Entropic distribution model of turbulent vortices energy
DOI:
https://doi.org/10.15587/1729-4061.2012.5750Keywords:
hyperbolic distribution, distribution of turbulent vortices, energy of the turbulent fluctuations, turbulent spectrumAbstract
Empirical data of frequency distribution of atmospheric turbulent fluctuations from the degree of intensity indicate non-Gaussian nature of such dependence. The so-called "heavy tail" distribution is observed. Such distributions, as opposed to Gaussian, tend to maintain high probability of fluctuations, which could be very intense. This could be a very important factor of the deterioration of the security of aircraft flight.
Nowadays, for the statistical description of such distributions it is often used either normal distribution law or Rayleigh distribution. These Gaussian hypotheses could be applied in the case of independent outcomes that could not be considered valid for the turbulent velocity fluctuations, since the turbulent vortices exercise mutual continuous energy exchange.
The article suggests the ratio, named by the authors as extreme hyperbolic distribution law for the detection of turbulent vortices of various intensities proposed. The dependences were offered according to its parameters. This law is derived from the maximum entropy method of distribution of a limited set of "resources" (here - energy) on the set of a finite number of "carriers" (here - vortices). The authors believe that this dependence corresponds to the most economical distribution of the kinetic energy among the turbulent vorticesReferences
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