Markov Property of Velocity Increments in Burgers Turbulence

We investigate the intermittency properties of a turbulent flow without pressure described by the Burgers equation. To this end, we make use of a phenomenogical description devised by R. Friedrich and J. Peinke [Phys. Rev. Lett. 78, 863 (1997)] that interprets the turbulent energy cascade as a Markov process in scale. The impact of Burgers-shocks on the Markov property of the velocity increments is discussed and compared to numerical simulations. Furthermore, we give a brief outlook on the use of the Markov property as a possible closure of a hierarchy of multi-increment probability density functions derived directly from the Burgers equation.