2. ATM OCN 100 Summer 2002 1 ATM OCN 100 – Summer 2002 LECTURE 18 (con’t.) THE THEORY OF WINDS: PART II - FUNDAMENTAL FORCES A. INTRODUCTION B. EXPLANATION Newton’s Laws of Motion C. DESCRIBING ATMOSPHERIC MOTION Numerical Weather Prediction

3. ATM OCN 100 Summer 2002 2

4. 3 Announcements u Exam is this Friday – Say tuned. u Office Hours will be from 1:00 pm to 4:00 PM tomorrow (Thurs) or see me this afternoon. u Review sheet for Exam #2 has been posted. u Answer key to Homework #4 will be posted. u Bring a No. 2 pencil.

5. ATM OCN 100 Summer 2002 4 Last 24 hrs in Madison

6. ATM OCN 100 Summer 2002 5

7. 6 Surface Weather Map from Today with Isobars & Fronts

8. ATM OCN 100 Summer 2002 7 Current Temperatures ( o F) & Isotherms

9. ATM OCN 100 Summer 2002 8 Tomorrow’s 6 AM Forecast

10. ATM OCN 100 Summer 2002 9 ATM OCN 100 - Summer 2002 LECTURE 18 THE THEORY OF WINDS: PART II - FUNDAMENTAL FORCES A. INTRODUCTION –How do winds originate? –What factors influence the winds?

11. ATM OCN 100 Summer 2002 10 B. EXPLANATIONS of ATMOSPHERIC MOTION B. EXPLANATIONS of ATMOSPHERIC MOTION u Practical Problems u Historical Concepts u Forces of Motion & Newton's Laws

12. ATM OCN 100 Summer 2002 11 NEWTON’S EQUATIONS of MOTION u 1st Law (Conservation of Inertia) Object at rest will remain at rest or object moving at constant velocity will continue until acted upon by a net force. u 2nd Law Force = mass x acceleration. u 3rd Law For every action, an equal & opposite reaction exists.

13. ATM OCN 100 Summer 2002 12 B. EXPLANATIONS of ATMOSPHERIC MOTION (con’t.) B. EXPLANATIONS of ATMOSPHERIC MOTION (con’t.) u Implications of Newtonian Laws u Vectors, Forces and Units –Velocity -- a vector (speed & direction) –Speed or magnitude of velocity-- a scalar [mph or meters per second, etc.] –Acceleration or rate of change of a velocity vector -- a vector [ft/sec/sec or meter/sec 2 ] –Force -- a vector -- What causes a mass to accelerate. [pounds, or Newtons]

14. ATM OCN 100 Summer 2002 13 C. DESCRIBING ATMOSPHERIC MOTION u Reasons for Atmospheric Motions: –Buoyancy Effects or Dynamic Effects

15. ATM OCN 100 Summer 2002 14 C. DESCRIBING ATMOSPHERIC MOTION u Complications involved with Atmospheric Motion: –Spherical planet; –Rotating planet & non-inertial frame of reference.

16. ATM OCN 100 Summer 2002 15 An example of an equation of motion NASA

17. ATM OCN 100 Summer 2002 16 DESCRIBING ATMOSPHERIC MOTION (con’t.) u Three-Dimensional Equation of Motion for the Atmosphere –A vector equation; –Entails specification of all forces per unit mass (i.e., equivalent to acceleration); –All forces do not act alone; –Vector sum of individual forces equals net force.

18. ATM OCN 100 Summer 2002 17 Numerical Weather Prediction

19. ATM OCN 100 Summer 2002 18 Numerical Weather Prediction

20. ATM OCN 100 Summer 2002 19 Numerical Weather Prediction

21. ATM OCN 100 Summer 2002 20 FORCES ASSOCIATED WITH ATMOSPHERIC MOTION u Following forces influence motion of air parcels: –Pressure Gradient Force –Gravitational Force or Gravity –Coriolis Effect or "Force" –Frictional Force or Friction –Centripetal Force or more specifically --

22. ATM OCN 100 Summer 2002 21 PRESSURE GRADIENT FORCE u Generated by differences in pressure within a fluid element; u Responsible for initiation of all air motion;

23. ATM OCN 100 Summer 2002 22 Explaining Differences in Air Pressure u Low Pressure u High Pressure

24. ATM OCN 100 Summer 2002 23 PRESSURE GRADIENT FORCE (con’t.) u A 3-dimensional vector that has: u Magnitude of pressure gradient force vector depends: –directly upon difference in pressure over a given distance (i.e., slope or grade equals “pressure gradient”). u Direction of pressure gradient force vector is: –from H igh pressure to L ow pressure, –along steepest direction of pressure gradient.

25. ATM OCN 100 Summer 2002 24 PRESSURE GRADIENT FORCE (con’t.)

26. ATM OCN 100 Summer 2002 25 PRESSURE GRADIENT FORCE (con’t.)

27. ATM OCN 100 Summer 2002 26 GRAVITATIONAL FORCE or GRAVITY u Produced by mutual physical attraction between massive bodies; u Gravity refers to acceleration; u Acts continuously, regardless of motion; u A vector quantity that has: –Direction – toward center of earth. –Magnitude ~ 9.8 m/s 2 (32 ft/s 2 )

28. ATM OCN 100 Summer 2002 27 GRAVITATIONAL FORCE or GRAVITY (con’t.) u Magnitude of gravity vector depends upon: –Mass of earth & object; –Distance between two objects; (inverse square relationship). – [NOTE: Isaac Newton quantified relationship] –Usually gravity is assumed 32 ft/s 2 = 9.8m/s 2. u Direction of gravity vector is –toward vicinity of earth’s center (i.e., essentially downward).

29. ATM OCN 100 Summer 2002 28 CORIOLIS EFFECT or FORCE u Produced by earth’s rotation; u A “fictitious force” used to explain apparent deflection of moving object on a rotating frame of reference;

30. ATM OCN 100 Summer 2002 29 CORIOLIS EFFECT or FORCE u Produced by earth’s rotation; u A “fictitious force” used to explain apparent deflection of moving object on a rotating frame of reference;

31. ATM OCN 100 Summer 2002 30 CORIOLIS EFFECT or FORCE (con’t.) Speed is dependent upon latitude:

32. ATM OCN 100 Summer 2002 31 An example of the Coriolis Effect Fig. 9.5 Moran & Morgan (1997) Time 1Time 2

33. ATM OCN 100 Summer 2002 32 CORIOLIS EFFECT or FORCE (con’t.)

34. ATM OCN 100 Summer 2002 33 Coriolis Effects upon the Wind Fig. 9.6 Moran & Morgan (1997)

35. ATM OCN 100 Summer 2002 34 CORIOLIS EFFECT or FORCE (con’t.) u Produced by earth’s rotation; u A “fictitious force” used to explain apparent deflection of moving object on a rotating frame of reference; u Acts only after motion is initiated; u Can only modify direction of motion; u A 3-dimensional vector, but consider only horizontal component described by:

36. ATM OCN 100 Summer 2002 35 CORIOLIS EFFECT or FORCE (con’t.) u Magnitude of horizontal Coriolis force vector depends upon: –Rotation rate of earth (Direct relationship); –Speed of object; (Direct relationship) –Latitude (specifically, sine of latitude).

37. ATM OCN 100 Summer 2002 36 CORIOLIS EFFECT or FORCE (con’t.) u Direction of horizontal component of Coriolis force vector: –Causes a deflection of moving object to right of direction of motion in Northern Hemisphere; but –Deflects moving object to left of intended motion in Southern Hemisphere.

38. ATM OCN 100 Summer 2002 37 FRICTIONAL FORCE or FRICTION u Produced by “viscosity” (interactions of moving fluid elements with one another or with a boundary surface) due to: –random molecular motions; –large random turbulent motions of fluid associated with either: F thermal turbulence F mechanical turbulence

39. ATM OCN 100 Summer 2002 38 An example of Turbulent Viscosity Fig. 9.5 Moran & Morgan (1997)

40. ATM OCN 100 Summer 2002 39 FRICTIONAL FORCE (con’t.) u Acts only after motion is initiated; u Acts to retard motion; u Magnitude of friction force vector depends upon: –Speed of motion of fluid; –Type of surface, e.g., “surface roughness”; –Temperature structure of fluid. u Direction of friction force vector is –opposite motion vector.

41. ATM OCN 100 Summer 2002 40 Relative Surface Roughness Source: Stull, 1995

42. ATM OCN 100 Summer 2002 41 Centripetal Force Fig. 9.3 Moran & Morgan (1997)

43. ATM OCN 100 Summer 2002 42 CENTRIPETAL FORCE u Produces curved motion; u Opposite the “centrifugal force”; u Acts only after motion is initiated; In reality, a net force Used to describe imbalance of other forces in curved motion;

44. ATM OCN 100 Summer 2002 43 CENTRIPETAL FORCE VECTOR (con’t.) u Centripetal force vector is described by: u Magnitude of centripetal force vector depends upon: –Speed of instantaneous motion (a direct relationship); –Radius of curvature (an inverse relationship). u Direction of centripetal force vector is –inward toward center of curvature.

45. ATM OCN 100 Summer 2002 44 SUMMARIZING u A 3-D Equation of Motion for Atmosphere (in word form) : Net force = Pressure gradient force + gravitation force + Coriolis force + friction. Net force = Pressure gradient force + gravitation force + Coriolis force + friction. u Notes: –The above is a vector equation! –Since a unit mass is used, force is equivalent to an acceleration.