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. 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)
Low pressure region
Brief reminder to the Coriolis force:
Exact:
Intuitive for : ac
Coriolis force

4. Secondary circulation
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 Ts300K)
BC:
Adiabatic (very fast) ascent of the air
CD:
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 T0200K)
DA:
air undergoes an adiabatic compression when loosing altitude fast

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

7. City of Huntington Beach
Where does the work go which the hurricane produces from the heat of the ocean
Work drives the wind
with surface speed
Devastation by
hurricane Katrina,
City of Huntington Beach
stationary state:
Generated work per time dissipated (friction)
( )
because
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
textbook Carnot cycle
tropical cyclones
=work done on environment
work used for turbulent dissipation
transformed back into
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