Three lectures on tropical cyclones
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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

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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


Steady state energetics

Steady-State Energetics


Three lectures on tropical cyclones

Energy Production


Three lectures on tropical cyclones

Distribution of Entropy in Hurricane Inez, 1966

Source: Hawkins and Imbembo, 1976


Three lectures on tropical cyclones

Total rate of heat input to hurricane:

Dissipative heating

Surface enthalpy flux

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


Three lectures on tropical cyclones

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


Three lectures on tropical cyclones

Annual Maximum Potential Intensity (m/s)


Three lectures on tropical cyclones

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


Dependence on sea surface temperature sst

Dependence on Sea Surface Temperature (SST):


Relationship between potential intensity pi and intensity of real tropical cyclones

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


Why do real storms seldom reach their thermodynamic potential

Why do real storms seldom reach their thermodynamic potential?

One Reason: Ocean Interaction


Strong mixing of upper ocean

Strong Mixing of Upper Ocean


Near inertial oscillations of the upper ocean

Near-Inertial Oscillations of the Upper Ocean


Three lectures on tropical cyclones

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


Three lectures on tropical cyclones

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

Unforced solution:


Three lectures on tropical cyclones

Mixing and Entrainment:


Mixed layer depth and currents

Mixed layer depth and currents


Sst change

SST Change


Three lectures on tropical cyclones

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

  • Hydrostatic and gradient balance above PBL

  • Moist adiabatic lapse rates on M surfaces above PBL

  • Parameterized convection

  • Parameterized turbulence


Three lectures on tropical cyclones

Transformed radial coordinate: Potential Radius:


Three lectures on tropical cyclones

Example of Distribution of R surfaces


Three lectures on tropical cyclones

Model behavior


Three lectures on tropical cyclones

Comparing Fixed to Interactive SST:


Three lectures on tropical cyclones

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


3 wind shear

3. Wind Shear


Effects of environmental wind shear

Effects of Environmental Wind Shear

  • Dynamical effects

  • Thermodynamic effects

  • Net effect on intensity


Three lectures on tropical cyclones

Streamlines (dashed) and θ surfaces (solid)


Three lectures on tropical cyclones

Mean Absolute Error of NOAA/NHC Tropical Cyclone Intensity Forecasts


Tropical cyclone motion

Tropical Cyclone Motion


Three lectures on tropical cyclones

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


Three lectures on tropical cyclones

Lagrangian chaos:


Three lectures on tropical cyclones

“Beta Gyres”


Three lectures on tropical cyclones

Operational prediction of tropical cyclone tracks:


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