Special Topics in Aerospace Engineering
Special Topics in Aerospace Engineering MAE 4504
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This 36 page Class Notes was uploaded by Dayton Klein II on Monday September 21, 2015. The Class Notes belongs to MAE 4504 at University of Virginia taught by Robert Johnson in Fall. Since its upload, it has received 32 views. For similar materials see /class/209793/mae-4504-university-of-virginia in Mechanical and Aerospace Engineering at University of Virginia.
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Date Created: 09/21/15
Part6c Circulation Cont Means of Transferring Heat Global Circulation Easterlies NVesterlies Polar Front Planetary Waves Gravity Waves Mars Circulation Giant Planet Atmospheres Zones and Belts Global Circulation on Earth Coriolis parameter f 0 but rotates fast enough so day night differences small unlike Venus Warm air rises to the tropopause Equator to pole Hadley Cell Equatorial low polar high Winds and Temperatures solid TC dashed vms heavy line tropopause H u vm 5391 LATITl m i1 Earth with Rotation f 0 Rising Tropical air returns at higher latitudes roughly three cells I Cequot 73232quot Ferrel Cell Su blruplcal 7 Jet Stream K V Hadley Cell Form midlatitude highs with transport southward weak easterlies f small and northward stronger westerlies larger f Also a polar high Note upper troposphere global flow Thermal Wind Horizontal gradient in T and or I Geostrophic flow can intensify with z Geostrophic wind Fa Vp gtllt V pf E local vertical Vh local horiz used earlier p z poeXpZH H kTmg Therefore small surface pressure difference but different T can give large pressure difference at high altitudes Using slope of V vs altitude proportional to the horizontal temperature gradient a V oc IVTIh 62 Horizontal temperature differences causes increasing pressure differences with altitude intensifying geostrophic flow Earth Global Circulation Cont Pressure Altitude hPa feel Subtropical WNW WPDPHS mam b jet stream 39 1W Eolarfranl 19 5quot Middiatmpapause V 39 quot900 Polar 396 w 39 Samoa 500 H39 Hadley cell mam W I Polar front call NW Puiarml Q i mma m l Polar Sub39mm u Subrm it nigpfwim high 12 3quot 905 Aniarciir 4505 was a from Note When a cold air mass and a warm air mass interact the differences in pressure increases with altitude H kTmg gt Stronger winds at higher altitudes westerlies become jets between 30 and 70 Geostrophic circulation around highs and lows can be organized as easterlies and westerlies 30 pica Q 5th Equatorial trough 011sz Ease ads 30 pica igh belt Northern Hemigphere IQ Hextern astgrn Pau c an c Equator Southern Hemisphere high PressureFlow Maps SearLeveressuye and Su ace Wmds Polar high also Jan 7 v A Red ITCZ MW Upper Troposphere Geostrophic but disconnected from land and sea masses Rossby Waves bring warm air north and cool air south lune gr v w 09 As seen from earlier slide westerly motion about the polar low Waves break offgt highs lows Wave crests move slowly west Upper Troposphere Wave Winter geopotential height fg dz of isobar Fig 54 Emw1m a height adquot the 39tl I 13mm surfing in dm km nh m bends12mm Whl39lzr i mzanian The hrs Hal 3 Emma is ma a1y mm Rossby Waves and Vorticity Include convection term a VvV7 2 2gtlt7 in 6t p 2 D 1 ua vi ufv ia p 6 t 6 6 y p 6 X 2 a u vi v fu ia p a t a X p a y continuity a V v 0 incompressible 3 Q 6 V 0 6 X 6 y Differentiate 1 With respect to y and 2 With respect to X subtract and then use 3 Define vorticity of the ow g 6 V 12 V x v 6 X 6 y Find i f0 asusual i iV V dt dt 0 Therefore Conserve Total Vorticity C f If f decreases air moves south then C must increase PLANETARY WAVES lt 05 bar Earth 52 j a w H Upper Troposphere Rossby Waves Westerlies Incompressible Flow Total Vorticity Conserved d fdt 0 C k VXV vorticity Northern Hemisphere C gt 0 counterclockwise C lt clockwise Southern Hemisphere Wanner air Equatorward swing Anticyclonica y curvgd ow Poleward swing Cyclenr39ca y curved New North Upper trough of 1 Low pressure r Colder air Upper ridge of Upper ridges High pressure High pressure South Pole lt 0 counterclockwise C gt0 clockwise f lt 0 increasing northward Wave Period rotation rate temperature difference Outer cylinder hot inner can A type of baroclinic wave transferred to fluid Usual turbulence large to small scale Here small scale goes to organized flow Rossby Waves and Jet Streams 50400kmlhr earth equator 3000kmlhr break off to form weather 1000 to 3000 Miles Long 1 to 3 Miles Thick Jet Stream Geopotential Heights of 300mbar Level uh Earth s Thermospheric flow near exobase Note