Lognormality Observed for Additive Processes: Application to Turbulence
The lognormal distribution has been observed across the natural and social sciences. It is always ascribed to a multiplicative process, i.e., a product of random variables, or equivalently to nonlinearity of the system, which always appears to be complex. However, we find that the lognormal distribution is also observable for a sum of random variables, i.e., an additive process in a linear system. The application is shown for large-scale fluctuations of fluid turbulence.
Keywordsstatistical description of complex systems
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- 4.Mouri, H.: Log-Normal Distribution from a Process that is not Multiplicative but is Additive. Phys. Rev. E 88, 042124 (2013)Google Scholar
- 5.Mouri, H., Hori, A., Takaoka, M.: Large-Scale Lognormal Fluctuations in Turbulence Velocity Fields. Phys. Fluids 21, 065107 (2009)Google Scholar
- 6.Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1965)Google Scholar
- 7.Monin, A.S., Yaglom, A.M.: Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. MIT Press, Cambridge (1975)Google Scholar
- 9.Landau, L.D., Lifshitz, E.M.: Fluid Mechanics. Pergamon, London (1959)Google Scholar