Part-8c Circulation (Cont)

Transcription

1 Part-8c Circulation (Cont) Global Circulation Means of Transfering Heat Easterlies /Westerlies Polar Front Planetary Waves Gravity Waves Mars Circulation Giant Planet Atmospheres Zones and Belts

2 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

3 Global circulation on Earth Coriolis parameter f~ 0 F cor v x k or v = [z x p]/ρf x x x x Red: directions of coriolis force Slow Easterlies Faster at Higher Latitudes Opposite in upper troposphere

4 Earth with Rotation f 0 Rising Tropical air returns Downward at lower latitudes roughly three cells f>0 x f=0 x f=0 f<0 Forming mid-latitude highs with transport southward (weak easterlies, f small) and northward (stronger westerlies, larger f) Note: upper troposphere global flow

5 Earth Global Circulation (Cont.)? Doldrums(rising air, weak winds ~5 o to -5 o of equator but can move up and down: ITCZ) Horse Latitudes: Dry weak wind due to descending air

6 Another View In obtaining the vertical temperature distribution we considered radiative transfer and the adiabatic lapse rate--the latter is, of course, due to vertical convection, differences in which, in turn drive horizontal flow. Radiation to space is the ultimate cooling effect

7 Winds and Temperatures solid: T(C) dashed: v(m/s) heavy line: tropopause

8 Earth Global Circulation (Cont.) Note: When a cold air mass and a warm air mass interact, the differences in pressure increases with altitude: H ~kt/mg --> Stronger winds at higher altitudes, westerlies become jets between 30 o and 70 o

9 Thermal Wind Described Earlier : Horizontal gradient in Lapse Rate Geostrophic flow can intensify with z Geostrophic wind : F a = -" h p or v = 1 # f ˆ z $ " h p ˆ z local vertical, " h is taken in local horiz. Using p = # R T ; obtain & v & z % & p & z = # g ' g f [ ˆ k $ (" h T) /T] Horizontal temperature differences causes increasing pressure differences with altitude, intensifying geostrophic flow

10 Geostrophic circulation around highs can be organized as easterlies and westerlies L Westerlies L H H H Easterlies L L L L

11 Another View

12 Pressure/Flow Maps Red: ITC

13 Upper Troposphere: Rossby Waves bring warm air north and cool air south Geostrophic but disconnected from land and sea masses As seen from earlier slide, westerly motion about the polar low. Waves break off--> highs + lows. Wave crests move slowly west

14 Upper Troposphere Wave Winter geopotential height [= g dz] of isobar

15 2 % D Rossby Waves and Vorticity Include convection term " v " t + (v v # $) v = % 2& v ' v % 1 ( $p " u " t + (u " " x + v " " y ) u = f v % 1 " p ( " x " v " t + (u " " x + v " " y ) u = %f u % 1 " p ( " y continuity ) $ # v = 0 ; incompressible " u " x + " v " y = 0 Differentiate 1. with respect to y and 2. with respect to x + subtract and then use 3. Define vorticity of the flow : * = " v " x % " u " y = ˆ k # $ ' v Find d [ dt + + f ] = 0 ; as usual d dt = " "t + v r $ Therefore, Conserve Total Vorticity [ + + f] If f decreases (air moves south), then + must increase

16 PLANETARY WAVES < ~ 0.5 bar Earth L Ω Upper Troposphere Rossby Waves Westerlies (Incompressible Flow) Total Vorticity Conserved d[ζ+f]/dt = 0 ζ = k xv vorticity Nothern Hemisphere ζ > 0 counterclockwise; ζ < clockwise H

17 Southern Hemisphere South Pole ζ< 0 counterclockwise; ζ >0 clockwise f < 0 increasing northward

18 Wave Period rotation rate + temperature difference Outer cylinder hot inner cool A type of baroclinic wave Angular momentum from boundary transferred to fluid, usually turbulence: large to small scale here small scale goes to organized flow

19 Gravity Waves " a z = - ( " a - ")g # z $ - g T (% d & ')z 2 Stable conditions : % d > ' : z $ & ( B z ; waves with the Brunt - Vaisala frequency Lenticular Clouds Lee Waves Rising air at Lows and falling at Highs also drive planet scale gravity waves mixing the troposphere with upper atmosphere

20 Waves Sound Waves (1D) Momentum du dt + 1 #p " #x = 0 Continuity d" dt + " #u #x = 0 u = u + $u ; " = " + $" Gravity Waves Stable Regions deviations from hydrostatic (2 - D) dw dt + 1 #p " #z 1 d" " dt + #u #x + #w #z + g = 0; du dt + 1 #p " #x = 0 ; continuity frequency = (g B) 1/2 ; B = 1 % ' T & Rossby Waves du dt = f v " 1 $# # $x dv dt = "f u " 1 $# # $y = 0; momentum dt dz + $ d $u $x + $v $y = 0 incompressible ( * = 1 ) T [+, + $ d ]

21 Gravity Waves at Mars

22 Stratosphere Quasi-Biennial Oscillation (QBO) equatorial lower stratosphere. Variations are related to those in the troposphere. When equatorial QBO is easterly (westerly), the polar jet in the northern hemispheric winter is weaker (stronger) than average. The correlation is also connected to the westerly jet in the troposphere.

