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: Surface enthalpy flux Dissipative heating 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: Air-sea enthalpy disequilibrium Surface temperature Outflow temperature Ratio of exchange coefficients of enthalpy and momentum

10. Annual Maximum Potential Intensity (m/s)

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

12. Thermodynamic disequilibrium necessary to maintain ocean heat balance: Ocean mixed layer Energy Balance (neglecting lateral heat transport): Greenhouse effect Mean surface wind speed Weak explicit dependence on T s Ocean mixed layer entrainment

13. Dependence on Sea Surface Temperature (SST):

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

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

18. Strong Mixing of Upper Ocean

19. Near-Inertial Oscillations of the Upper Ocean

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

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

22. Mixing and Entrainment:

23. Mixed layer depth and currents

24. SST Change

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

26. 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

27. Transformed radial coordinate: Potential Radius:

28. Example of Distribution of R surfaces

29. Model behavior

30. Comparing Fixed to Interactive SST:

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

33. 2. Sea Spray

36. 3. Wind Shear

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

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

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

44. Tropical Cyclone Motion

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

49. Lagrangian chaos:

50. “Beta Gyres”

51. Operational prediction of tropical cyclone tracks: