2. describe the airflow in high- and low-pressure systems, and explain how these motions create weather (pp );

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1 11 Winds Learnin Goals After studyin this hapter, students should be able to: 1. show how ertain fores interat to produe the winds (pp );. desribe the airflow in hih- and low-pressure systems, and explain how these motions reate weather (pp ); 3. explain the thermal wind onept (pp. 65 7); and 4. explain how differenes in heatin and oolin at the loal sale an ause winds (pp. 7 76).

2 Summary 1. The pressure radient fore drives the wind. This fore has a manitude proportional to the pressure radient and is direted from hih to low pressure.. The Coriolis fore auses winds to be defleted to the riht of their path in the northern hemisphere and to the left of their path in the southern hemisphere. The Coriolis fore inreases with latitude and wind speed. 3. The entripetal fore, or aeleration, keeps the winds movin in a urved path by pullin toward the entre of rotation. This fore has a manitude proportional to the wind speed and inversely proportional to the radius of urvature. 4. The fore of frition slows winds near Earth s surfae, so that wind speed inreases with heiht. The effets of surfae frition are arried upward by turbulene. Turbulene inreases with rouher surfaes, faster winds, and reater instability. As turbulene inreases, wind shear dereases, and the effets of surfae frition are arried hiher above the surfae. The depth of the atmosphere to whih the effets of surfae frition are transferred is referred to as the planetary boundary layer. 5. The eostrophi wind equation approximates the wind speed for straiht flow above the planetary boundary layer. Without frition or urvature, the pressure radient fore is balaned by the Coriolis fore, and the winds flow parallel to the isobars or ontours. 6. The radient wind equation approximates the wind speed for urved flow above the planetary boundary layer. The imbalane between the pressure radient fore and the Coriolis fore keeps the air movin alon a urved path by reatin a entripetal fore that pulls the air in toward the entre of rotation. For the same pressure radient, radient winds are faster around hihs than they are around lows. 7. In areas of low pressure, air onveres at the surfae, rises, and diveres aloft. The risin air leads to the formation of louds. If upper-level diverene is reater than surfae onverene, the low will intensify. In areas of hih pressure, air diveres at the surfae, sinks from above, and onveres aloft. The sinkin air leads to lear skies. If upper-level onverene is reater than surfae diverene, the hih will intensify. 8. Horizontal temperature radients reate upper-air pressure radients that hane with heiht. As a result of horizontal temperature radients, therefore, winds hane with heiht. We an use the thermal wind onept to study the relationship between the hane in winds with heiht in an atmospheri layer and the averae temperature radient of that layer. This onept helps provide us with an appreiation that the layers of the atmosphere work toether as a system. 9. Differenes in heatin between land and water an ause land sea breeze irulation systems. Durin the day, a thermal hih forms over the ooler water, while a thermal low forms over the warmer land; this reates a sea breeze. At niht, the pressure radient is reversed, reatin a land breeze. 10. Warmin auses air to rise up slopes as a valley wind. Coolin auses air to sink down slopes as a mountain wind.

