Quasi-linear regime and rare-event tails of decaying Burgers turbulence

Abstract

We study the decaying Burgers dynamics in $d$ dimensions for random Gaussian initial conditions. We focus on power-law initial energy spectra, such that the system shows a self-similar evolution. This is the case of interest for the "adhesion model" in cosmology and a standard framework for "decaying Burgers turbulence". We briefly describe how the system can be studied through perturbative expansions at early time or large scale (quasi-linear regime). Next, we develop a saddle-point method, based on spherical instantons, that allows to obtain the asymptotic probability distributions $\cP(η_r)$ and $\cP(\ctheta_r)$, of the density and velocity increment over spherical cells, reached in the quasi-linear regime. Finally, we show how this approach can be extended to take into account the formation of shocks and we derive the rare-event tails of these probability distributions, at any finite time and scale. This also gives the high-mass tail of the mass function of point-like singularities (shocks in the one dimensional case).

32 pages

References in corpus (5)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Burgers Turbulence
• Large-N expansions applied to gravitational clustering
• Using the Zeldovich dynamics to test expansion schemes
• Velocity and velocity-difference distributions in Burgers turbulence

Cited by in corpus (9)

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• Mass function and bias of dark matter halos for non-Gaussian initial conditions
• Mass functions and bias of dark matter halos
• Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities
• Divergence of Perturbation Theory in Large Scale Structures
• Eulerian and Lagrangian propagators for the adhesion model (Burgers dynamics)
• Density fields and halo mass functions in the Geometrical Adhesion toy Model
• Exact Results for Propagators in the Geometrical Adhesion Model
• Statistics of shocks in a toy model with heavy tails