holat ekvatorda g'arbga qarab harakatlanadigan, kuzatuvchi ko'rganidek pastga qarab siljigan tanada sodir bo'ladi).

Uzunlik o'lchovlari va Rossbi raqami

Koriolis kuchining ahamiyatini aniqlashda vaqt, makon va tezlik o'lchovlari muhim ahamiyatga ega. Tizimda aylanish muhimmi yoki yo'qligini uning yordamida aniqlash mumkin Rossbi raqami, bu tezlikning nisbati, U, ning mahsulotiga tizimning Coriolis parametri,${ displaystyle f = 2 omega sin varphi ,}$va uzunlik ko'lami, L, harakatning:

${ displaystyle Ro = { frac {U} {fL}}.}$

Rossbi raqami - inertial va Coriolis kuchlarining nisbati. Rossbining kichik raqami tizimga Coriolis kuchlari kuchli ta'sir ko'rsatayotganini va katta Rossbi soni inersial kuchlar ustun bo'lgan tizimni bildiradi. Masalan, tornadolarda Rossbi soni katta, past bosimli tizimlarda past, okean tizimlarida esa 1 atrofida. Natijada, tornadolarda Coriolis kuchi ahamiyatsiz, muvozanat bosim va markazdan qochirma kuchlar o'rtasida bo'ladi. . Past bosimli tizimlarda markazdan qochiruvchi kuch ahamiyatsiz va muvozanat Coriolis va bosim kuchlari o'rtasida bo'ladi. Okeanlarda barcha uchta kuchlarni taqqoslash mumkin.^[30]

Atmosfera tizimi U = Ning fazoviy masofasini egallagan 10 m / s (22 milya) L = 1000 km (621 milya), Rossbining soni taxminan 0,1 ga teng.

Beysbol o'yini to'pni U = 45 m / s (100 milya) ga L = 18,3 m (60 fut) masofaga uloqtirishi mumkin. Rossby soni bu holda 32000 bo'ladi.

Beysbol o'yinchilari qaysi yarim sharda o'ynashimizga ahamiyat bermaydilar. Ammo boshqarilmaydigan raketa beysbol bilan bir xil fizikaga bo'ysunadi, ammo Coriolis kuchining ta'sirini sezish uchun etarlicha uzoq masofaga sayohat qilishi va uzoq vaqt havoda bo'lishi mumkin. Shimoliy yarim sharda uzoq masofali snaryadlar shu joyga qadar, ammo ular o'ng tomonga tushdi. (Janubiy yarim sharda otilganlar chap tomonga tushishdi.) Darhaqiqat, aynan shu ta'sir Koriolisning e'tiborini o'ziga qaratdi.^[31][32][33]

Oddiy holatlar

To'pni aylanayotgan karuselga uloqtirdi

Karusel soat sohasi farqli ravishda aylanmoqda. Chap panel: to'p soat 12:00 da uloqtiruvchi tomonidan uloqtiriladi va to'g'ri chiziq bilan karusel markaziga boradi. U harakatlanayotganda uloqtiruvchi soat yo'nalishi bo'yicha teskari yo'nalishda aylanadi. O'ng panel: Hozir soat 12: 00da qolgan otuvchi tomonidan ko'rilgan to'pning harakati, chunki ularning nuqtai nazari bo'yicha burilish yo'q.

Rasm soat 12:00 dan boshlab soat millariga qarshi aylanuvchi karuselning o'rtasiga uloqtirilgan to'pni tasvirlaydi. Chap tomonda to'pni karusel ustidagi harakatsiz kuzatuvchi ko'radi va to'p markazga to'g'ri chiziq bo'ylab yuradi, to'p tashlovchi esa karusel bilan soat sohasi farqli ravishda aylanadi. O'ng tomonda to'pni karusel bilan aylanayotgan kuzatuvchi ko'radi, shuning uchun to'p tashlovchi soat 12:00 da qoladigan ko'rinadi. Rasmda aylanayotgan kuzatuvchi ko'rgan to'pning traektoriyasini qanday tuzish mumkinligi ko'rsatilgan.

Chap tomonda, ikkita o'q to'pni tashlaydiganga nisbatan topadi. Ushbu o'qlardan biri uloqtiruvchidan karuselning o'rtasigacha (to'pni uloqtirishning ko'rish qobiliyatini ta'minlaydi), ikkinchisi esa karuselning o'rtasidan to'pga yo'naltirilgan. (To'p o'rtaga yaqinlashganda ushbu o'q qisqaradi.) Ikki o'qning siljigan versiyasi nuqta bilan ko'rsatilgan.

O'ng tomonda xuddi shu nuqta o'qlar ko'rsatilgan, ammo endi juftlik qat'iy ravishda aylantirildi, shuning uchun to'p otuvchini karuselning markaziga qarab o'qi soat 12:00 ga to'g'ri keladi. Juftlikning boshqa o'qi to'pni karusel markaziga nisbatan topib, aylanayotgan kuzatuvchi ko'rganidek to'pning holatini ta'minlaydi. Ushbu protsedurani bir nechta pozitsiyalar bo'yicha bajarib, aylanadigan mos yozuvlar doirasidagi traektoriya o'ng paneldagi egri yo'l bilan ko'rsatilgandek o'rnatiladi.

