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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. 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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  1. Three Lectures on Tropical Cyclones Kerry Emanuel Massachusetts Institute of Technology Spring School on Fluid Mechanics of Environmental Hazards

  2. Lecture 2:Physics

  3. Steady-State Energetics

  4. Energy Production

  5. Distribution of Entropy in Hurricane Inez, 1966 Source: Hawkins and Imbembo, 1976

  6. Total rate of heat input to hurricane: Dissipative heating Surface enthalpy flux In steady state, Work is used to balance frictional dissipation:

  7. Plug into Carnot equation: If integrals dominated by values of integrands near radius of maximum winds,

  8. Theoretical Upper Bound on Hurricane Maximum Wind Speed: Surface temperature Ratio of exchange coefficients of enthalpy and momentum Outflow temperature Air-sea enthalpy disequilibrium

  9. Annual Maximum Potential Intensity (m/s)

  10. Observed Tropical Atlantic Potential Intensity Emanuel, K., J. Climate, 2007 Data Sources: NCAR/NCEP re-analysis with pre-1979 bias correction, UKMO/HADSST1

  11. 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

  12. Dependence on Sea Surface Temperature (SST):

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

  14. Why do real storms seldom reach their thermodynamic potential? One Reason: Ocean Interaction

  15. Strong Mixing of Upper Ocean

  16. Near-Inertial Oscillations of the Upper Ocean

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

  18. Special class of solutions for which p=w=0: Unforced solution:

  19. Mixing and Entrainment:

  20. Mixed layer depth and currents

  21. SST Change

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

  23. 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

  24. Transformed radial coordinate: Potential Radius:

  25. Example of Distribution of R surfaces

  26. Model behavior

  27. Comparing Fixed to Interactive SST:

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

  29. 2. Sea Spray

  30. 3. Wind Shear

  31. Effects of Environmental Wind Shear • Dynamical effects • Thermodynamic effects • Net effect on intensity

  32. Streamlines (dashed) and θ surfaces (solid)

  33. Mean Absolute Error of NOAA/NHC Tropical Cyclone Intensity Forecasts

  34. Tropical Cyclone Motion

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

  36. Lagrangian chaos:

  37. “Beta Gyres”

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