Ocean currents II. Wind-water interaction and drag forces Ekman transport, circular and geostrophic flow General ocean flow pattern

Transcription

1 Ocean current II Wind-water interaction and drag orce Ekan tranport, circular and geotrophic low General ocean low pattern

2 Wind-Water urace interaction Water otion at the urace o the ocean (ixed layer) i driven by wind eect. Friction caue drag eect on the water, tranerring oentu ro the atopheric wind to the ocean urace water.

3 The drag orce Wind generate vertical and horizontal otion in the water, triggering convective otion, cauing turbulent ixing down to about 100 depth, which deine the iotheral ixed layer. The drag orce F on the water depend on wind velocity v: F or C wind A depending on urace roughne, and particularly a water v C drag interaction C the eergence o coeicient 0.00, wave! Katuhika Hokuai: The Great Wave o Kanagawa A dienionle cro ectional actor area

4 The Beauort Scale i an epirical eaure decribing wind peed baed on the oberved ea condition (1 knot = / = 1.85 k/h)!

5 For land and city people Bt 6 Bt 7 Bt 8 Bt 9 Bt 10 Bt 11 Bt 1

6 Converion ro cale to wind velocity: A trong breeze o B=6 correpond to wind peed o v=39 to 49 k/h at which long wave begin to or and white oa cret becoe requent. The drag orce can be calculated to: v B 3/ F F C A v a a A v 45 k h A N or C F A N For a trong gale (B=1), v=35 /, the drag tre on the water will be: F a / A v 35 C N

7 Ekan tranport The rictional drag orce o wind with velocity v or wind tre x generating a water velocity u, i balanced by the Corioli orce, but drag decreae with depth z. F A C a v c Fc A Au in u A 1 in Corioli paraeter z A z z z F / A 1 u / A z z z 1 τ orce in vector ter zˆ u z a zˆ u deine vector direction o tranport M τ zˆ u z Ek 0 0 zˆ u dz u dz zˆ M Ek N Ekan a tranport vector

8 depth vector Ekan tranport 0 M Ek u dz auption i a orele linear increae o M Since the horizontal wind direction u, oving the water i perpendicular to the depth vector z, the direction o the rictional drag orce i perpendicular to both vector and the agnitude i: Ek z z u z 1 M in Ek u z in 90 0 M Ek water denity with depth

9 Exaple or Ekan tranport What drag orce (preure) doe it take at a latitude o 35 o N to ove water over a depth o 10 within 1 inute by 100 to the right? M z Ek M Ek u z in 35 in z M Ek , , N Weak orce, done by wind o B with : v C k h

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11 Typical urace wind tre condition Annual ean wind tre on the ocean in unit (N/ ). The green hade repreent the agnitude o the tre. Typical wind tre value in the Weterlie reach 0.1 to 0. N/. The tronget tre coponent can be oberved or the Roaring Fortie, the weaket coponent i in the oldru.

12 z M Ek M Ek z C a v in M Calculate the a tranport M Ek or a typical wind tre o = 0.5 N/ at the outhern latitude o 40 o S. in Ek v in N About ton o water are hited within 1 ec by 1 eter to the let! eterine the wind velocity or a typical drag coeicient C =0.00? M Ek M Ek v C C a a k h About B=1- on the Beauord Scale

13 Ipact on ocean current The direction o Ekan tranport depend on the heiphere. In the northern heiphere thi tranport i at a 90 o angle to the right o the wind direction, and in the outhern heiphere it occur at a 90 o angle to the let o the wind direction. Thi generate gyre, circular otion in ocean bain liited by continental coat.

14 Reality i Reality ore i coplex ore coplex becaue becaue o additional o additional orce due orce to riction due to and the drag teperature orce eect, provided which by the add atopheric to the eddy wind oration circulation phenoenon! and by the riction orce exerted by deeper water layer!