To'p havoda harakat qiladi va uning ustiga aniq kuch yo'q. Statsionar kuzatuvchiga shar to'g'ri chiziq bo'ylab harakat qiladi, shuning uchun bu traektoriyani nol aniq kuch bilan kvadratga aylantirishda muammo bo'lmaydi. Biroq, aylanadigan kuzatuvchi a ni ko'radi kavisli yo'l. Kinematikaning ta'kidlashicha, kuch (ga itarish) to'g'ri a uchun bir lahzalik sayohat yo'nalishi soat miliga qarshi Ushbu egrilikni keltirib chiqarish uchun aylanish) mavjud bo'lishi kerak, shuning uchun aylanadigan kuzatuvchi egri traektoriyani keltirib chiqarish uchun zarur bo'lgan aniq quvvatni ta'minlash uchun markazdan qochirma va Koriolis kuchlarining kombinatsiyasini chaqirishga majbur.

Qaytarilgan to'p

Karuselning qushlarning ko'rinishi. Karusel soat yo'nalishi bo'yicha aylanadi. Ikkita nuqtai nazar tasvirlangan: aylanish markazidagi karusel bilan aylanadigan kameraning (chap panel) va inertsional (statsionar) kuzatuvchining (o'ng panel). Ikkala kuzatuvchi ham istalgan vaqtda to'pning karusel markazidan qanchalik uzoq bo'lishiga rozi bo'lishadi, lekin uning yo'nalishi bo'yicha emas. Vaqt oralig'i ishga tushirilishdan sakrashgacha bo'lgan vaqtning 1/10 qismidir.

Rasmda aylanadigan stolga uloqtirilgan to'p karuselning chetidan sakrab chiqqandan keyin to'pni ushlab olgan uloqtirgichga qaytib boradigan murakkab vaziyat tasvirlangan. Coriolis kuchining uning traektoriyasiga ta'siri yana ikki kuzatuvchi ko'rganidek namoyon bo'ladi: karusel bilan aylanadigan kuzatuvchi ("kamera" deb nomlanadi) va inersial kuzatuvchi. Rasmda oldinga va orqaga qaytish yo'llarida xuddi shu to'p tezligiga asoslangan qushlarning ko'zlari tasvirlangan. Har bir doira ichida chizilgan nuqtalar bir xil vaqtni ko'rsatadi. Chap panelda, aylanish markazidagi kameraning nuqtai nazari bilan silkituvchi (tabassum yuzi) va rels ikkalasi ham belgilangan joylarda joylashgan bo'lib, to'p temir yo'l tomon harakatlanayotganda juda kamon hosil qiladi va to'g'ridan-to'g'ri harakat qiladi. orqaga qaytishda marshrut. To'p uloqtiruvchisi nuqtai nazaridan, to'p borgandan ko'ra tezroq qaytganday tuyuladi (chunki u qaytaruvchi parvozda uloqtiruvchi to'pga qarab aylanadi)

Karuselda orqaga qaytish uchun to'pni to'g'ridan-to'g'ri temir yo'lga uloqtirish o'rniga, uloqtiruvchi to'pni nishonning o'ng tomoniga uloqtirishi kerak, shunda to'p kameraga zarba berish uchun harakat yo'nalishining chap tomonida doimiy ravishda turishi kerak. temir yo'l (chap chunki karusel aylanmoqda soat yo'nalishi bo'yicha). To'p ichkariga va orqaga qaytish trayektoriyalarida harakatlanish yo'nalishidan chap tomonda turganday ko'rinadi. Egri yo'l bu kuzatuvchidan to'pga chapga aniq kuchni tan olishni talab qiladi. (Bu kuch "o'ylab topilgan", chunki u qisqa vaqt ichida muhokama qilinganidek, harakatsiz kuzatuvchi uchun yo'qoladi.) Ba'zi uchirish burchaklari uchun yo'l traektoriyasi taxminan radial bo'lgan qismlarga ega va Coriolis kuchi birinchi navbatda aniq burilish uchun javobgardir. koptok (markazdan qochiruvchi kuch aylanish markazidan radiusli bo'lib, ushbu segmentlarda ozgina burilishga olib keladi). Yo'l radiusdan uzoqlashganda, markazdan qochiruvchi kuch burilishga katta hissa qo'shadi.

To'pning havodan o'tishi erga qarab turgan kuzatuvchilar tomonidan ko'rib chiqilganda to'g'ri (o'ng panel). O'ng panelda (statsionar kuzatuvchi) to'p otish (tabassum yuzi) soat 12 da, to'pning sakrab chiqadigan temir yo'li birinchi holatidadir (1). Inertial tomoshabin nuqtai nazaridan birinchi (1), ikkita (2), uchta (3) pozitsiyalar ketma-ketlikda joylashgan. 2-pozitsiyada to'p relsga uriladi va 3-pozitsiyada to'p uloqtiruvchiga qaytadi. To'p erkin parvozda bo'lgani uchun to'g'ri chiziqlar bo'ylab harakatlanadi, shuning uchun bu kuzatuvchi aniq kuch ishlatilmasligini talab qiladi.

Yerga tatbiq etilgan

Havoning Yer yuzasi bo'ylab "siljishi" harakatiga ta'sir qiluvchi kuch Coriolis atamasining gorizontal qismidir

${ displaystyle -2 , { boldsymbol { Omega times v}}}$

Ushbu komponent Yer yuzidagi tezlikka nisbatan ortogonaldir va ifoda bilan berilgan

${ displaystyle omega , v 2 , sin phi}$

qayerda

${ displaystyle omega}$ bu Erning aylanish tezligi

${ displaystyle phi}$ shimoliy yarim sharda ijobiy, janubiy yarim sharda salbiy kenglikdir

Shimoliy yarim sharda bu belgi musbat bo'lganida, yuqoridan qaralgandek, bu kuch / tezlanish harakat yo'nalishidan o'ng tomonda, belgi salbiy bo'lgan janubiy yarim sharda bu kuch / tezlanish yo'nalishining chap tomonida joylashgan. harakat

Aylanadigan shar

Koordinatalar tizimi latitude kenglik bilan x- sharqqa qarshi, y-shimolga va z-aksis yuqoriga qarab (ya'ni sharning markazidan radial ravishda tashqariga).

Kenglik bilan joylashishni ko'rib chiqing φ shimoliy-janubiy o'qi atrofida aylanayotgan sharda.^[34] Bilan mahalliy koordinatalar tizimi o'rnatildi x o'qi gorizontal ravishda sharqqa, y eksa gorizontal ravishda shimoliy va z o'qi vertikal yuqoriga qarab. Ushbu mahalliy koordinatalar tizimida ko'rsatilgan aylanish vektori, harakat tezligi va Coriolis tezlashishi (sharq tartibida tarkibiy qismlar ro'yxati (e), shimoliy (n) va yuqoriga (siz)) quyidagilar:

${ displaystyle { boldsymbol { Omega}} = omega { begin {pmatrix} 0 cos varphi sin varphi end {pmatrix}} ,}$     ${ displaystyle { boldsymbol {v}} = { begin {pmatrix} v_ {e} v_ {n} v_ {u} end {pmatrix}} ,}$

${ displaystyle { boldsymbol {a}} _ {C} = - 2 { boldsymbol { Omega times v}} = 2 , omega , { begin {pmatrix} v_ {n} sin varphi -v_ {u} cos varphi - v_ {e} sin varphi v_ {e} cos varphi end {pmatrix}} .}$

Atmosfera yoki okean dinamikasini ko'rib chiqishda vertikal tezlik kichik, tortishish kuchi tufayli tezlashuv bilan taqqoslaganda Coriolis tezlanishining vertikal komponenti kichik. Bunday holatlar uchun faqat gorizontal (sharqiy va shimoliy) komponentlar muhimdir. Yuqoridagilarning gorizontal tekislik bilan chegaralanishi (sozlash) v_siz = 0):

${ displaystyle { boldsymbol {v}} = { begin {pmatrix} v_ {e} v_ {n} end {pmatrix}} ,}$     ${ displaystyle { boldsymbol {a}} _ {c} = { begin {pmatrix} v_ {n} - v_ {e} end {pmatrix}} f ,}$

qayerda ${ displaystyle f = 2 omega sin varphi ,}$ Coriolis parametri deb nomlanadi.

Sozlash orqali v_n = 0 bo'lsa, darhol ko'rish mumkin (ijobiy φ va for uchun) sharqiy harakat janubga qarab tezlashishga olib keladi. Xuddi shunday, sozlash v_e = 0, shimolga qarab harakatlanish sharqqa qarab tezlashishga olib keladi. Umuman olganda, gorizontal ravishda kuzatilgan holda, tezlanishni keltirib chiqaradigan harakat yo'nalishi bo'yicha, gorizontal yo'nalishdan qat'i nazar, tezlashuv har doim 90 ° o'ngga va bir xil o'lchamda buriladi.

Boshqa holat sifatida, ekvatorial harakat sozlamasini φ = 0 ° ko'rib chiqing. Ushbu holatda, Ω shimolga parallel yoki n-aksis va:

${ displaystyle { boldsymbol { Omega}} = omega { begin {pmatrix} 0 1 0 end {pmatrix}} ,}$     ${ displaystyle { boldsymbol {v}} = { begin {pmatrix} v_ {e} v_ {n} v_ {u} end {pmatrix}} ,}$  ${ displaystyle { boldsymbol {a}} _ {C} = - 2 { boldsymbol { Omega times v}} = 2 , omega , { begin {pmatrix} -v_ {u} 0 v_ {e} end {pmatrix}} .}$

Shunga ko'ra, sharqqa qarab harakatlanish (ya'ni sharning aylanishi bilan bir xil yo'nalishda) yuqoriga qarab tezlanishni ta'minlaydi Eötvös ta'siri, va yuqoriga qarab harakatlanish g'arbga qarab tezlanishni keltirib chiqaradi.

Meteorologiya

Bu past bosimli tizim ustida Islandiya Coriolis kuchi va bosim gradyan kuchi o'rtasidagi muvozanat tufayli soat sohasi farqli ravishda aylanadi.

A atrofida oqimning sxematik tasviri past- Shimoliy yarim sharda bosim maydoni. Rossbining soni kam, shuning uchun markazdan qochiruvchi kuch deyarli ahamiyatsiz. Bosim gradiyenti kuchi ko'k o'qlar bilan, Coriolis tezlashishi (har doim tezlikka perpendikulyar) qizil o'qlar bilan ifodalanadi.

Shamolning taxminan 50 dan 70 m / s gacha (110 dan 160 milya / soatgacha) tezligi uchun hisoblab chiqilgan boshqa kuchlar mavjud bo'lmaganda havo massalarining inertial doiralarini sxematik ravishda ko'rsatish.

