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

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

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:

Surface temperature

Ratio of exchange coefficients of enthalpy and momentum

Outflow temperature

Air-sea enthalpy disequilibrium


Annual Maximum Potential Intensity (m/s)


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:

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):


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


Why do real storms seldom reach their thermodynamic potential?

One Reason: Ocean Interaction


Strong Mixing of Upper Ocean


Near-Inertial Oscillations of the Upper Ocean


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


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

Unforced solution:


Mixing and Entrainment:


Mixed layer depth and currents


SST Change


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

  • Hydrostatic and gradient balance above PBL

  • Moist adiabatic lapse rates on M surfaces above PBL

  • Parameterized convection

  • Parameterized turbulence


Transformed radial coordinate: Potential Radius:


Example of Distribution of R surfaces


Model behavior


Comparing Fixed to Interactive SST:


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


3. Wind Shear


Effects 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 Motion


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


Lagrangian chaos:


“Beta Gyres”


Operational prediction of tropical cyclone tracks:


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