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GEU 0047: Meteorology Lecture 8 Air Pressure and Winds

GEU 0047: Meteorology Lecture 8 Air Pressure and Winds. How can you know this wind direction?. Pressure. The steady drumbeat of countless numbers of atoms and molecules, exchanging momentum with the walls of a container and providing the “Pressure”. Gas Law.

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GEU 0047: Meteorology Lecture 8 Air Pressure and Winds

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  1. GEU 0047: MeteorologyLecture 8Air Pressure and Winds

  2. How can you know this wind direction?

  3. Pressure • The steady drumbeat of countless numbers of atoms and molecules, exchanging momentum with the walls of a container and providing the “Pressure”.

  4. Gas Law • The pressure is related to the density and temperature of the gas through its internal energy. • Kinetic Energy = 1/2 m v2 • Exchange of Momentum, the drumbeat of atoms and molecules. • Equation of State • PV = NkT N = number k = Boltzman's constant = 1.38 x 10-23 J/K • PV = nRT n = grams per mole / molar mass R = Gas constant = 8.31 Joules/mole/K

  5. Partial Pressures Pressure = PN2 + PO2 + + PAr + PH20 + PCO2 + ... Pressure = Force / Area (Snow shoes on thin ice, high heels on asphalt) Force = Weight of overlying air = mass x gravity

  6. Weight Pressure = Force / Area Force = Weight of overlying column of air = mass x gravity

  7. Pressure Units Units of Pressure • Force / Area = Newton/m2 = Pascal Weather RelatedSea Level 5,000 feet 10,000 feet Pascals 101,325 Millibars 1013.25 500 250 Atmospheres 1.0 0.5 0.2 Inches of Mercury 30.0 15.0 7.5 PSI 14.7 7.4 3.0

  8. Pressure Records

  9. Fluid Pressure at Height (or Depth) Since pressure (P) = Force / Area and the force is the weight (W = mg) of the overlying column... P = mg/A Multiply the top and bottom by the volume (V) P = Vmg/VA m/V is the density and V/A is just the height for a Therefore, P = r g h

  10. Pressure and Columns At what depth do we encounter a pressure = 1 atm. In a) water, b) gasoline, c) mercury?

  11. Pressure and Columns At what depth do we encounter a pressure = 1 atm. In a) water, b) gasoline, c) mercury? 1 atm = 101325 Pascals P = rgh ha = P/rag hb = P/rbg hc = P/rcg

  12. Pressure and Columns At what depth do we encounter a pressure = 1 atm. In a) water, b) gasoline, c) mercury? 1 atm = 101325 Pascals P = rgh ha = P/rag = 101325/1000*9.8 hb = P/rbg = 101325/680*9.8 hc= P/rcg = 101325/13600*9.8

  13. Inches of Mercury At what depth do we encounter a pressure = 1 atm. In a) water, b) gasoline, c) mercury? 1 atm = 101325 Pascals P = rgh ha = P/rag = 10.3 meters hb = P/rbg = 15.2 meters hc= P/rcg = 0.76 meters 1 atm ~ 30 inches mercury (0.76 meters)

  14. Pressure and Altitude • There is a large difference in pressure with altitude.

  15. Pressure Changes Horizontal: Changes ~ 1 mb over 10,000s of meters Vertical: 1 mb over 10s of meters Barometric Pressure must be corrected for Altitude (and Temperature). Vertical atmospheric motions are more important than horizontal ones because of temperature and pressure changes in this direction are much larger than similar distances in the horizontal direction.

  16. Pressure and Altitude Station pressure: Local Reading Local Values must be corrected for elevation and reduced to sea level for comparison.

  17. Pressure Lapse Rate In an average standard atmosphere with a lapse rate of ~ 6.5 oC/1000 m, atmospheric pressure decreases are approximated by ~ 100 mb/1000 m. Station pressure at its elevation is then corrected to sea level with this standard gradient. Example: Station Pressure 894 mb, Elevation +1100 m Equivalent Sea Level Pressure = 894 + 1100*(100/1000) = 1004 mb

  18. Pressure Gradients DP/Dd = Pressure Gradient (Change in Pressure/Distance) Example: DP/Dz = - rg DP = change in pressure Dz = change in altitude r = density (air) g = gravity (9.8 m/s2) Pressure Gradient Force (PGF): Force due to pressure differences, and the cause of air movement (winds).

