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Three Lectures on Tropical Cyclones. Kerry Emanuel Massachusetts Institute of Technology. Spring School on Fluid Mechanics of Environmental Hazards. Lecture 2: Physics. Steady-State Energetics. Energy Production. Distribution of Entropy in Hurricane Inez, 1966.

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Three lectures on tropical cyclones

Three Lectures on Tropical Cyclones

Kerry Emanuel

Massachusetts Institute of Technology

Spring School on Fluid Mechanics of Environmental Hazards


Lecture 2 physics

Lecture 2:Physics




Distribution of Entropy in Hurricane Inez, 1966

Source: Hawkins and Imbembo, 1976


Total rate of heat input to hurricane:

Dissipative heating

Surface enthalpy flux

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


Plug into Carnot equation:

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


Theoretical upper bound on hurricane maximum wind speed
Theoretical Upper Bound on Hurricane Maximum Wind Speed:

Surface temperature

Ratio of exchange coefficients of enthalpy and momentum

Outflow temperature

Air-sea enthalpy disequilibrium



Observed Tropical Atlantic Potential Intensity

Emanuel, K., J. Climate, 2007

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


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

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

Ocean mixed layer entrainment

Greenhouse effect

Weak explicit dependence on Ts

Mean surface wind speed




Why do real storms seldom reach their thermodynamic potential

Why do real storms seldom reach their thermodynamic potential?

One Reason: Ocean Interaction




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


Special class of solutions for which p=w=0: viscosity and linearized about a state of rest:

Unforced solution:


Mixing and Entrainment: viscosity and linearized about a state of rest:


Mixed layer depth and currents
Mixed layer depth and currents viscosity and linearized about a state of rest:


Sst change
SST Change viscosity and linearized about a state of rest:


Comparison with same atmospheric model coupled to 3-D ocean model; idealized runs:Full model (black), string model (red)


Computational models of hurricanes a simple model
Computational Models of Hurricanes: A simple model model; idealized runs:

  • Hydrostatic and gradient balance above PBL

  • Moist adiabatic lapse rates on M surfaces above PBL

  • Parameterized convection

  • Parameterized turbulence




Model behavior model; idealized runs:


Comparing Fixed to Interactive SST: model; idealized runs:


A good simulation of Camille can only be obtained by assuming that

it traveled right up the axis of the Loop Current:


2 sea spray
2. Sea Spray assuming that


3 wind shear
3. Wind Shear assuming that


Effects of environmental wind shear
Effects of Environmental Wind Shear assuming that

  • Dynamical effects

  • Thermodynamic effects

  • Net effect on intensity


Streamlines (dashed) and assuming thatθ surfaces (solid)




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


Lagrangian chaos: vertical vector average of the flow in which they are embedded


“Beta Gyres” vertical vector average of the flow in which they are embedded


Operational prediction of tropical cyclone tracks: vertical vector average of the flow in which they are embedded


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