1. Announcements Midterm exam #1 will be given back in class Friday. First homework assignment due next Monday.

2. The Coriolis force: A)Causes the wind to blow from high to low pressure B)Causes the wind to blow perpendicular to lines of constant pressure C)Causes apparent deflection of a ball in a rotating reference frame, like a merry-go-round. D)All of the above

3. Survey question: If you flush a toilet in the southern hemisphere: A)The water will swirl counterclockwise. B)The water will swirl clockwise. C)The water can swirl either direction or may not even swirl at all. D) I don’t know.

4. Summary of Lecture 15 Newton’s first law of motion: an object will remain at rest and an object in motion will maintain a constant velocity if the net force is zero. Newton’s second law of motion: F = ma. Change acceleration by a change in speed or direction. The simplified equation of horizontal atmospheric motion has four force terms: pressure gradient force, Coriolis force, centripetal force, and friction. The pressure gradient force is due to the difference in pressure over a distance. The Coriolis force is an apparent force due to the rotation of the Earth, and depends on speed (of the wind) and latitude. It causes deflection from the reference point of an observer in a rotating frame. Coriolis force deflects the wind to the right or left depending on which hemisphere. Geostrophic wind occurs when the pressure gradient force balances the Coriolis force and the wind is parallel to the isobars. A good approximation for upper level winds.

5. NATS 101 Section 4: Lecture 16 Why does the wind blow? Part II

6. Last time we talked about two of the force terms in the simplified equation for horizontal air motion Geostrophic Balance: PRESSURE GRADIENT = CORIOLIS

7. Simplified equation of horizontal atmospheric motion TermForceCause 1Pressure gradient forceSpatial differences in pressure 2Coriolis forceRotation of the Earth 3Centripetal forceCurvature of the flow 4Friction forceActs against direction of motion due to interaction with surface (1)(2)(3)(4) FOCUS ON LAST TWO THIS TIME…

8. The centripetal force and friction force are typically much smaller, but they are very important for two reasons: 1.Cause mass divergence and convergence 2.Can be relatively large in special cases that are meteorologically important (i.e. cool)

9. MASS DIVERGENCEMASS CONVERGENCE INITIAL WIND FASTER WIND INITIAL WIND SLOWER WIND MASS LOSTMASS GAINED AIR RISING BELOW AIR SINKING ABOVE AIR RISING ABOVE AIR SINKING BELOW

10. To begin a discussion of centripetal force, let’s address the popular belief about how water goes down the drain…

11. Popular belief: The way the toilet flushes or the sink drains depends on which hemisphere you’re in. Bart vs. Australia Simpson’s episode: Bart calls an Australian boy to see if his toilet really does flush clockwise…We’ll see what the surprising answer is later.

12. Centripetal Force = Arises from a change in wind direction with a constant speed (v) due to the curvature of the flow around a radius (r) Center of circle V 1 Initial velocity V 2 Final velocity -V 1 V2V2 Centripetal acceleration (a) (towards the center of circle) The centripetal acceleration is always directed toward the center of the axis of rotation. Note to be physically correct, the expression should have a negative sign, so +V 2 /r is actually the centrifugal acceleration. a

13. CENTRIPETAL FORCE You experience acceleration without a change in speed, for example, on a tilt-a-whirl carnival ride. The force is directed toward the center of the wheel. An equal an opposite (fictitious) centrifugal force is exerted by the inertia of your body on the wheel—so you stay put and don’t fall off even when upside down. CENTRIFUGAL FORCE Centripetal Force

14. WINDS IN GEOSTROPIC BALANCE CENTRIPETAL ACCELERATION NEEDED ACCOUNT FOR THE CURVATURE OF THE FLOW

15. Assume PGF constant size along entire channel Height 1 Height 2 Flow around curved height iso-lines L H Centripetal acceleration (towards low pressure) Centripetal acceleration (towards high pressure) When wind curves, it must have an centripetal acceleration towards the axis of rotation, so it is NOT geostrophic.

16. Height 1 Height 2 Gradient Balance: Curved Flow WIND AROUND LOW PRESSURE Centripetal + PGF = Coriolis WIND AROUND HIGH PRESSURE Centripetal + Coriolis = PGF PGF Coriolis Cent. PGF Coriolis WIND

17. The effect of curvature has curious—and counter intuitive--implication for winds around high and low pressure, if the pressure gradient is constant

18. Changes in wind speed around highs and lows due to gradient balance WIND AROUND LOW PRESSURE Centripetal + PGF = Coriolis OR, better to think… PGF = Coriolis – Centripetal Effectively REDUCES the pressure gradient force Wind slows down. WIND AROUND HIGH PRESSURE PGF = Centripetal + Coriolis Effectively INCREASES the pressure gradient force, Wind speeds up.

