On the cascade in fully developed turbulence. The propagator approach versus the Markovian description
Laboratoire des Images et des Signaux,
Groupe non linéaire (UPRESA CNRS 5083) , LIS-ENSIEG, BP 46, 38402 Saint-Martin d'Hères Cedex, France
Revised: 28 April 1999
Published online: 13 August 2012
The aim of the paper is to a provide a link between two approaches that describe the cascade in fully developed turbulence. Precisely, we show that the propagator approach (B. Castaing) and the Markovian description (Friedrich & Peinke) are equivalent in the log-normal case. To prove this, we use an Itô stochastic differential equation in scale - Friedrich & Peinke approach -that can be explicitly integrated. The solution corresponds to the propagator approach. This is done for scale-invariant cascades as well as non scale-invariant cascade.
PACS: 47.27.Gs – Isotropic turbulence; homogeneous turbulence / 02.50.-r – Probability theory, stochastic processes, and statistics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999