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Hurricanes and the Carnot cycle

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. Some basics about tropical cyclones.

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Hurricanes and the Carnot cycle

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  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.

  2. Some basics about tropical cyclones for details read • 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 counterclockwise circulation in the Northern Hemisphere • Categorization of tropical cyclones: maximum averaged wind speed 17 m/s or less tropical depression 18 to 32 m/s tropical storm called hurricanes in the western North Atlantic and eastern North Pacific regions 33 m/s or greater typhoons in the western North Pacific severe tropical cyclones elsewhere

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

  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 air undergoes isothermal expansion as it flows toward the lower pressure of the storm center while in contact with thesurface of the ocean (heat bath @ Ts300K) AB: 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 bath @ T0200K) CD: DA: air undergoes an adiabatic compression when loosing altitude fast

  6. A B Ts=300K D T0=200K C C D B A PV-Diagram of the hurricane Carnot engine

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

  8. We know the textbook efficiency of a Carnot engine: important difference to textbook Carnot cycle tropical cyclones textbook Carnot cycle work used for turbulent dissipation =work done on environment transformed back into heat @Ts back into the front end of the Carnot cycle heat from the ocean and Heat from turbulent dissipation where E:=b/a theoretical upper bound on hurricane wind speed note T0 <Ts

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