  19. Pressure Gradient Force F = m a, acceleration a = F/m = Dv/Dt P = F/A pressure r = m/V density acceleration a = F/m = -(1/r)*DP/Dd Wind is accelerated perpendicular to isobars from High to Low pressure. Wind velocity ~ (1/r)*DP/Dd

  20. Isobars Contours of Constant Pressure Topographical Analogy: Just as close topographic lines indicate steep terrain, close isobars mean steep pressure gradient, large pressure force and therefore strong winds. SURFACE MAP

  21. Pressure Gradient Force (PGF) Air moves from High pressure to Low pressure. The force provided by the pressure difference is the pressure gradient force. Force is directed perpendicular to the isobars from Highs to Lows.

  22. Isobar Levels Standard isobaric levels Each isobaric level picks out a general altitude to study. These are constant altitude charts, similar to the surface map.

  23. Fig. 8-12, p. 199

  24. Isobar Levels

  25. Bernoulli’s Equation Recall that WORK = change in both Potential Energy and Kinetic Energy. W = Force * Distance = P A x = P V Finally, P2, v2, x2, h2, A2 h2 Initially, P1, v1, x1, h1, A1

  26. Bernoulli’s Equation D KE = 1/2 m (v2-v1)2 D PE = mg (h2-h1) Finally, P2, v2, x2, h2, A2 h2 Initially, P1, v1, x1, h1, A1

  27. Bernoulli’s Equation D KE = 1/2 m (v2-v1)2 D PE = mg (h2-h1) DW = DKE + DPE Leads to the equation of continuity... P + 1/2 r v2 + r g h = constant The sum of pressure, kinetic energy per volume and potential energy per volume have the same value along all points in a streamline.

  28. Bernoulli’s Principle Pressure is lower for faster steady flow than for slower Airplane Wings Higher v, Lower P Lower v, Higher P

  29. Wind Speed Vectors Vectors are arrows representing wind direction and speed.

  30. Bernoulli Winds

  31. Ridge and Trough Wavelike patterns of constant pressure surfaces reflect pressure changes due to air temperature differences.

  32. Constant Pressure Surfaces At what height do you experience a Pressure of 500 mb?

  33. Density and Pressure • The warmer air column is less dense. • At the same height, the pressure is higher in the warmer air column.

  34. Latitude Pressure Gradient • At the same altitude, the pressure is higher on average in the warmer (i.e. lower) latitudes.

  35. Temperature PGF versus Altitude

  36. Air Forces Force = Pressure Gradient Force + Coriolis + Friction • For any fixed height, the pressure decreases toward cooler latitudes. • Isobars for a fixed altitude show this decrease to the North (South) in the Northern (Southern) Hemisphere. • In the absence of rotation, air (in the upper level) would tend to flow from the equator toward the poles.

  37. Global Circulation • In the absence of rotation, air would tend to flow from the equator toward the poles. Hot, less dense air rising at the equator, becomes denser as it cools and descends at the poles, traveling back to tropical areas to heat up again.

  38. Coriolis

  39. Outsider’s view Outsider’s view Insider’s view Insider’s view From http://www.windpower.dk/tour/wres/coriolis.htm

  40. Coriolis FORCE A. Force: due to a rotating frame of reference. B. Objects moving in a straight line with respect to the stars, will experience an apparent deflection to the RIGHT in the N.Hemisphere and an apparent deflection to the LEFT in the S. Hemisphere. C. The Coriolis force is strongest at the poles and zero at the equator. D. The Coriolis force is proportional to the speed. E. The "force" affects the direction NOT the speed. But since velocity is a vector, with both direction and speed, the velocity change is the same as acceleration and the Coriolis force is the culprit.

  41. Coriolis Force Equation Relative to a carousel, someone walking on a carousel moves in a straight line with respect to the fixtures. Relative to others and equipment on the ground, the person moves in an arc as if affected by a force. The (horizontal) Coriolis Force Fc = 2W v sin f v = wind speed W = angular velocity (earth rotation, 360 degrees/24 hours) f = latitude (sin 0 = 0.0 equator, sin 90 = 1.0 poles)

  42. Coriolis Deflection Fc = 2W v sin f Increase of the Coriolis Force with wind speed.

  43. Pressure Gradient Force • Air flows from high pressure to low pressure, so on average, from the equators to the poles.

  44. Geostrophic flow • Remember that the coriolis force depends upon velocity. As air is accelerated by the PGF its speed increases and the coriolis deflection grows. Equilibrium is reached when the PGF and coriolis effect are equal.

  45. PGF = Coriolis 1/r*DP/Dd =2 W v sin f The wind velocity v = DP/Dd * (1/r2 W sin f) Utilizing the coriolis parameter fc = 2 W sin f The wind velocity v = (1/rfc)*DP/Dd = vg This is known as the geostrophic wind equation.

  46. Geostrophic flow • With the inclusion of the Coriolis Force, air flows parallel to isobars of constant pressure.

  47. Westerlies • At mid latitudes, air moving from S. to N. in the northern hemisphere flows from west to east.

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