Three Lectures on Tropical Cyclones

Three Lectures on Tropical Cyclones

Kerry EmanuelMassachusetts Institute of Technology

Spring School on Fluid Mechanics of Environmental HazardsSpring School on Fluid Mechanics of Environmental Hazards

Lecture 2:Lecture 2:PhysicsPhysics

Steady-State EnergeticsSteady-State Energetics

Energy ProductionEnergy Production

Distribution of Entropy in Hurricane Inez, 1966Distribution of Entropy in Hurricane Inez, 1966

Source: Hawkins and Imbembo, 1976

Total rate of heat input to hurricane:

0 * 300

2 | | | |r

k DQ C k k C rdr V V

Surface enthalpy fluxDissipative heating

In steady state, Work is used to balance frictional dissipation:

0 3

02 | |

r

DW C rdr V

Plug into Carnot equation:

0 03 *00 0

| | | |r r

s oD k

o

T TC rdr C k k rdr

T V V

If integrals dominated by values of integrands near radius of maximum winds,

2 *| |max 0C T Tk s oV k kC TD o

Theoretical Upper Bound on Hurricane Theoretical Upper Bound on Hurricane Maximum Wind Speed:Maximum Wind Speed:

*2| |0

C T Tk s oV k kpot TC

oD

Air-sea enthalpy disequilibrium

Surface temperature

Outflow temperature

Ratio of exchange coefficients of enthalpy and momentum

0o 60oE 120oE 180oW 120oW 60oW

60oS

30oS

0o

30oN

60oN

0 10 20 30 40 50 60 70 80

Annual Maximum Potential Intensity (m/s)Annual Maximum Potential Intensity (m/s)

Observed Tropical Atlantic Potential IntensityObserved Tropical Atlantic Potential Intensity

Data Sources: NCAR/NCEP re-analysis with pre-1979 bias correction, UKMO/HADSST1

Emanuel, K., J. Climate, 2007

Thermodynamic disequilibrium necessary to Thermodynamic disequilibrium necessary to maintain ocean heat balance:maintain ocean heat balance:

Ocean mixed layer Energy Balance (neglecting lateral heat transport):

*0| |k entrainC k k F F F

sV

2

| |entrains o

poto D s

F F FT TV

T C

V

Greenhouse effect

Mean surface wind speedWeak explicit dependence

on Ts

Ocean mixed layer entrainment

Dependence on Sea Surface Temperature Dependence on Sea Surface Temperature (SST):(SST):

Relationship between potential Relationship between potential intensity (PI) and intensity of real intensity (PI) and intensity of real

tropical cyclonestropical cyclones

Why do real storms seldom reach their Why do real storms seldom reach their thermodynamic potential?thermodynamic potential?

One Reason: Ocean Interaction

Strong Mixing of Upper Ocean

Near-Inertial Oscillations of the Upper Near-Inertial Oscillations of the Upper OceanOcean

1

1

10

0

2 sin

x

y

u pfv F

t x

v pfu F

t y

pg

z

u v w

x y z

f

Navier-Stokes equations for incompressible fluid, omitting viscosity and linearized about a state of rest:

x

y

ufv F

tv

fu Ft

Special class of solutions for which p=w=0:

22

2x

y

Fuf u fF

t t

sin cosu A ft B ft Unforced solution:

Mixing and Entrainment:Mixing and Entrainment:

Mixed layer depth and currentsMixed layer depth and currents

SST ChangeSST Change

Comparison with same atmospheric model coupled to 3-D ocean model; idealized runs:

Full model (black), string model (red)

Computational Models of Hurricanes: Computational Models of Hurricanes: A simple modelA simple model

• Hydrostatic and gradient balance above PBL• Moist adiabatic lapse rates on M surfaces

above PBL• Parameterized convection• Parameterized turbulence

2 2

2 2

f fR M rV r

Transformed radial coordinate: Transformed radial coordinate: Potential Radius:Potential Radius:

Example of Distribution of R surfacesExample of Distribution of R surfaces

Model behaviorModel behavior

Comparing Fixed to Interactive SST:Comparing Fixed to Interactive SST:

A good simulation of Camille can only be obtained by assuming thatA good simulation of Camille can only be obtained by assuming thatit traveled right up the axis of the Loop Current:it traveled right up the axis of the Loop Current:

2. Sea Spray2. Sea Spray

3. Wind Shear3. Wind Shear

Effects of Environmental Wind ShearEffects of Environmental Wind Shear

• Dynamical effects

• Thermodynamic effects

• Net effect on intensity

Streamlines (dashed) and θ surfaces (solid)

Mean Absolute Error of NOAA/NHC Tropical Cyclone Intensity Forecasts

Tropical Cyclone MotionTropical Cyclone Motion

Tropical cyclones move approximately with a suitably defined vertical vector average of the flow in which they

are embedded

145 150 155 160 16515

20

25

30

35

Longitude

La

titu

de

20

30

40

50

Lagrangian chaos:Lagrangian chaos:

““Beta Gyres”Beta Gyres”

Operational prediction of tropical cyclone tracks: