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

• 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 less tropical depression

18 to 32 m/s tropical storm

33 m/s or greater

called hurricanesin the western North Atlanticand eastern North Pacific regions

typhoons in thewestern North Pacific

severe tropical cyclones elsewhere

Structural elements of a tropical cyclone

•Basic flows Primary circulation origin of circulation is the Coriolis force

2CF m v

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:

2 212

2y xt vt v t

inertial rot

d d

dt dt

Intuitive for :v

ac

Exact:

inertial rotv v r

2inertial rot rota a v r

2rot inertial rotm a m a m v m r

Coriolis force

Low pressure region

•Eye, Eyewall and Rainbands

Secondary circulation

Very high wind speed due to

conservation of a

ngular momentum

click for animation

The hurricane as a Carnot heat engine see for details

AB: 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 @ Ts300K)

BC: 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 @ T0200K)

CD:

DA: air undergoes an adiabatic compression when loosing altitude fast

AB

CD

AB

C D

Ts=300K

T0=200K

PV-Diagram of the hurricane Carnot engine

Where does the work go which the hurricane produces from the heat of the ocean

stationary state: Generated work per time dissipated (friction)

• dissipation 3

Devastation by hurricane Katrina,City of Huntington Beach

• rate of heat transfer from the ocean to the atmosphere b

( )3

drag

dWF v

dt because 2

dragF v

quantifies the thermodynamic disequilibrium

between the ocean and atmosphere

Work drives the windwith surface speed v

We know the textbook efficiency of a Carnot engine: 0: SCarnot

in S

W T T

Q T

0

0

sT Tv E

T

theoretical upper bound on hurricane wind speed

important difference to textbook Carnot cycle

textbook Carnot cycle

=work done on environmentW

tropical cyclones

work used for turbulent dissipation

transformed back into heat @Ts

back into the front endof the Carnot cycle

3inQ a v b v

Heat from turbulent dissipation

heat from the ocean

3W a vand

3

3

a v

a v b v

2 2a v b a v 2

1a v b

1

v E

where E:=b/a

note T0 <Ts