Transcript Folie 1 - University of Nebraska–Lincoln

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
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
Structural elements of a tropical cyclone
•Basic flows
Primary circulation
origin of circulation is the Coriolis force
velocity in the rotating frame
F C  2m v  
angular velocity of rotating frame (earth)
Fictitious force in the rotating reference frame of the earth
Low pressure region
Brief reminder to the Coriolis force:
Intuitive for v   : y   xt  vt 2  1  2 v  t 2
2
ac
Exact:  d 
 dt inertial
d
    
 dt rot
vinertial  vrot    r
ainertial  arot  2  vrot      r 
Coriolis force
m arot  m ainertial  2m  vrot  m    r 
•Eye, Eyewall and
Rainbands
Secondary circulation
click for animation
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 bath @ 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 bath @ T0200K)
DA: air undergoes an adiabatic compression when loosing altitude fast
PV-Diagram of the hurricane Carnot engine
A
B
D
Ts=300K
C
T0=200K
C
B
D
A
Where does the work go which the hurricane produces from the heat of the ocean
Work drives the wind
with surface speed v
Devastation by
hurricane Katrina,
City of Huntington Beach
stationary state: Generated work per time dissipated (friction)
dW
3
3 (


F
v


because
drag
• dissipation  
dt
•
Fdrag  v2 )
rate of heat transfer from the ocean to the atmosphere
 b
quantifies the thermodynamic disequilibrium
between the ocean and atmosphere
We know the textbook efficiency of a Carnot engine: Carnot :
W
Qin

TS  T0
TS
important difference to textbook Carnot cycle
tropical cyclones
textbook Carnot cycle
work used for turbulent dissipation
W =work done on environment
transformed back into heat @Ts
back into the front end
of the Carnot cycle
heat from the ocean
Qin  a v3  b v
and
W  a v3
Heat from turbulent dissipation
a v3
 3
a v b v
  a v2  b   a v2
a v2 

b
1 
v

E
1 
where E:=b/a
v
Ts  T0
E
T0
theoretical upper bound on hurricane wind speed
note T0 <Ts