3 Key Terms Antiylone An area of hih pressure around whih winds blow lokwise in the northern hemisphere and ounterlokwise in the southern hemisphere. (p. 59) Bakin Rotatin ounterlokwise with heiht. (p. 70) Barolini The atmospheri ondition in whih isotherms ross isobars. (p. 66) Barotropi The atmospheri ondition in whih isotherms parallel isobars. (p. 66) Centripetal fore The net fore, direted toward the entre of rotation, that ats on a rotatin objet. (p. 49) Coriolis fore An apparent fore, resultin from the rotation of Earth, that auses objets movin freely above Earth s surfae to appear to be defleted from a straiht-line path, relative to Earth s surfae. (p. 49) Cylone An area of low pressure around whih winds blow ounterlokwise in the northern hemisphere and lokwise in the southern hemisphere. (p. 59) Eddies Irreular whirlin motions that haraterize turbulent flow. (p. 55) Eddy visosity Lare-sale resistane to flow due to the random, irreular motions assoiated with turbulene. (p. 55) Frition The fore that resists motion whenever objets move, or try to move, relative to eah other. (p. 49) Geostrophi wind A wind, depited on a weather map as blowin parallel to straiht isobars or heiht ontours, that develops when the pressure radient fore is balaned by the Coriolis fore. (p. 57) Gradient wind A wind, depited on a weather map as flowin parallel to urved isobars or heiht ontours, that develops when the pressure radient fore and the Coriolis fore are unbalaned. (p. 59) Laminar flow A type of flow in whih layers of the fluid flow over eah other with no disruption between the layers. (p. 55) Land breeze A breeze that flows from the land to the oean at niht. (p. 7) Mesosale A sale of a few kilometres to a few hundred kilometres. (p. 7) Moleular visosity Small-sale resistane to flow due to the random motions of moleules in laminar flow. (p. 55) Momentum The produt of mass and veloity. (p. 54) Mountain wind Air blowin downslope. Also known as katabati winds. (p. 74) Planetary boundary layer The layer of air losest to the surfae that is influened by frition from the surfae. (p. 55) Ride An elonated area of hih pressure. (p. 61) Sea breeze A breeze that flows from the oean to the land durin the day. (p. 7) Thermal wind The hane in eostrophi wind with heiht due to the horizontal variation of temperature. (p. 64) Trouh An elonated area of low pressure. (p. 61)

4 alley wind Air blowin upslope. Also known as anabati winds. (p. 74) etor A onept used to represent phenomena that have both speed and diretion. (p. 63) eerin Rotatin lokwise with heiht. (p. 70) isosity Resistane to flow. (p. 54) Wind The mostly horizontal movement of air relative to Earth s surfae. (p. 49) Key Equations Pressure radient fore Coriolis fore PGF = 1 ρ ( P x ) CF = f Centripetal fore Geostrophi wind speed (pressure) C L F = R = ( 1 ρf ) ( P x ) Geostrophi wind speed (heiht) Winds around a ylone Winds around an antiylone = ( f ) ( z x ) r = ( 1 f ) ( r R ) r = + ( 1 f ) ( r R ) Answers to Seleted Review Questions (p. 78) 1. What determines the manitude and diretion of the pressure radient fore? The manitude of the pressure radient fore is determined by the pressure radient over a distane. The diretion of the fore is from reions of hih pressure to reions of low pressure.

5 3. In what diretion does the entripetal fore at? What determines the manitude of this fore? The entripetal fore ats toward the entre of rotation, ontinually pullin in toward that entre. The entripetal fore is proportional to the wind speed and inversely proportional to the radius of urvature. 5. Why does the effet of surfae frition extend upward into the atmosphere? What fators determine the depth of the atmosphere that will be influened by surfae frition? The effet of surfae frition extends upward into the atmosphere beause of turbulene. Wind speed, surfae rouhness, and atmospheri stability determine the depth of the atmosphere that will be influened by surfae frition. 7. Why are radient winds faster around hih-pressure areas than they are around lowpressure areas? Gradient winds flow faster around hih-pressure areas beause the Coriolis fore must be reater than the pressure radient fore to maintain urvin flow. 9. How do onverene and diverene lead to vertial motions? Desribe the patterns of onverene, diverene, and vertial motions in hih- and low-pressure systems. As air flows inward toward the entre of a low, it auses onverene at the surfae and fores air to rise. As air flows outward away from the entre of a hih, surfae air will divere and air from above will sink to fill the void. In hih-pressure systems, diverene ours at the surfae, onverene ours aloft, and air sinks. In low-pressure systems, onverene ours at the surfae, diverene ours aloft, and air rises. 11. How do temperature radients produe upper-level pressure radients? Why do suh pressure radients inrease with heiht? The temperature radient auses pressure surfaes to slope upward from an area of old air to an area of warmer air. This reates a pressure radient where the diretion is from areas of warm air to areas of old air. The pressure radients inrease with heiht beause pressure dereases more slowly with heiht in warm air than it does in old air. 13. How do land sea breeze irulation systems develop? How do valley and mountain winds develop? Land sea breeze irulation systems develop due to temperature differenes between land and water. Durin the day, a thermal hih-pressure system develops over the older water and a thermal low-pressure system develops over the warmer land. This reates a sea breeze. At niht, the pressure radient is reversed, reatin a land breeze. alley and mountain winds develop due to temperature differenes that result from variations in terrain. Durin the day, air alon the slopes will warm makin pressure slihtly lower alon the slopes. The warm, less dense air will rise up the mountainside as a valley wind. At