19. Height 1 Height 2 WIND AROUND LOW PRESSURE Centripetal + PGF = Coriolis WIND AROUND HIGH PRESSURE Centripetal + Coriolis = PGF PGF Coriolis Cent. SLOWEST WIND FASTEST WIND SLOWEST WIND AT THE BASE OF A TROUGH FASTEST WIND AT THE TOP OF THE RIDGE

20. Height 1 Height 2 PGF Coriolis Cent. SLOWEST WIND FASTEST WIND WIND INCREASES WIND DECREASES Because of the effect of centripetal force, winds increase to the east of trough and decrease to the east of a ridge. THERE MUST BE COMPENSATING VERTICAL MOTION DUE TO CHANGES IN WIND SPEED AHEAD OF THE TROUGH AN RIDGE.

21. MASS DIVERGENCEMASS CONVERGENCE INITIAL WIND FASTER WIND INITIAL WIND SLOWER WIND MASS DIVERGENCE AND COVERGENCE AT UPPER LEVELS (DUE TO CURVATURE OF THE FLOW) Stratosphere (acts as a lid) AIR RISING AIR SINKING AHEAD OF A TROUGHAHEAD OF A RIDGE

22. Height 1 Height 2 PGF Coriolis Cent. SLOWEST WIND FASTEST WIND WIND INCREASES MASS DIVERGENCE WIND DECREASES MASS CONVERGENCE RISING MOTION AHEAD OF TROUGH SINKING MOTION AHEAD OF RIDGE Relationship between upper level troughs and ridges and vertical motion

23. Relationship between upper level troughs and ridges and vertical motion SINKING MOTION TYPICALLY STABLE RISING MOTION MAY BE CONDITIONALLY UNSTABLE (if clouds form and air is saturated) SurfaceHigh Surface Low UPPER LEVEL ~300 mb SURFACE

24. RISING MOTION SINKING MOTION SINKING MOTION TROUGH RIDGE

25. RISING MOTION SURFACE LOW (in Colorado) IS LOCATED DIRECTLY AHEAD OF TROUGH AT 300-MB, BECAUSE AIR IS RISING AHEAD OF THE TROUGH TROUGH UPPER LEVEL SURFACE

26. Gradient balance and flow around lows and highs (Northern Hemisphere) Cent. force Cent. force Cent. force Counterclockwise flow around lows Clockwise flow Around highs

27. Flow around low pressure Counterclockwise flow Clockwise flow (because Coriolis force reverses with respect to wind direction) NORTHERN HEMISPHERESOUTHERN HEMISPHERE

28. There is another force balance possibility if the Coriolis force is very small or zero, so it’s negligible. In that case, the pressure gradient force would balance the centripetal force.

29. Cyclostrophic Balance L Centrifugal force Pressure gradient force Pressure gradient balances the centrifugal force. Occurs where flow is on a small enough scale where the Coriolis force becomes negligible. PGF + centripetal force = 0 OR PGF = Centrifugal force Important in (the really cool) meteorological phenomena that have really strong winds and tight pressure gradients!

30. Examples of Cyclostrophic Flow HURRICANES TORNADOES And the flushing toilet, too!!

31. The Great Mystery of the Flushing Toilet Solved! PGF Centrifugal force To Bart and Lisa: “A swirling, flushing toilet is in cyclostrophic balance, so the way it flushes depends more on the shape of the drain—and nothing to do with whether you’re in Australia or not!”

32. One last force to consider… Friction

33. Effect of Friction Force (at the surface) Friction acts to slow the wind at the surface The slower wind decreases the magnitude of the Coriolis force. Weaker Coriolis force no longer balances the pressure gradient force. Wind crosses the isobars, more toward the pressure gradient.

34. Surface friction and flow around surface highs and lows Air curves inward toward surface low pressure. Mass convergence and rising motion Air curves outward away from surface high pressure Mass divergence and sinking motion.

35. Zoom-in on surface low in Colorado from earlier.

36. Summary of Force Balances: Why the wind blows Force BalanceForces InvolvedWhere it happens GeostrophicPressure gradient and Coriolis Winds at upper levels (with no curvature) GradientPressure gradient, Coriolis, and centripetal (or centrifugal) Winds at upper levels with curvature. CyclostrophicPressure gradient and centrifugal Smaller-scale, tight rotations like tornadoes and hurricanes Gradient + Friction Pressure gradient, Coriolis, centripetal, and friction Surface winds

37. Reading Assignment and Review Questions Reading: Chapter 9 Chapter 8 Questions Questions for Review (8 th ed.): 15,16,17,18,21,22 (9 th ed.): 16,17,18,19,22,23 Questions for Thought: 9,10,13,14,15