ISSN:
1434-6036
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract The preturbulent region of the Lorenz model is investigated with the aim to determine the attractive region around the stable fixed points as a function of the Rayleigh parameterr. Close to the turbulent threshold, i.e. for small deviations ɛ=r T−r, the attractive region is a highly anisotropic ellipsoid in the phase space. Its volumeV obays the power lawV(ε)=const ɛα with the critical exponent α=5/2. A Landau type approximation, on the other hand, leads to α-3/2. The reason for this discrepancy is discussed. In addition we develop a series expression which allows to calculate the maximal domain of attraction also for large deviations ε. Numerical results from the two lowest terms of the series are represented for 0〈ε≲6.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01304097
