Sailing the Deep Blue Sea of Decaying Burgers Turbulence

Abstract

We 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, not time-reversal invariant and not Gaussian. We discuss in some details 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.

18 pages, one figure in eps format, Latex, published version

References in corpus (7)

• Slow modes in passive advection
• On the decay of Burgers turbulence
• Inverse versus direct cascades in turbulent advection
• Inverse cascade and intermittency of passive scalar in 1d smooth flow
• Anomalous scaling in passive scalar advection: Monte-Carlo Lagrangian trajectories
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• Assortative Exchange Processes
• Statistics of shocks in a toy model with heavy tails