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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