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Part-6c Circulation (Cont) Means of Transferring Heat Global Circulation Easterlies /Westerlies 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: T(C) dashed: v(m/s) heavy line: tropopause Earth with Rotation f≠0 Rising Tropical air returns at higher latitudes roughly three cells f>0 x • • x f=0 f=0 • f<0 Form mid-latitude 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 Γ Geostrophic flow can intensify with z Geostrophic wind : Fa = -"p v ** v = - 1 ) k $ [%" p] h #f ) k local vertical , " h local horiz. (used // earlier) p & poexp(-z/H) ; H = kT/mg 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 'v ( "T h 'z Horizontal temperature differences causes increasing pressure differences with altitude, intensifying geostrophic flow 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 30o and 70o Geostrophic circulation around highs and lows can be organized as easterlies and westerlies Pressure/Flow Maps Polar high also Red: ITCZ Upper Troposphere Geostrophic but disconnected from land and sea masses Rossby Waves bring warm air north and cool air south As seen from earlier slide, westerly motion about the polar low. Waves break off--> highs + lows. Wave crests move slowly west Upper Troposphere Wave Winter geopotential height [= ∫g dz] of isobar Rossby Waves and Vorticity Include convection term v v v 1 "v v v + ( v # $) v = % 2& ' v % $p "t ( 2%D "u " " 1"p + (u + v ) u=f v% "t "x "y ("x "v " " 1"p 2. + (u + v ) v = %f u % "t "x "y ("y v continuity ) $ # v = 0 ; incompressible "u "v 3. + =0 "x "y Differentiate 1. with respect to y and 2. with respect 1. to x + subtract and then use 3. "v "u ˆ v Define vorticity of the flow : * = % =k # $'v "x "y Find d d " r [+ + f ] = 0 ; as usual = + v • $ dt dt "t Therefore, Conserve Total Vorticity [+ + f ] If f decreases (air moves south), then + must increase PLANETARY WAVES < ~ 0.5 bar Earth Ω L H Upper Troposphere Rossby Waves Westerlies (Incompressible Flow) Total Vorticity Conserved d[ζ+f]/dt = 0 ζ = k•∇xv vorticity Northern Hemisphere ζ > 0 counterclockwise; ζ < clockwise Southern Hemisphere South Pole ζ< 0 counterclockwise; ζ >0 clockwise f < 0 increasing northward Wave Period rotation rate + temperature difference Outer cylinder hot inner cool A type of baroclinic wave Angular momentum from boundary transferred to fluid, Usual turbulence: large to small scale Here small scale goes to organized flow Rossby Waves and Jet Streams ~50-400km/hr (earth equator 3000km/hr break off to form weather Polar Jet Geopotential Heights of 300mbar Level Earth’s Thermospheric flow near exobase Note: Day / Night effects Unlike troposphere Gravity Waves g # (%d & ' )z T Stable conditions : %d > ' : ˙z˙ $ & ( B2 z ; waves with the Brunt - Vaisala frequency " a ˙z˙ = - ( " a - ")g ˙z˙ $ - ! Lenticular Clouds Lee Waves Rising air at Lows and falling at Highs also drive planet scale gravity waves mixing the troposphere with upper atmosphere Gravity Waves at Mars Mars Circulation fluid density is low coriolis effect can be significant Axial Tilt : Warm Summer Pole Strong Gradients Strong Irregular Westerlies L Latitude L H Winter H H summer Weak Easterlies T Dust storms at Mars 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 What are winds relative to on a gas ball? Galileo 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 FAST ROTOR Horizontal L L H H L H L H Vertical View L H H L Giant Planet Atmospheres Zones: westerlies (eastern flow; prograde) Bright clouds (condensed from NH3 act to cool air, higher) 8(4) per hemisphere jupiter (Saturn) Belts: easterlies (retrograde) Dark clouds (warmer, drier descending air) 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 Zonal Wind Speeds vs. Latitude at cloud level Positve u(m/s): Westerlies Simulation of Eddys converting to flow Cassini image of Jupiter showing small scale eddies and larger scale zonal flow Galileo probe: high speed winds extend 1000’s km deep 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 Jupiter and Saturn: Westerly Equatorial Flow Uranus and Neptune: Easterly (like earth) determined by depth of molecular fluid layer 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 Uranus and Neptune Atmospheres ~83%H2, 15%He and 2% CH4 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 Good pictures of Vertical structure 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.