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Three Lectures on Tropical CyclonesPowerPoint Presentation

Three Lectures on Tropical Cyclones

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### Three Lectures on Tropical Cyclones

### Lecture 2:Physics

### Why do real storms seldom reach their thermodynamic potential?

Kerry Emanuel

Massachusetts Institute of Technology

Spring School on Fluid Mechanics of Environmental Hazards

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:

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

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): heat balance:

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

One Reason: Ocean Interaction

Strong Mixing of Upper Ocean potential?

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

Special class of solutions for which p=w=0: viscosity and linearized about a state of rest:

Unforced solution:

Mixing and Entrainment: viscosity and linearized about a state of rest:

Mixed layer depth and currents viscosity and linearized about a state of rest:

SST Change viscosity and linearized about a state of rest:

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 model; idealized runs:

- Hydrostatic and gradient balance above PBL
- Moist adiabatic lapse rates on M surfaces above PBL
- Parameterized convection
- Parameterized turbulence

Transformed radial coordinate: Potential Radius: model; idealized runs:

Example of Distribution of R surfaces model; idealized runs:

Model behavior model; idealized runs:

Comparing Fixed to Interactive SST: model; idealized runs:

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 assuming that

3. Wind Shear assuming that

Effects of Environmental Wind Shear assuming that

- Dynamical effects
- Thermodynamic effects
- Net effect on intensity

Streamlines (dashed) and assuming thatθ surfaces (solid)

Tropical Cyclone Motion Forecasts

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

Lagrangian chaos: vertical vector average of the flow in which they are embedded

“Beta Gyres” vertical vector average of the flow in which they are embedded

Operational prediction of tropical cyclone tracks: vertical vector average of the flow in which they are embedded

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