23 Earth s Thermospheric flow near exobase Note: Day / Night effects Unlike troposphere

24 Because Mars Atmosphere Interacts Strongly with the Surface: In Some Sense Earth Like

25 Mars Circulation fluid density is low coriolis effect can be significant Latitude Axial Tilt : Warm Summer Pole Strong Gradients Strong Irregular Westerlies L L H H H Winter Weak Easterlies summer T

26 Giant Planets Temperature and Cloud Structure Gas Giants Jupiter (71,300km) and Saturn (60,300km) Ice Giants Uranus and Neptune (~25,000km) Clouds ~0.3-2bars indicative of winds Winds relative to magnetic field rotation rate Galileo

27 Giant Planets fast rotors Emitted Radiation: Nearly Isotropic heating from below which affects the transport/ flow

28 Gas Giants Sun + Internal Heat (~1.7 x solar) (J =1/25, S = 1/100 Earth) Fast rotors (~10hr)->High Wind Speeds Small Scale Eddies Feed Zonal Flow Jupiter: Zonal Winds : Westerlies (bright) Eq. ~150m/s J; 400m/s S Belts : Easterlies (dark) Red Spot : High (counter clockwise) Saturn : Yearly (30 year) Storms X=1-D/Rp where D is thickness of H2 layer

29 FAST ROTOR L L L L H H H H L Vertical View H H L

30 Giant Planet Atmospheres Zones: westerlies (eastern flow; prograde) Bright clouds (condensed from NH 3 act to cool air, higher) 8(4) per hemisphere jupiter (Saturn) Belts: easterlies (retrograde) Dark clouds (warmer, drier descending air)

31 Jupiter s Atmosphere Dominate by circulation cells and zonal winds marked by different colored cloud layers which are higher in belts than in zones Black small circle is Io

32 Zonal Wind Speeds vs. Latitude at cloud level Positve u(m/s): Westerlies

33 Simulation of Eddys converting to flow

34 Cassini image of Jupiter showing small scale eddies and larger scale zonal flow Galileo probe: high speed winds extend 1000 s km deep

35 Jupiter Model Shells of Rotating Gas Seen as Surface Winds

36 Simulations of Equatorial and High Latitude Jets on Jupiter in a Deep Convection Model M. Heimpel et al. Nature 438, 2005 Jupiter and Saturn: Westerly Equatorial Flow Uranus and Neptune: Easterly (like earth) determined by depth of molecular fluid layer

37 Simulation Results a Cassini data b flow speed + to the east (westerlies) c model red to east; blue to west Model Turbulent (high Re) Low Rossby

38 Some Definitions BAROTROPIC- density a function of pressure [ρ(p,t)]; regions of nearly uniform temperature; buoyancy forces small; lack of fronts: e.g. southeast U.S. in the summer or the tropics (hence, barotropic). BAROCLINIC-density is a function of p and T [ρ(p,t)]; surfaces of constant pressure can intersect: bouyancy forces are important; thermal winds result. Distinct air mass regions exist; fronts separate warmer from colder air. In a synoptic scale baroclinic environment you will find the polar jet, troughs of low pressure (mid-latitude cyclones) and fronts. There are clear density gradients caused by the fronts. SYNOPTIC Scale- (large scale) weather systems with horizontal dimensions of hundreds of km; momentum equations can be scaled (horiz: coriolis + pressure gradient; vert: hydrostatic). Mesoscale: intermediate. MERIDIONAL: north/ south ZONAL: east / west MONSOON- (from seasonal) wind pattern that reverses direction on a seasonal basis (e.g., monsoonal winds in the Indian ocean). Synoptic scale sea breeze: hot air over land replaced by moist air from over ocean; upward diversion by mountains produces heavy rain.

39 Uranus and Neptune Atmospheres ~83%H 2, 15%He and 2% CH 4 Cores liquid primarily icy materials (water, ammonia and methane) and rocky materials (Si etc.) Internal T ~5000K (vs 20000K 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

40 Extrasolar Giant Planets Revived interest in Jovian planets < 70 Jupiter or they become stars Seen initially as wobbling stars Now seen transiting solar diskusually close to star <0.1AU Close planets--> New Models of planet formation Probably do not have moons Phase-locked (meaning for a gas planet? Winds? Escaping gas?) Protoplanet forms in disk clearing out a Region. Spiral in and stop--why? Why are J,S,U,N far away