15 Huboldt Current The cold Peruvian current (an eatern boundary current) low toward the equator along the coat o Ecuador and Peru. It low with a peed o 0.1 to 0.15[/]. In the abence o an El Niño, prevailing urace wind caue Ekan tranport to the let or away ro the coat, with ubequent upwelling o cold water. Kon Tiki, Heyerdahl thei o populating Polyneia ro the Eat rather than ro the North-Wet by taking advantage o Huboldt current or ea travel.

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17 Preure condition Preure gradient toward ocean depth can be expreed in ter o the alinity and teperature dependence o ocean water denity dp g dz P g z neglecting P P S, T, P z P g z urace urace z urace z z 100 z 1k 4k re 1at P P P S, T, P 5 10 re Pa Pa k 10 Pa 7 4k 4 10 Pa Approxiately a linear increae o preure with depth in contrat the atophere diplay an exponential decreae o preure with altitude Pa 3 Flow at larger depth i directed by the preure gradient and the Corioli orce, geotrophic low.

18 Geotrophic low A geotrophic current i an oceanic low in which the preure gradient orce i balanced by the Corioli eect. The direction o geotrophic low i parallel to the iobar, with the high preure to the right o the low in the Northern Heiphere, and the high preure to the let in the Southern Heiphere. Fluid or gaeou edia ove ro high preure to low preure region. The orce puhing the water i called the preure gradient orce F p. In a geotrophic low, water ove along the line o equal preure (iobar), intead o oving ro a high preure to low preure region. Thi occur due to Earth rotation that caue the Corioli orce F c. The Corioli orce act at right angle to the low. When it balance the preure gradient orce (F p =F c ), the reulting low becoe the geotrophic low.

19 Flow velocity Variation o preure condition or iobar with depth are aociated with teperature and alinity condition and can caue horizontal low. The preure gradient i balanced by the Corioli orce. Thi allow an etiate o the low peed. 1 Fc Fp zˆ u P yielding a low velocity 1 u zˆ P 0 u urace g re z L The preure gradient i alo aected along coatline with upward loping ground level. With being the Corioli paraeter and g the earth acceleration. L repreent the ditance over which the alinity and teperature dependent denity anoaly change. Between 0 o N and 40 o N, L 000k.

20 Geotrophic ocean low Conider the gul trea a a aple. The i a preure or denity with depth that in cobination with the previouly dicued Corioli orce aect the direction and deterine the urace low velocity u urace g re z L With being the Corioli paraeter and g the earth acceleration. L repreent the ditance over which the alinity and teperature dependent denity anoaly change. Between 0 o N and 40 o N, L 000k.

21 Etiate the gul trea urace velocity u urace auing a ditance between 0 o N and 40 o N o L=000 k or a depth o z=1000! u u urace urace g in re Overall agreeent within the range o local peed variation. The axiu peed i oberved at the wetern boundarie o the Gul trea with v 1/, while in the interior o the gyre, the peed i uch lower, v 10c/. 30 z L ,000,

22 Gul trea low velocity

23 Ocean current iulation or dierent teperature zone NASA/Goddard Space Flight Center Scientiic Viualization Studio

24 Single water drop low The low pattern i coplex and the low velocity varie greatly. Both obervable are deined by coatal boundarie, drag orce at the urace, denity gradient at deep depth, and the Corioli orce.

25 Geotrophic low induced variation in ocean urace height The curvature o the low and the horizontal velocity gradient acro the low caue a preure gradient perpendicular to the low direction, which tranlate into variation o the ocean urace height.

26 ; L g u L k L u or 1000 ; : 1 4 Ocean Surace Height

27 Exaple Gul o Mexico Flow pattern Water height Map o ea level obtained ro atellite altietry eaureent are ued to derive urace ocean current. Higher value o ea level (orange and red) are aociated with gyre and war eddie, while lower value are aociated to colder eature. riter trajectorie illutrate circulation eature. Sea height anoaly ap how the dierence o ea level ro average condition, while ea height ap how abolute value o the ea level. Altitude anoalie

28 Changing average ea altitude level Sea level trend between 199 and 009 with repect to a reerence level, baed on atellite altitude eaureent. Yellow and red region how riing ea level, while green and blue region how alling ea level. Baed on obervational data uch a tide level eaureent and atellite baed altietry