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

Annual Maximum Potential Intensity (m/s)

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

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

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: