An object moving with speed v around a point at distance r, has an angular velocity. m/s m

Transcription

1 Roion The mosphere roes wih he erh n moions wihin he mosphere clerly follow cure phs (cyclones, nicyclones, hurricnes, ornoes ec.) We nee o epress roion quniiely. For soli objec or ny mss h oes no isor uring roion, we use he erm ngulr elociy (Greek omeg). Ler, we will ssign he erm oriciy o he roion of flui such s he mosphere. Angulr elociy epresses he re of roion of boy n is efine s he ngle in rins hrough which he boy urns in uni ime. The unis of re herefore rins/secon. Remember hough h rin is frcion of complee reoluion ( rins 360 o ) n i is no funmenl imension (like ime or lengh) h mus be crrie hrough in ny clculion inoling. An objec moing wih spee roun poin isnce r, hs n ngulr elociy r r m/s m s Angulr elociy is ecor quniy. We op he conenion h he ecor ssocie wih he roion is ligne wih he is of roion in he sense of righ-hn screw (he righ hn rule: wih your humb ligne wih is of roion n poining in he irecion of he ecor, your fingers, curling roun he plm of your hn, will gie he irecion of roion).

2 The ngulr elociy of he erh The erh roes owrs he es n, herefore, he ecor ngulr elociy poins ouwrs from he norh pole (n ino he souh pole). The mgniue of is one reoluion ( rins) per y bu we mus clcule i from he urion of he sierel y, relie o he srs n no o he sun. The sierel y is 3 hrs 56 minues N (3 hrs 56 min) r/s Since mos mosphere moion is prllel o he erh s surfce n he mosphere is ery hin shee encircling he globe, we re concerne primrily wih he mgniue of he componen of he erh s ngulr elociy long he locl ericl irecion. This is roion in locl horizonl plne.

3 N z is liue ngle z is he locl ericl componen of he ngulr elociy. A he norh pole, z (- he S-pole) A he equor, 0 z In generl, z sin. The Coriolis effec The Coriolis effec is he ppren eiion of ny boy or mss of ir in moion h resuls from he roion of he erh. The mosphere is couple o he erh only hrough griy n fricion he surfce. Oherwise, i is free o moe inepenenly. Any nlysis of he moion of he mosphere in erms of Newon s lws of moion mus be me in frme of reference oriene o he srs (in ineril frme of reference). Howeer, he erh roes in his frme of reference n is herefore non-ineril frme. To compense for he influence of he erh s roion, we inrouce n ppren force, he Coriolis force, h llows us o re he mosphere using he bsic lws of moion. Consier n objec (or mss of ir) moing on surfce h is roing bou some locl ericl is wih ngulr elociy. Suppose he objec is no subjec o ny eernl forces n is hus moing consn spee owrs some reference poin ousie he 3

4 roing surfce. O A' A,B' B * reference poin (fie sr) A he sr, he poin A is ligne wih he reference poin n he objec hes irecly for i. Howeer, in he inerl of ime i kes for he objec o rech his ril isnce, poin A hs roe o A. The objec rries poin B on he surfce which hs roe o B, in line wih he reference poin. Anlyzing he moion s n obserer on he roing surfce, we woul see he objec moing in cure ph s shown on he plo below. A O B * The cure ph O o B is s seen by he surfce boun obserer, while he srigh line O o B is he ph s iewe by n obserer ousie he roion coorine sysem. The cure ph ppers s eiion o he righ of he moion in his cse in which he roion is niclockwise (s is he roion of he norhern hemisphere). In he roing frme of reference, we cn eplin his moion by inroucing he Coriolis force n Coriolis ccelerion. 4

5 The mgniue of he Coriolis ccelerion Consier n objec in moion in he norhern hemisphere subjec only o he Coriolis force cing o urn i o he righ from is curren irecion of moion. O << Le Coriolis ccelerion be, hen he isnce rele o he righ where is he rel ime, which cn be rele o he spee of he objec n he isnce rele such h n, herefore Now, he siewys moion cn lso be clcule from he ngulr elociy of he rge bou he origin. Le his ngulr elociy be, hen 5

6 Equing hese wo epressions for, we obin giing (no moion, no force) If is h ue o he erh s roion bou locl ericl is, such h sin hen ( f sin ) where f sin is clle he Coriolis prmeer Clculing f ifferen liues, Liue f(s - ) (mi liues 0-4 ) (wice ) 6

7 This ocumen ws cree wih WinPDF ilble hp:// The unregisere ersion of WinPDF is for eluion or non-commercil use only.