Apollon 17 dan Yerning taniqli tasviridagi bulut shakllari shu kabi aylanishni bevosita ko'rinadigan qiladi

Ehtimol, Coriolis effektining eng muhim ta'siri okeanlar va atmosferaning keng ko'lamli dinamikasida bo'lishi mumkin. Meteorologiyada va okeanografiya, Yer harakatsiz bo'lgan aylanadigan mos yozuvlar tizimini postulyatsiya qilish qulay. Ushbu vaqtinchalik postulatsiyani joylashtirishda markazdan qochiruvchi va Coriolis kuchlari joriy etildi. Ularning nisbiy ahamiyati amaldagi tomonidan belgilanadi Rossbi raqamlari. Tornadolar Rossbining yuqori raqamlariga ega, shuning uchun tornado bilan bog'liq bo'lgan markazdan qochiruvchi kuchlar juda katta ahamiyatga ega, ammo tornadolar bilan bog'liq bo'lgan Coriolis kuchlari amaliy maqsadlar uchun ahamiyatsiz.^[35]

Yer yuzidagi okean oqimlari shamol sathidan suv sathidan kelib chiqqanligi sababli Coriolis kuchi ham okean oqimlarining harakatiga ta'sir qiladi va tsiklonlar shuningdek. Okeanning ko'plab yirik oqimlari iliq va yuqori bosimli hududlar atrofida aylanadi girlar. Qon aylanishi havodagidek ahamiyatli bo'lmasa-da, Coriolis effektidan kelib chiqadigan burilish bu girlarda spiral naqsh hosil qiladi. Spiralli shamol naqshlari bo'ron shakllanishiga yordam beradi. Koriolis effektidan kuch qancha kuchli bo'lsa, shamol shunchalik tez aylanib, qo'shimcha quvvat oladi, bo'ron kuchini oshiradi.^[36]

Yuqori bosimli tizimlar ichidagi havo Coriolis kuchi radial ravishda ichkariga yo'naltirilgan va tashqi radial bosim gradiyenti bilan deyarli muvozanatlashadigan yo'nalishda aylanadi. Natijada havo Shimoliy yarim sharda yuqori bosim atrofida va Janubiy yarim sharda soat yo'nalishi bo'yicha teskari yo'nalishda harakatlanadi. Past bosimli atrofdagi havo teskari yo'nalishda aylanadi, shunda Coriolis kuchi radial tomon yo'naltiriladi va ichki radialni deyarli muvozanatlaydi bosim gradyani.^[37]

Past bosimli maydon atrofida aylaning

Agar atmosferada past bosimli maydon paydo bo'lsa, havo unga qarab oqishga intiladi, lekin Coriolis kuchi tomonidan uning tezligiga perpendikulyar ravishda buriladi. Keyinchalik muvozanat tizimi aylana harakatini yoki tsiklonik oqimni yaratishi mumkin. Rossbi soni past bo'lgani uchun, kuch balansi asosan o'rtasida bosim gradyanli kuch past bosimli maydonga va past bosim markazidan uzoqlashadigan Koriolis kuchiga qarab harakat qiladi.

Gradientdan pastga tushish o'rniga atmosfera va okeandagi katta miqyosli harakatlar bosim gradyaniga perpendikulyar ravishda sodir bo'ladi. Bu sifatida tanilgan geostrofik oqim.^[38] Aylanmaydigan sayyorada suyuqlik eng to'g'ri chiziq bo'ylab oqib o'tib, bosim gradyanlarini tezda yo'q qiladi. Shunday qilib geostrofik muvozanat "inertial harakatlar" holatidan juda farq qiladi (quyida ko'rib chiqing), bu nima uchun o'rta kenglik tsiklonlari inertial aylana oqimidan kattaroq tartibda kattaroqligini tushuntiradi.

Ushbu burilish shakli va harakat yo'nalishi deyiladi Buot-byulleten qonuni. Atmosferada oqim shakli a deb nomlanadi siklon. Shimoliy yarim sharda past bosimli maydon atrofida harakatlanish yo'nalishi soat sohasi farqli o'laroq. Janubiy yarim sharda harakat yo'nalishi soat yo'nalishi bo'yicha, chunki aylanish dinamikasi u erda aks ettirilgan tasvirdir.^[39] Yuqori balandliklarda tashqariga yoyilgan havo teskari yo'nalishda aylanadi.^[40] Ushbu mintaqada mavjud bo'lgan zaif Koriolis effekti tufayli ekvator bo'ylab kamdan-kam siklonlar hosil bo'ladi.^[41]

Inersiya doiralari

Tezlik bilan harakatlanadigan havo yoki suv massasi ${ displaystyle v ,}$ faqat Koriolis kuchiga bo'ysungan holda "inersiya doirasi" deb nomlangan dumaloq traektoriyada harakatlanadi. Kuch zarrachaning harakatiga to'g'ri burchak ostida yo'naltirilganligi sababli, radiusi aylana atrofida doimiy tezlik bilan harakat qiladi. ${ displaystyle R}$ tomonidan berilgan:

${ displaystyle R = { frac {v} {f}} ,}$

qayerda ${ displaystyle f}$ bu Coriolis parametri ${ displaystyle 2 Omega sin varphi}$, yuqorida kiritilgan (qaerda ${ displaystyle varphi}$ kenglik). Shuning uchun massa to'liq doirani to'ldirish uchun sarflangan vaqt ${ displaystyle 2 pi / f}$. Coriolis parametri odatda o'rtacha kenglik qiymati taxminan 10 ga teng⁻⁴ s⁻¹; shuning uchun odatdagi atmosfera tezligi 10 m / s (22 milya) uchun radius 100 km (62 milya) ni tashkil etadi va bu davr taxminan 17 soatni tashkil qiladi. Odatda tezligi 10 sm / s (0,22 milya) bo'lgan okean oqimi uchun inersiya doirasining radiusi 1 km (0,6 milya) ga teng. Ushbu inersial doiralar Shimoliy yarim sharda soat yo'nalishi bo'yicha (bu erda traektoriyalar o'ngga egilgan) va Janubiy yarim sharda soat sohasi farqli ravishda.

Agar aylanuvchi tizim parabolik aylanadigan stol bo'lsa, u holda ${ displaystyle f}$ doimiy va traektoriyalar aniq doiralardir. Aylanadigan sayyorada, ${ displaystyle f}$ kenglik bilan farq qiladi va zarrachalarning yo'llari aniq doiralarni hosil qilmaydi. Parametrdan beri ${ displaystyle f}$ kenglikning sinusi sifatida o'zgarib turadi, ma'lum bir tezlik bilan bog'liq bo'lgan tebranish radiusi qutblarda eng kichik (kenglik = ± 90 °) va ekvator tomon o'sib boradi.^[42]

Boshqa quruqlik effektlari

Coriolis effekti katta miqyosdagi okean va atmosfera aylanishi kabi mustahkam xususiyatlarning shakllanishiga olib keladi reaktiv oqimlar va g'arbiy chegara oqimlari. Bunday xususiyatlar mavjud geostrofik muvozanat, ya'ni Koriolis va bosim gradyani kuchlar bir-birini muvozanatlashtiradi. Koriolis tezlashishi, shuningdek, okean va atmosferada ko'plab to'lqinlarning tarqalishi uchun javobgardir, shu jumladan Rossbi to'lqinlanmoqda va Kelvin to'lqinlar. Bu, shuningdek, deb atalmish uchun muhim ahamiyatga ega Ekman okeandagi dinamikalar va "deb nomlangan keng ko'lamli okean oqimining shakllanishida Sverdrup balansi.

Eötvös ta'siri

"Koriolis effekti" ning amaliy ta'siri asosan gorizontal harakatlanish natijasida hosil bo'lgan gorizontal tezlashtirish komponentidan kelib chiqadi.

Coriolis effektining boshqa tarkibiy qismlari mavjud. G'arbiy tomon harakatlanuvchi narsalar pastga, Sharqqa sayohat qiladigan narsalar yuqoriga qarab buriladi.^[43] Bu sifatida tanilgan Eötvös ta'siri. Koriolis effektining bu jihati ekvator yaqinida eng katta. Eötvös effekti tomonidan ishlab chiqarilgan kuch gorizontal komponentga o'xshaydi, ammo tortishish va bosim tufayli ancha katta vertikal kuchlar bu uning ahamiyatsiz ekanligini ko'rsatadi gidrostatik muvozanat. Biroq, atmosferada shamollar gidrostatik muvozanatdan bosimning kichik og'ishlari bilan bog'liq. Tropik atmosferada bosimning og'ish kattaligi tartibi shunchalik kichikki, bosimning og'ishiga Evotvos ta'sirining hissasi katta.^[44]

Bundan tashqari, yuqoriga qarab harakatlanadigan narsalar (ya'ni, tashqariga) yoki pastga (ya'ni, in) navbati bilan g'arbiy yoki sharq tomon buriladi. Bu effekt ekvator yaqinida ham eng katta ta'sir ko'rsatadi. Vertikal harakat odatda cheklangan darajada va davomiylikda bo'lganligi sababli, effekt hajmi kichikroq va aniqlash uchun aniq asboblarni talab qiladi. Masalan, idealizatsiya qilingan raqamli modellashtirish tadqiqotlari shuni ko'rsatadiki, bu ta'sir atmosferada uzoq vaqt (2 hafta yoki undan ko'proq) isitish yoki sovitish hisobga olingan holda tropik katta shamol maydoniga taxminan 10% ta'sir qilishi mumkin.^[45][46] Bundan tashqari, impulsning katta o'zgarishi, masalan, orbitaga kosmik kemani uchirish kabi holatlarda, ta'sir sezilarli bo'ladi. Ekvatordan to'g'ridan-to'g'ri sharqiy yo'nalishga egilib, orbitaga chiqishning eng tezkor va eng kam tejamkor yo'li.

Intuitiv misol

A orqali harakatlanadigan poezdni tasavvur qiling ishqalanishsiz bo'ylab temir yo'l liniyasi ekvator. Harakatlanayotganda u butun dunyo bo'ylab sayohatni bir kunda (465 m / s) yakunlash uchun kerakli tezlikda harakat qiladi deb faraz qiling.^[47] Koriolis effektini uchta holatda ko'rib chiqish mumkin: poezd g'arbga, tinch holatga kelganda va sharqqa sayohat qilganida. Har holda, Coriolis effektini quyidagidan hisoblash mumkin aylanadigan mos yozuvlar doirasi kuni Yer avval, so'ngra aniq bilan tekshirilgan inersial ramka. Quyidagi rasmda kuzatuvchi tomonidan Yerning shimoliy qutbidan yuqorida joylashgan sobit nuqtadan inersiya doirasidagi (yaqin) dam olish paytida ko'rgan uchta holat tasvirlangan. aylanish o'qi; poezd bir necha qizil piksel bilan belgilanadi, chap tomonda chap tomonda, chap tomonda joylashgan, boshqalarda harakatlanadi ${ displaystyle (1 { text {day}} ; { overset { land} {=}} ; 8 { text {s}}):}$

1. Poyezd g'arbiy tomon harakatlanadi: u holda u aylanish yo'nalishiga qarab harakat qiladi. Shuning uchun, Yerning aylanadigan ramkasida Coriolis atamasi aylanish o'qiga qarab pastga yo'naltirilgan (pastga). Ushbu qo'shimcha kuch pastga qarab, ushbu yo'nalishda harakatlanayotganda poezdning og'irlashishiga olib kelishi kerak.

• Agar kimdir ushbu poyezdga Yer markazining tepasida joylashgan, aylanmaydigan ramkadan qarasa, bu tezlikda Yer uning ostida aylanayotganda harakatsiz bo'lib qoladi. Demak, unga ta'sir qiladigan yagona kuch tortishish kuchi va trekning reaktsiyasi. Ushbu kuch katta (0,34% ga)^[47] yo'lovchilar va poezd dam olayotganda (Yer bilan birga aylanadigan) kuchga qaraganda. Ushbu farq Coriolis effekti aylanadigan ma'lumotnomada hisobga olinadi.

2. The train comes to a stop: From the point of view on the Earth's rotating frame, the velocity of the train is zero, thus the Coriolis force is also zero and the train and its passengers recuperate their usual weight.

• From the fixed inertial frame of reference above Earth, the train now rotates along with the rest of the Earth. 0.34% of the force of gravity provides the markazlashtiruvchi kuch needed to achieve the circular motion on that frame of reference. The remaining force, as measured by a scale, makes the train and passengers "lighter" than in the previous case.

3. The train travels east. In this case, because it moves in the direction of Earth's rotating frame, the Coriolis term is directed outward from the axis of rotation (up). This upward force makes the train seem lighter still than when at rest.

10 kilogrammli ob'ekt Yerning ekvatori bo'ylab harakatlanish tezligiga bog'liq bo'lgan kuchning grafigi (aylanadigan doirada o'lchanganidek). (Grafikdagi ijobiy kuch yuqoriga yo'naltirilgan. Ijobiy tezlik sharqqa, salbiy tezlik esa g'arbga yo'naltirilgan).

• From the fixed inertial frame of reference above Earth, the train travelling east now rotates at twice the rate as when it was at rest—so the amount of centripetal force needed to cause that circular path increases leaving less force from gravity to act on the track. This is what the Coriolis term accounts for on the previous paragraph.
• As a final check one can imagine a frame of reference rotating along with the train. Such frame would be rotating at twice the angular velocity as Earth's rotating frame. Natijada markazdan qochiradigan kuch component for that imaginary frame would be greater. Since the train and its passengers are at rest, that would be the only component in that frame explaining again why the train and the passengers are lighter than in the previous two cases.

This also explains why high speed projectiles that travel west are deflected down, and those that travel east are deflected up. This vertical component of the Coriolis effect is called the Eötvös ta'siri.^[48]

The above example can be used to explain why the Eötvös effect starts diminishing when an object is travelling westward as its tangential speed increases above Earth's rotation (465 m/s). If the westward train in the above example increases speed, part of the force of gravity that pushes against the track accounts for the centripetal force needed to keep it in circular motion on the inertial frame. Once the train doubles its westward speed at 930 m/s that centripetal force becomes equal to the force the train experiences when it stops. From the inertial frame, in both cases it rotates at the same speed but in the opposite directions. Thus, the force is the same cancelling completely the Eötvös effect. Any object that moves westward at a speed above 930 m/s experiences an upward force instead. In the figure, the Eötvös effect is illustrated for a 10 kilogram object on the train at different speeds. The parabolic shape is because the markazlashtiruvchi kuch is proportional to the square of the tangential speed. On the inertial frame, the bottom of the parabola is centered at the origin. The offset is because this argument uses the Earth's rotating frame of reference. The graph shows that the Eötvös effect is not symmetrical, and that the resulting downward force experienced by an object that travels west at high velocity is less than the resulting upward force when it travels east at the same speed.

Draining in bathtubs and toilets

Contrary to popular misconception, bathtubs, toilets, and other water receptacles do not drain in opposite directions in the Northern and Southern Hemispheres. This is because the magnitude of the Coriolis force is negligible at this scale.^{[49][50][51][52]} Forces determined by the initial conditions of the water (e.g. the geometry of the drain, the geometry of the receptacle, pre-existing momentum of the water, etc.) are likely to be orders of magnitude greater than the Coriolis force and hence will determine the direction of water rotation, if any. For example, identical toilets flushed in both hemispheres drain in the same direction, and this direction is determined mostly by the shape of the toilet bowl.

In 1962, Prof. Ascher Shapiro performed an experiment at MIT to test the Coriolis force on a large basin of water, 2 metres across, with a small wooden cross above the plug hole to display the direction of rotation, covering it and waiting for at least 24 hours for the water to settle. Under these precise laboratory conditions, he demonstrated the effect and consistent counterclockwise rotation. Consistent clockwise rotation in the southern hemisphere was confirmed in 1965 by Dr Lloyd Trefethen at the University of Sydney. See the article "Bath-Tub Vortex" by Shapiro in the journal Nature (15 December 1962, vol. 196, p. 1080–1081) and the follow-up article "The Bath-Tub Vortex in the Southern Hemisphere" by Dr Trefethen in the same journal (4 September 1965, vol.207, p. 1084-1085).

Shapiro: "Both schools of thought are in some sense correct. For the everyday observations of the kitchen sink and bath-tub variety, the direction of the vortex seems to vary in an unpredictable manner with the date, the time of day, and the particular household of the experimenter. But under well-controlled conditions of experimentation, the observer looking downward at a drain in the northern hemisphere will always see a counter-clockwise vortex, while one in the southern hemisphere will always see a clockwise vortex. In a properly designed experiment, the vortex is produced by Coriolis forces, which are counter-clockwise in the northern hemisphere."

