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 18 to 32 m/s 33 m/s or greater tropical depression tropical storm called
hurricanes
in the western North Atlantic and eastern North Pacific regions 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
F C
2
m v
velocity in the rotating frame 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:
xt
vt
2 1 2 2 a c 2 Exact:
d dt inertial
rot v inertial a inertial
v rot
a rot r
2
v rot
m a rot
m a inertial
Coriolis force 2
m
v rot
m
r
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 @ T s 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 @ T 0 200K) D A: air undergoes an adiabatic compression when loosing altitude fast
PV-Diagram of the hurricane Carnot engine
A D B
T s =300K
C
T 0 =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) • dissipation 3
dW dt
F drag v
3 because
F drag
v
2 • rate of heat transfer from the ocean to the atmosphere quantifies the thermodynamic disequilibrium
b
between the ocean and atmosphere
We know the textbook efficiency of a Carnot engine :
Carnot
:
W Q in
T S
T S T
0 important difference to textbook Carnot cycle textbook Carnot cycle tropical cyclones
W
=work done on environment work used for turbulent dissipation transformed back into heat @T s heat from the ocean
Q in
a v
3
b v
Heat from turbulent dissipation
a v a v
3 3
b v
and back into the front end of the Carnot cycle
W
a v
3
a v
2
b
v
T s
T
0
E T
0
a v
2
a v
2 1
b v
1
E
where E:=b/a theoretical upper bound on hurricane wind speed note T 0