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Hurricanes and the Carnot cycle We are going to show that hurricanes are ( in good approximation ) a natural realization of the Carnot cycle. rare South.

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Presentation on theme: "Hurricanes and the Carnot cycle We are going to show that hurricanes are ( in good approximation ) a natural realization of the Carnot cycle. rare South."— Presentation transcript:

1 Hurricanes and the Carnot cycle We are going to show that hurricanes are ( in good approximation ) a natural realization of the Carnot cycle. rare South Atlantic tropical cyclone viewed from the International Space Station on March 26, 2004.South Atlantic tropical cycloneInternational Space Station

2 Some basics about tropical cyclones tropical cyclones: a storm system with a closed circulation (cyclonic) around a center of low pressure that originates over tropical oceans and is driven principally by heat transfer from the ocean for details read Categorization of tropical cyclones: maximum averaged wind speed counterclockwise circulation in the Northern Hemisphere 17 m/s or lesstropical depression 18 to 32 m/s tropical storm 33 m/s or greater called hurricanes in the western North Atlantic and eastern North Pacific regions typhoons in the western North Pacific severe tropical cyclones elsewhere

3 Structural elements of a tropical cyclone Basic flows Primary circulation origin of circulation is the Coriolis force Fictitious force in the rotating reference frame of the earth velocity in the rotating frame angular velocity of rotating frame (earth) Brief reminder to the Coriolis force: Intuitive for : acac Exact: Coriolis force Low pressure region

4 Eye, Eyewall and Rainbands Secondary circulation Very high wind speed due to conservation of angular momentum click for animation

5 The hurricane as a Carnot heat engine see for details A B: air undergoes isothermal expansion as it flows toward the lower pressure of the storm center while in contact with the surface of the ocean (heat T s 300K) B C: Adiabatic (very fast) ascent of the air air flows out at the top of its trajectory and is incorporated from the extreme low pressure region into other weather systems via an isothermal compression (heat T 0 200K) C D: D A: air undergoes an adiabatic compression when loosing altitude fast

6 A B C D AB C D T s =300K T 0 =200K PV-Diagram of the hurricane Carnot engine

7 Where does the work go which the hurricane produces from the heat of the ocean stationary state:Generated work per time dissipated (friction) dissipation Devastation by hurricane Katrina, City of Huntington Beach rate of heat transfer from the ocean to the atmosphere ( ) because quantifies the thermodynamic disequilibrium between the ocean and atmosphere Work drives the wind with surface speed

8 We know the textbook efficiency of a Carnot engine:efficiency of a Carnot engine theoretical upper bound on hurricane wind speed important difference to textbook Carnot cycle textbook Carnot cycle =work done on environment tropical cyclones work used for turbulent dissipation transformed back into s back into the front end of the Carnot cycle Heat from turbulent dissipation heat from the ocean and where E:=b/a note T 0


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