Trefethen: "Clockwise rotation was observed in all five of the later tests that had settling times of 18 h or more."

Although there are many YouTube videos showing the common situation where the effect is not visible, versions of the delicate original experiment which verify the effect are rare.

The Coriolis force still affects the direction of the flow of water, but only minutely. Only if the water is so still that the effective rotation rate of the Earth is faster than that of the water relative to its container, and if externally applied torques (such as might be caused by flow over an uneven bottom surface) are small enough, the Coriolis effect may indeed determine the direction of the vortex. Without such careful preparation, the Coriolis effect is likely to be much smaller than various other influences on drain direction^[53] such as any residual rotation of the water^[54] and the geometry of the container.^[55] Despite this, the idea that toilets and bathtubs drain differently in the Northern and Southern Hemispheres has been popularized by several television programs and films, including Qochish rejasi, To'yni buzuvchilar, Simpsonlar epizod "Bart Avstraliyaga qarshi ", Qutbdan qutbga,^[56][57] va X-fayllar epizod "Die Hand Die Verletzt ".^[58] Several science broadcasts and publications, including at least one college-level physics textbook, have also stated this.^[59][60]

The formation of a spiral vortex over the plug hole may be explained by the conservation of burchak momentum: The radius of rotation decreases as water approaches the plug hole, so the rate of rotation increases, for the same reason that an ice skater's rate of spin increases as they pull their arms in. Any rotation around the plug hole that is initially present accelerates as water moves inward.

A letter to the editor by Richard Hake in the American Journal of Physics explained how simpler versions of the experiments of Shapiro and Trefethen can be carried out on a merry-go-round.^[61]

Ballistic trajectories

The Coriolis force is important in tashqi ballistik for calculating the trajectories of very long-range artilleriya chig'anoqlar. The most famous historical example was the Parij qurol, used by the Germans during Birinchi jahon urushi to bombard Parij from a range of about 120 km (75 mi). The Coriolis force minutely changes the trajectory of a bullet, affecting accuracy at extremely long distances. It is adjusted for by accurate long-distance shooters, such as snipers. Kengliklarida Sakramento, California, a 1,000 yd (910 m) northward shot would be deflected 2.8 in (71 mm) to the right. There is also a vertical component, explained in the Eötvös effect section above, which causes westward shots to hit low, and eastward shots to hit high.^[62][63]

The effects of the Coriolis force on ballistic trajectories should not be confused with the curvature of the paths of missiles, satellites, and similar objects when the paths are plotted on two-dimensional (flat) maps, such as the Merkator proektsiyasi. The projections of the three-dimensional curved surface of the Earth to a two-dimensional surface (the map) necessarily results in distorted features. The apparent curvature of the path is a consequence of the sphericity of the Earth and would occur even in a non-rotating frame.^[64]

Visualization of the Coriolis effect

Fluid assuming a parabolic shape as it is rotating

Object moving frictionlessly over the surface of a very shallow parabolic dish. The object has been released in such a way that it follows an elliptical trajectory.
Chapda: The inertial point of view.
To'g'ri: The co-rotating point of view.

The forces at play in the case of a curved surface.
Qizil: gravity
Yashil: the normal kuch
Moviy: the net resultant markazlashtiruvchi kuch.

To demonstrate the Coriolis effect, a parabolic turntable can be used.On a flat turntable, the inertia of a co-rotating object forces it off the edge. However, if the turntable surface has the correct paraboloid (parabolic bowl) shape (see the figure) and rotates at the corresponding rate, the force components shown in the figure make the component of gravity tangential to the bowl surface exactly equal to the centripetal force necessary to keep the object rotating at its velocity and radius of curvature (assuming no friction). (Qarang banked navbat.) This carefully contoured surface allows the Coriolis force to be displayed in isolation.^[65][66]

Discs cut from cylinders of quruq muz can be used as pucks, moving around almost frictionlessly over the surface of the parabolic turntable, allowing effects of Coriolis on dynamic phenomena to show themselves. To get a view of the motions as seen from the reference frame rotating with the turntable, a video camera is attached to the turntable so as to co-rotate with the turntable, with results as shown in the figure. In the left panel of the figure, which is the viewpoint of a stationary observer, the gravitational force in the inertial frame pulling the object toward the center (bottom ) of the dish is proportional to the distance of the object from the center. A centripetal force of this form causes the elliptical motion. In the right panel, which shows the viewpoint of the rotating frame, the inward gravitational force in the rotating frame (the same force as in the inertial frame) is balanced by the outward centrifugal force (present only in the rotating frame). With these two forces balanced, in the rotating frame the only unbalanced force is Coriolis (also present only in the rotating frame), and the motion is an inertial circle. Analysis and observation of circular motion in the rotating frame is a simplification compared with analysis and observation of elliptical motion in the inertial frame.

Because this reference frame rotates several times a minute rather than only once a day like the Earth, the Coriolis acceleration produced is many times larger and so easier to observe on small time and spatial scales than is the Coriolis acceleration caused by the rotation of the Earth.

In a manner of speaking, the Earth is analogous to such a turntable.^[67] The rotation has caused the planet to settle on a spheroid shape, such that the normal force, the gravitational force and the centrifugal force exactly balance each other on a "horizontal" surface. (Qarang ekvatorial bo'rtma.)

The Coriolis effect caused by the rotation of the Earth can be seen indirectly through the motion of a Fuko mayatnik.

