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Meteorology (Weather) - Tornado outbreaks as patterned mathematical processes
Expert: Ryan Hastings - 11/2/2009
Question
Would you care to verify that
//sin x cos x-sin^2x =the cardioid
You see, this is a derivation of the balancing terms of the pressure field and horizontal velocity equations found in first year dynamic meteorology from
du/dt=-1/rhopartial pressure/partial x+fv
dv/dt=-1/rhopartial pressure/partial y-fu
The point is that past tornado outbreaks can be resolved to show that the cardioid is involved in placing storm cells in a cardioid series/sequenced process, hence, tornado outbreaks are not random but deterministic!
Answer
Well, first off tornado outbreaks are not random events at all. They are caused by a number of well-known atmospheric processes, and it's not uncommon for the possibility of a major outbreak to be recognized several days before the event. They are not random, but there is a limit to our ability to predict them more than a few days in advance because the atmosphere is a chaotic system.
The equations you mention are the result of rewriting the Navier-Stokes equations for an observer in a rotating frame and scaling them for the synoptic scale. As such, they're okay for getting a first approximation for large scale behavior; but they're mostly useful as a starting place for deriving quasigeostrophic theory. Certainly the mathematics of the occurrence of a tornado itself would require including the stress tensor as well as finding a way to treat turbulence. And for predicting storm cells you'll definitely need some form of the conservation equations for energy and mass and an equation relating vertical velocity to buoyancy.
I do not understand what you mean when you say that "the cardioid is involved in placing storm cells in a cardioid series/sequenced process."
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