Saturday, August 21, 2004

Should Miami be evacuated ? (Doit-on evacuer Miami ?)

What are the chances that the sharp turn of Hurricane Charley turns out to be due to Nonnormality as seen in Generalized Stability Theory ? In a few words, many different climatic models do tend to refer to the largest eigenvalue of the linearized version of these models to make an inference on what they can predict: i.e. if the eigenvalues are all negatives, then the system is subcritical and will wither away. The problem with this assumption is that eigenvalues are only telling you something about an asymptotic behavior not a short term one. The other problem is that if you deal with the linearized version of a nonlinear system of equations (like the Navier stokes equation that governs fluid flows such as the air in a hurricane) and if nonnormality is large (it seems to be an accepted fact when dealing with fluid flow) there is a great chance that you will never have time to "live" close to the initial conditions of the system since transient growth will make your assumption on the linearization totally invalid. This is also a sign that scientists predicting hurricane paths do not seem to have understood a specific strong coupling between two different physical phenomena. What is concerning is that the first paper was published in 1994 and the second one in 1998....

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