Coriolis effects in other areas

Coriolis flow meter

A practical application of the Coriolis effect is the ommaviy oqim o'lchagich, an instrument that measures the ommaviy oqim tezligi va zichlik of a fluid flowing through a tube. The operating principle involves inducing a vibration of the tube through which the fluid passes. The vibration, though not completely circular, provides the rotating reference frame that gives rise to the Coriolis effect. While specific methods vary according to the design of the flow meter, sensors monitor and analyze changes in frequency, phase shift, and amplitude of the vibrating flow tubes. The changes observed represent the mass flow rate and density of the fluid.^[68]

Molekulyar fizika

In polyatomic molecules, the molecule motion can be described by a rigid body rotation and internal vibration of atoms about their equilibrium position. As a result of the vibrations of the atoms, the atoms are in motion relative to the rotating coordinate system of the molecule. Coriolis effects are therefore present, and make the atoms move in a direction perpendicular to the original oscillations. This leads to a mixing in molecular spectra between the rotational and vibrational darajalar, from which Coriolis coupling constants can be determined.^[69]

Giroskopik prekretsiya

When an external torque is applied to a spinning gyroscope along an axis that is at right angles to the spin axis, the rim velocity that is associated with the spin becomes radially directed in relation to the external torque axis. This causes a Torque Induced force to act on the rim in such a way as to tilt the gyroscope at right angles to the direction that the external torque would have tilted it. This tendency has the effect of keeping spinning bodies in their rotational frame.

Hasharotlarning parvozi

Flies (Diptera ) and some moths (Lepidoptera ) exploit the Coriolis effect in flight with specialized appendages and organs that relay information about the burchak tezligi ularning tanalari.

Coriolis forces resulting from linear motion of these appendages are detected within the rotating frame of reference of the insects' bodies. In the case of flies, their specialized appendages are dumbbell shaped organs located just behind their wings called "halterlar ".^[70]

The fly's halteres oscillate in a plane at the same beat frequency as the main wings so that any body rotation results in lateral deviation of the halteres from their plane of motion.^[71]

In moths, their antennae are known to be responsible for the sezish of Coriolis forces in the similar manner as with the halteres in flies.^[72] In both flies and moths, a collection of mechanosensors at the base of the appendage are sensitive to deviations at the beat frequency, correlating to rotation in the pitch va roll planes, and at twice the beat frequency, correlating to rotation in the yaw samolyot.^[73][72]

Lagrangian point stability

In astronomy, Lagrangiyalik fikrlar are five positions in the orbital plane of two large orbiting bodies where a small object affected only by gravity can maintain a stable position relative to the two large bodies. The first three Lagrangian points (L₁, L₂, L₃) lie along the line connecting the two large bodies, while the last two points (L₄ va L₅) each form an equilateral triangle with the two large bodies. L₄ va L₅ points, although they correspond to maxima of the samarali salohiyat in the coordinate frame that rotates with the two large bodies, are stable due to the Coriolis effect.^[74] The stability can result in orbits around just L₄ yoki L₅sifatida tanilgan turpole orbitalari, qayerda troyanlar topish mumkin. It can also result in orbits that encircle L₃, L₄va L₅sifatida tanilgan horseshoe orbits.

Shuningdek qarang

Izohlar

Adabiyotlar

Qo'shimcha o'qish

Physics and meteorology

Tarixiy

Tashqi havolalar

• The definition of the Coriolis effect from the Glossary of Meteorology
• The Coriolis Effect — a conflict between common sense and mathematics PDF-fayl. 20 bet. A general discussion by Anders Persson of various aspects of the coriolis effect, including Foucault's Pendulum and Taylor columns.
• The coriolis effect in meteorology PDF-fayl. 5 pages. A detailed explanation by Mats Rosengren of how the gravitational force and the rotation of the Earth affect the atmospheric motion over the Earth surface. 2 figures
• 10 Coriolis Effect Videos and Games - from the About.com Weather Page
• Coriolis Force - dan ScienceWorld
• Coriolis Effect and Drains Saytida joylashgan NEWTON veb-saytidan maqola Argonne milliy laboratoriyasi.
• Coriolis video katalogi
• Coriolis Effect: Grafik animatsiya, aniq tushuntirish bilan vizual Yer animatsiyasi
• Suyuqlik dinamikasiga kirish SPINLab o'quv filmi laboratoriya tajribalari yordamida Coriolis effektini tushuntiradi
• Shimoliy yarim sharda vannalar soat sohasi farqli ravishda drenaj qiladimi? Sesil Adams tomonidan.
• Yomon Koriolis. Coriolis effekti haqidagi noto'g'ri ma'lumotni ochib beruvchi maqola. Alistair B. Freyzer tomonidan, Atrof-muhit bo'yicha meteorologiya professori Pensilvaniya shtati universiteti
• Coriolis effekti: oddiy (oddiy) tushuntirish, ish beruvchiga tushuntirish
• Koriolis effektining Yer yuzidagi animatsiyasini kuzating
• Animatsiya klipi ikkala inertial ramkadan va aylanadigan mos yozuvlar tizimidan ko'rinadigan sahnalarni ko'rsatish, Koriolis va markazdan qochiruvchi kuchlarni tasavvur qilish.
• Vinsent Mallet Coriolis kuchlari @ INWIT
• NASA qaydlari
• Interaktiv Coriolis favvorasi Coriolis effektini o'rganish uchun aylanish tezligini, tomchi tezligini va mos yozuvlar doirasini boshqarishga imkon beradi.
• Aylanadigan koordinatsion tizimlar, inersial tizimlardan transformatsiya