Michel Bauer and Denis Bernard 1999 J. Phys. A: Math. Gen. 32 5179 doi:10.1088/0305-4470/32/28/301
Michel Bauer and Denis Bernard
Show affiliationsWe study Lagrangian trajectories and scalar transport statistics in decaying Burgers turbulence. We choose velocity fields solutions of the inviscid Burgers equation whose probability distributions are specified by Kida's statistics. They are time-correlated, and neither time-reversal invariant nor Gaussian. We discuss in some detail the effect of shocks on trajectories and transport equations. We derive the inviscid limit of these equations using a formalism of operators localized on shocks. We compute the probability distribution functions of the trajectories although they do not define Markov processes. As physically expected, these trajectories are statistically well defined but collapse with probability one at infinite time. We point out that the advected scalars enjoy inverse energy cascades. We also make a few comments on the connection between our computations and persistence problems.
47.27.E- Turbulence simulation and modeling
47.40.Nm Shock wave interactions and shock effects
02.50.-r Probability theory, stochastic processes, and statistics
76F55 Statistical turbulence modeling (See also 76M35)
62Exx Distribution theory (See also 60Exx)
Issue 28 (16 July 1999)
Received 22 December 1998, in final form 10 May 1999
Michel Bauer and Denis Bernard 1999 J. Phys. A: Math. Gen. 32 5179
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