Space Science: Atmospheres Part- 8 Read CH Chap. 2 dePL 4.5 GENERAL CIRCULATION HADLEY CELL ROTATING FRAME CORIOLIS FORCE TOTAL TIME DERIVATIVE GEOSTROPHIC FLOW GRADIENT WIND CYCLOSTROPHIC FLOW INERTIAL FLOW CYCLONIC

General Circulation DIFFERENTIAL HEATING => FLOW Both longitudinal and latitudinal Global Percentage Heat Input Per Day E V* M J dT/Te 0.68% 0.36% 38% 1.5x10-3 % *If one use the planet rotation rate then the ratio becomes >100%

Horizontal Pressure Differences In troposphere T ~ [Ts -  z] (p/po) = (T/To); x = /(-1); =cp/cv   High Lapse Low Lapse pH pL pH pL => Z po po Often called a thermal wind General picture: Circulation Cells Local Scale : Land / Sea Breezes Planetary Scale : Hadley Cell remember: d2z/dt2 ~ - (gz/T)[ w - ]

Sea Breeze clouds Land Breeze

z Buoyancy Equation LAND SEA Early am T Noon Evening Night cloud Sea Breeze Evening Night Land Breeze Buoyancy Equation

are directly from surface Mars Troposphere heating and cooling are directly from surface and rates are high 1200 800 20 30 200 200 Rapid surface heating 2400 1600 200 200 Rapid convection T T Like a land/ sea breeze but on a planetary scale          Te is essentially at the surface

VENUS TROPOSPHERE GIANT HADLEY CELL Clouds Pole IR Equator Hot air rises in equatorial regions cooled air falls in polar regions But Venus also has horizontal day-night circulation! Therefore, even in absence of rotation the circulation can be complex

DAY – NIGHT VENUS ROTATION Day Night Tropospheric Winds PERIOD ~ 243 days (retrograde) Day Night Tropospheric Winds ~ 4 day rotation Also thermospheric Winds (Cyclostrophic )

Hadley Cells on Earth

Effect of Rotation H = High Pressure; L= low Pressure ITCZ =Intertropical Convergence Zone

Black small circle is Io Jupiter’s Atmosphere Dominate by circulation cells and zonal winds marked by different colored cloud layers Black small circle is Io

Planet Rotation Write Newton’s Law in the rotating frame in which we measure positions, speeds and accelerations Acceleration of a parcel of air = - Pressure Gradient + Gravity + Coriolis + Centrifugal + Viscosity Usually obtain approximate solutions Hydrostatic Law = Gravity and Pressure Compare forces (accelerations) Ekman Number = Viscous / Inertial Ekman = 1/Reynolds Boundary Layer --> viscous Rossby Number = Convection/Coriolis

Rotating Reference Frame: Simple Case q

Rotating Reference Frame (Cont.) Force or Momentum Equation Applies in an Inertial Frame

Rotating Frame (cont.)

Substitute the Velocity

Acceleration in Inertial Frame has 3 components in a Rotating Frame

variations in air density Continuity Equation variations in air density Rate of change = - divergence of of density the flow If we follow a parcel of air, then it is useful to rewrite density changes on left

In Rotating Coordinate follow an air mass

Write Eqs: in Scaled Variables typically non - dimensional First: Meteorologists use reduced pressure (hydrostatic piece of Eq.) “Surface” no longer // to planet’s surfaee Momentum Eq:new variables(incompressible)

Size Scales

Geostrophic Flow

Simplify – Go back to Regular Units Geostrophic Flow Simplify – Go back to Regular Units k f

Geostrophic Flow Prob.H 7.1, 7.4, 7.5 (Steady flow) H Non-rotating L j’ H Rotating i’ L j ’ L i’ H

Simple Picture Coriolis ‘Force’ Start W Observer v v¢ W v

Geostrophic Flow (cont.) (approach to steady state) t=0 L H L H L L Southern Hemisphere Flow is Opposite L

FORCES Steady flow Pressure Gradient = 2 r v x W Coriolis H OPPOSITE ABOUT A LOW ® ® Pressure Gradient = 2 r v x W counter clockwise: cyclonic clockwise: anti cyclonic

Near surface pressures suggest flow pattern

2 –D Flow: ‘Flat’ Surface Gradient Wind Equation Curved Motion r

Gradient Wind Equation discuss direction normal to the flow Ignore Eq. 1: discuss direction normal to the flow Northern Southern centrifugal centrifugal coriolis coriolis Counterclock cyclonic Clockwise anticyclonic Period = ½ period of the focault pendulum

centrifugal = - press. grad. CYCLOSTOPHIC FLOW Case 2 centrifugal = - press. grad. cent. p. L Venus : Polar Vorticity

Centripetal term is zero GEOSTROPHIC FLOW Centripetal term is zero (e.g., large scale flow) L H L L L ( anticyclonic ) Nothern Hemisphere Southern Hemisphere (cyclonic) H L L L

Ü Þ GRADIENT WIND Ü Ü Anamolous Þ Þ L H L cor. p. cor. ® ® p. c. c. p. North ( f > 0 ) Regular cor. p. Þ cor. Ü Ü Þ L H ® ® p. c. c. Anamolous p. Ü Þ L Ü c. cor.

Problems Geostrophic Flow Dp = 5 mb between Washington and Charlottesville Find v. Cyclostrophic Flow Dp = 5 mb over 10 km Inertial Flow at Charlottesville v = 20 m/s r = ? Pressure Force =0