ATM OCN 100 - Summer 2002 LECTURE 18

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

3. B. EXPLANATIONS of ATMOSPHERIC MOTION • Practical Problems • Historical Concepts • Forces of Motion & Newton's Laws

4. NEWTON’S EQUATIONS of MOTION • 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. • 2nd LawForce = mass x acceleration. • 3rd LawFor every action, an equal & opposite reaction exists.

5. B. EXPLANATIONS of ATMOSPHERIC MOTION (con’t.) • Implications of Newtonian Laws • 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/sec2] • Force -- a vector-- What causes a mass to accelerate.[pounds, or Newtons]

6. C. DESCRIBING ATMOSPHERIC MOTION • Reasons for Atmospheric Motions: • Buoyancy Effects or Dynamic Effects

7. C. DESCRIBING ATMOSPHERIC MOTION • Complications involved with Atmospheric Motion: • Spherical planet; • Rotating planet & non-inertial frame of reference.

8. An example of an equation of motionNASA

9. DESCRIBING ATMOSPHERIC MOTION(con’t.) • 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.

10. Numerical Weather Prediction

11. Numerical Weather Prediction

12. Numerical Weather Prediction

13. FORCES ASSOCIATED WITH ATMOSPHERIC MOTION • Following forces influence motion of air parcels: • Pressure Gradient Force • Gravitational Force or Gravity • Coriolis Effect or "Force" • Frictional Force or Friction • Centripetal Forceor more specifically --

14. PRESSURE GRADIENT FORCE • Generated by differences in pressure within a fluid element; • Responsible for initiation ofall air motion;

15. Low Pressure High Pressure Explaining Differences in Air Pressure

16. PRESSURE GRADIENT FORCE(con’t.) • A 3-dimensional vector that has: • Magnitudeof pressure gradient force vector depends: • directly upon difference in pressure over a given distance (i.e., slope or grade equals “pressure gradient”). • Directionof pressure gradient force vector is: • fromHigh pressure to Low pressure, • along steepest direction of pressure gradient.

17. PRESSURE GRADIENT FORCE(con’t.)

18. GRAVITATIONAL FORCE or GRAVITY • Produced by mutual physical attraction between massive bodies; • Gravity refers to acceleration; • Acts continuously, regardless of motion; • A vector quantity that has: • Direction – toward center of earth. • Magnitude ~ 9.8 m/s2 (32 ft/s2)

19. CORIOLIS EFFECT or FORCE • Produced by earth’s rotation; • A “fictitious force” used to explain apparent deflection of moving object on a rotating frame of reference;

20. CORIOLIS EFFECT or FORCE • Produced by earth’s rotation; • A “fictitious force” used to explain apparent deflection of moving object on a rotating frame of reference;

21. CORIOLIS EFFECT or FORCE(con’t.)Speed is dependent upon latitude:

22. An example of the Coriolis EffectFig. 9.5 Moran & Morgan (1997) Time 1 Time 2

23. CORIOLIS EFFECT or FORCE(con’t.)

24. Coriolis Effects upon the WindFig. 9.6 Moran & Morgan (1997)

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

26. CORIOLIS EFFECT or FORCE(con’t.) • Magnitudeof horizontal Coriolis force vector depends upon: • Rotation rate of earth (Direct relationship); • Speed of object;(Direct relationship) • Latitude (specifically, sine of latitude).

27. CORIOLIS EFFECT or FORCE(con’t.) • Directionof horizontal component of Coriolis force vector: • Causes a deflection of moving object to rightof direction of motion in Northern Hemisphere;but • Deflects moving object to leftof intended motion in Southern Hemisphere.

28. FRICTIONAL FORCE or FRICTION • 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: • thermal turbulence • mechanical turbulence

29. An example of Turbulent ViscosityFig. 9.5 Moran & Morgan (1997)

30. FRICTIONAL FORCE(con’t.) • Acts only after motion is initiated; • Acts to retard motion; • Magnitude of friction force vector depends upon: • Speed of motion of fluid; • Type of surface, e.g., “surface roughness”; • Temperature structure of fluid. • Directionof friction force vector is • opposite motion vector.

31. Relative Surface RoughnessSource: Stull, 1995

32. Centripetal ForceFig. 9.3 Moran & Morgan (1997)

33. CENTRIPETAL FORCE • Produces curved motion; • Opposite the “centrifugal force”; • Acts only after motion is initiated;In reality, a net force Used to describe imbalance of other forces in curved motion;

34. CENTRIPETAL FORCEVECTOR(con’t.) • Centripetal force vector is described by: • Magnitude of centripetal force vector depends upon: • Speed of instantaneous motion(a direct relationship); • Radius of curvature(an inverse relationship). • Direction of centripetal force vector is • inward toward center of curvature.

35. SUMMARIZING • A 3-D Equation of Motion for Atmosphere (in word form): Net force = Pressure gradient force + gravitation force + Coriolis force + friction. • Notes: • The above is a vector equation! • Since a unit mass is used, force is equivalent to an acceleration.