Backwards semi-martingales into Burgers' turtulence
Florent Nzissila, Octave Moutsinga, Fulgence Eyi Obiang

TL;DR
This paper models turbulence in the inviscid Burgers equation using Markov processes for turbulent intervals and clusters, revealing that the associated velocity processes are backward semi-martingales, thus linking turbulence dynamics with stochastic processes.
Contribution
It introduces a novel Markov process framework for turbulent intervals and clusters in Burgers' turbulence, showing their velocity processes are backward semi-martingales.
Findings
Markov processes describe turbulent interval and cluster dynamics.
Velocity processes are backward semi-martingales.
Provides stochastic process perspective on Burgers' turbulence.
Abstract
In fluid dynamics governed by the one dimensional inviscid Burgers equation , the stirring is explained by the sticky particles model. A Markov process describes the motion of random turbulent intervals which evolve inside an other Markov process , describing the motion of random clusters concerned with the turbulence. Then, the four velocity processes are backward semi-martingales.
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