Day I Night effects Unlike troposphere NEUTHHL TEMPERHTURE DB 100 ME HT I11 LLJ III LJ D D H E l ElEI CI ll ELK 12D TELIZJ E39U ELI LUCRL TIME HHS U DE03 1 BDQE03 INTERVAL 2SOUUEUI IELEITGCN1BEPEBSKD1 DATHRHIN 6 D 94739E03 r IIHVN Gravity Waves pa2 pa mg a 2 m m Stable conditions Pd gty 2 z a z waves With the Brunt Vaisala frequency Rising air at Lows and falling at Highs also drive planet scale gravity waves mixing the troposphere with upper atmosphere Gravity Waves at Mars 0 ac IZD 155 200 220 230 T39K Latitude Mars Circulation uid density is low coriolis effect can be signi cant Axial Tilt Warm Summer Pole Strong Gradients Strong Irregular Westerlies Winter L a H HN I I l l e lt lt lt lt summer Weak Easterlies T Dus t storms at Mars Mars Glnhal Dust Sxmm June 5 20m sepmmum zuol Huhbla Space Telescope mm mm J sell mm M Wolquot SSH and ma mm Hm 4 man stsduxunm 515c1PkcmJI Temperature and Cloud Structure Gas Giants Jupiter 71300km and Saturn 60300km Ice Gian Uranus and Neptune 25000km Thaml pm lal Jupllev39s cloudslmclwe Salum39l cloud wuan ll w w an w v w m rm quotm l5u39i mlli quotquot nl25u llquot quot Clouds 032bars i indicative of winds g l in Galileo I What are winds relative to on a n gas ball n wnm spad mm Gas Giants Sun Internal Heat 17 x solar J 125 S 1100 Earth Fast rotors 10hrgtHigh Wind Speeds Small Scale Eddies Feed Zonal Flow Jupiter Zonal Winds Westerlies bright Eq 150ms J 400ms S Belts Easterlies dark Red Spot High counter clockwise Saturn Yearly 30 year Storms Planet Rpkm X T011 HMWVm39Q Fsmrmm39Q Jupiter 71400 08 9925 544 130 Saturn 00330 05 1000 201 40 HD2094580 90400 05 0707 3 12gtlt106 X1DRp where D is thickness of H2 layer FAST ROTOR Horizontal 6 t Vertical View Giant Planet Atmospheres ION am am LOU m m m Nessa m 554 MM Mum com um Com mm w low n91 L m sum antssut msm quotSM Zones westerlies eastern flow prograde Bright clouds condensed from H act to cool air hi her 84 per hemisphere jupiter Saturn Belts easterlies retrograde Dark clouds warmer drier descending air 3 139 x amp swag Ammmgp mm Dronm nm e by c n cu a u mm GEMS and zama W mds man ked by a fferemt eo m ed 1de layers which are higher in be ts than I39m zones Black small circle is Io Latitude Zonal Wind Speeds vs Latitude at cloud level 90H 3 1 Jupiter Cs Saturn than Neptune 45M E l lt5 i 3L K 1 4 I 4 E0 lt15 2 5 39 lt tjf E E 2 i x 903 3 f 1 j 5 39 0 100 200 O 200 400 0 200 400 400 Ums Positve umls Westerlies Simulation of Eddys converting to flow has 4mm quot L r 2quot nu um af i 1 like 1 aquot m run 339 23 I II Qw ycm I I quot 39 39 Ica V 3p39l f l 3 hapmdmm g r 41 7393 l2 39 39 3 quot 77 7V 7 r 139 7 7 I39d Fll 39l 39 H A mmpultr nmdllafiminn 7 quot quot M 1 j L vie Mmion 39 quot in W Ivy Gml II Iquot Winn I39R mum II i l M ginm n niacinInn Mn on am my afbolh u ddm and like Jamal l llllIL 13H all in quottin quotwralhrr but 1Hqu a quotn Hi can a Allhnul Iii mrgy mi faz lers mame it IdnururinA uwl l 539 hum Ih uid lamim play I a Fundt Mm Thi mndrl n proJinn sh wratht law an mzmahly minimu 1vy unnlighu and inpct MIRll Hin rJ quot39 hick hymn With It vmd w IP41 MI m dri m kg lufu39n39r39l luluml turn may In mul irh MK thn39 rimming inningquot Eh u J 1 J J v Ki Kg 9 gt4 xxs FHA Ki Kg 9 3 E 2 r53 29 3 f 2 39 x r y K r9 EL r E7 r 67 g m CH DH c E I J 4 LL 3 Jupiter Model Shells of Rotating Gas Seen as Surface Winds Simulations of Equatorial and High Latitude Jets on Jupiter in a Deep Convection Model M Heimpel et al Nature 438 2005 J Tangent 39oylinde Liquid metal core 1 n 3 l i 39 r l K i 39 5 v 4 7 l i 39 I n i I I n l r 3 Z l r39 I I I I 39 I x g l x t39 7 39 39 39 t quot3Hquot Moleoula r uid 7 Deep zonal ow I Jupiter and Saturn Westerly Equatorial Flow Uranus and Neptune Easterly like earth determined by depth of molecular fluid layer Rauhylmmwlley u waxsaynwwmw 4 A x l 1 4 1 v2 h If 75 i X Bu 9 Eu 2 gt 3 45 5 r m a 5 g 5 u a E vs 5 E 4m m 3 13 45 Am 69 m5 775 75 H k w on ma van w Vebcvly m r39 Simulation Results a Cassini data b flow speed to the east westerlies c mode red to east blue to west Model Turbulent high Re Low Rossby Uranus and Neptune Atmospheres 83H2 15He and 2 CH4 Cores liquid primarily icy materials water ammonia and methane and rocky materials Si etc Internal T 5000K vs ZOOOOK Jupiter Equatorial winds are easterlies as at earth implying shallow layer Magnetic fields not well aligned with the rotation axis Uranus is tipped on its side likely due to impact Tipped Uranus and its rings Thermosphere 7 7 quot1 a Vquot39 quot Good pictures of Vertical structure Shuttle Aurora
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