The Exact Solution of one Fokker-Planck Type Equation used by R. Friedrich and J. Peinke in the Stochastic Model of a Turbulent Cascade
A. A. Donkov, A. D. Donkov, E. I. Grancharova
TL;DR
This paper derives an exact solution for a Fokker-Planck equation modeling turbulent cascades as Markov processes, providing a precise mathematical foundation for understanding turbulence dynamics.
Contribution
It presents the first exact solution to a Fokker-Planck equation used in turbulence modeling, advancing the theoretical understanding of stochastic cascade processes.
Findings
Exact solution derived for the Fokker-Planck equation
Enhanced mathematical understanding of turbulent cascade models
Application of Suzuki's approach to turbulence equations
Abstract
The exact solution of the Cauchy problem for a Fokker-Planck equation used by R. Friedrich and J. Peinke for the description of a turbulent cascade, considered as a stochastic process of Markovian type, is obtained in the frame of M. Suzuki approach.
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Taxonomy
TopicsComplex Systems and Time Series Analysis · Stochastic processes and financial applications · Advanced Thermodynamics and Statistical Mechanics