6 niht, the air alon the mountain slopes ools. This oolin reverses the pressure radient, ausin old, dense air to drain down the slope as a mountain wind. Answers to Seleted Problems (p. 79) 1. Calulate the Coriolis parameter, f, for a) 10 latitude and b) 80 latitude. f = Ω sin φ a) f = ( s 1 ) (sin 10 ) = s 1 b) f = ( s 1 ) (sin 80 ) = s 1 3. a) Calulate the eostrophi wind for the heiht ontours shown in the diaram, below. The heihts are iven in deametres, the distane between the ontours is 500 km, and the Coriolis parameter is s 1. b) At whih point 1,, or 3 does the wind speed alulated in a) best apply? z a) f x 9.8m / s s 1 = 94.1 m/s 480m 500,000 m b) The wind speed alulated in a) best applies at point. 5. For a eostrophi wind speed of 1 m/s, a radius of urvature of 1000 km, and f of s 1, alulate a) the radient wind speed for a ylone and b) the radient wind speed for an antiylone.

7 r 1 f r R Solve for r usin the quadrati formula. r f R a) Use a positive radius of urvature for yloni flow: r 1 1 1m / s 41m / s ,000,000 m = 10.4 m/s b) Use a neative radius of urvature for antiyloni flow: r 1 1 1m / s 41m / s ,000,000 m = 15.4 m/s 7. Calulate the manitude of the thermal wind for a hane in thikness of 380 m over 1000 km. The Coriolis parameter is s 1. T = T = h f x 9.8m / s s 380m 1,000,000 m = 37. m/s Study Questions For suested answers, see below. 1. What is the relationship between wind shear and turbulene?

8 . How does an imbalane of fores keep a radient wind movin in a urved path around a low pressure area? 3. What is the relationship between the loations of upper-air rides and trouhs and the loations of surfae hihs and surfae lows? 4. How does terrain influene the anle at whih winds flow aross isobars? 5. Why is the thermal wind not an atual wind? What does the thermal wind relationship state about the differene between the eostrophi wind at the top and bottom of an atmospheri layer? Additional Problems For answers, see below. 1. a) Calulate the pressure radient fore that results from a pressure radient of 0.4 kpa/50 km. Use a value of 1.14 k/m 3 for the density of air. b) If this fore ated for one half hour, what would be the wind speed?. Determine the Coriolis fore for a wind speed of 7.3 m/s at 4 latitude. 3. Calulate the entripetal fore for winds with a speed of 11. m/s at 75 km from the entre of a low-pressure system. 4. a) Calulate the eostrophi wind speed if the pressure hanes 3.1 kpa over a distane of 1050 km at latitude 65 and a heiht of 7 km in the atmosphere. At this heiht, air density is about 0.6 k/m 3. b) At the same latitude, the heiht of the 500 hpa surfae inreases 30 m over a distane of 00 km. Calulate the eostrophi wind speed in this ase. 5. What would the eostrophi wind speed be at 14 latitude for a pressure radient of.8 kpa over a distane of 900 km? The air density is 0.8 k/m For a eostrophi wind speed of 6. m/s at 57 latitude and a radius of urvature of 350 km, alulate the radient wind speed around a) a ylone and b) an antiylone. 7. Calulate the manitude of the thermal wind for a hane in thikness of 410 m over 1100 km. The Coriolis parameter is s The diaram below shows thikness ontours, in metres, on the 500 hpa hart. The distane between the three ontour lines is 650 km. The 500 hpa wind vetor is drawn on the diaram; its speed is 8 m/s. a) Calulate the manitude of the thermal wind at 33 latitude.

9 b) Draw the thermal wind on the diaram. Use a sale based on the lenth of the 500 hpa wind vetor. ) Draw the surfae wind on the diaram. Estimate the speed of the surfae wind. d) If advetion is ourrin, is it warm or old advetion?

10 Answers to Study Questions 1. Turbulene helps redue wind shear beause as turbulene inreases, the vertial transport of momentum inreases; the result is that wind speeds tend to beome more uniform with heiht. However, wind shear, in turn, enerates turbulene. (p. 56). An air parel in simple eostrophi flow around low pressure will first bein to move in a straiht line and parallel to the isobars. If the air parel ontinues to move in a straiht line, it will bein to slow beause the pressure radient fore will bein to at aainst it. As the air slows, the Coriolis fore will derease, makin it smaller than the pressure radient fore, so that the wind follows a urved path. (p. 59) 3. Surfae hihs are likely to form just upstream of an upper-air trouh beneath the onverene zone in the upper troposphere. Surfae lows are likely to form just downstream of an upper-air trouh where diverene ours in the upper troposphere. The net outflow assoiated with the diverene an remove mass from the air olumn, dereasin the surfae pressure. (pp. 61 6) 4. Rouhness is reater over land than over water, and it inreases even more in mountainous areas. As air flows over rued terrain, frition auses it to slow to about half the speed it would have in eostrophi flow; in suh ases, wind will ross isobars at an anle of about 45. When air flows over smoother surfaes, suh as the oean, the wind speed will not be redued as muh, and the winds will ross the isobars at anles of about 5 to 10. (p. 63) 5. The thermal wind is a measure of the wind shear, or the hane in wind with heiht. The thermal wind relationship states that the differene between the eostrophi wind at the top of an atmospheri layer and that at the bottom of an atmospheri layer is proportional to the mean horizontal temperature radient of the layer. (p. 65) Answers to Additional Problems 1. a) 1 P PGF x 1 PGF 1.14k / b) = a t m = m/s = m/s 1800 s =.5 m/s k m s 50,000 m

11 . CF = f 3. C L F = R = ( s 1 ) (sin 4 ) (7.3 m/s) = m/s 11.m / s = 75,000m = m/s 4. a) Calulate the Coriolis parameter: f = Ω sin φ f = ( s 1 ) (sin 65 ) f = s 1 1 f P x = 1 3.1kPa 1050 km k / m s = 37.9 m/s z b) = f x = 9.8m / s s 1 30m 00,000 m = 11.3 m/s 5. Calulate the Coriolis parameter: f = Ω sin φ

12 f = ( s 1 ) (sin 14 ) f = s 1 1 f P x = 1.8kPa k / m s 900km = m/s 6. Calulate the Coriolis parameter: f = Ω sin φ f = ( s 1 ) (sin 57 ) f = s 1 r 1 f r R Solve for r usin the quadrati formula. r f R a) Use a positive radius of urvature for yloni flow: r m / s 46.m / s ,000 m = 5.3 m/s b) Use a neative radius of urvature for antiyloni flow: r m / s 46.m / s ,000 m

13 = 7.6 m/s Δh 7. T = f Δx T = 9.8m / s s 1 410m 1,100,000 m = 45.7 m/s 8. Calulate the Coriolis parameter: f = Ω sin φ f = ( s 1 ) (sin 33 ) f = s 1 T = T = f h x 9.8m / s s 1 10m 650,000 m =.9 m/s b) T ) T 1 1 = 6.5 m/s d) warm advetion