Burgers Turbulence
By J. Bec, Kostya Khanin. Energy Transfers in Fluid Flows, 2007
275 citations recorded by the source corpus.
The last decades witnessed a renewal of interest in the Burgers equation. Much activities focused on extensions of the original one-dimensional pressureless model introduced in the thirties by the Dutch scientist J.M. Burgers, and more precisely on the problem of Burgers turbulence , that is the study of the solutions to the one- or multi-dimensional Burgers equation with random initial conditions or random forcing. Such work was frequently motivated by new emerging applications of Burgers model to statistical physics, cosmology, and fluid dynamics. Also Burgers turbulence appeared as one of the simplest instances of a nonlinear system out of equilibrium. The study of random Lagrangian systems, of stochastic partial differential equations and their invariant measures, the theory of dynamical systems, the applications of field theory to the understanding of dissipative anomalies and of multiscaling in hydrodynamic turbulence have benefited significantly from progress in Burgers turbulence. The aim of this review is to give a unified view of selected work stemming from these rather diverse disciplines.
Subfields: Applied Mathematics, Computational Mechanics, Finance
View Paper: https://www.semanticscholar.org/paper/39ecf81dab5b07bc1467edeac3e13336fe218e79
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Citations in the corpus
- Cascades and transitions in turbulent flows (2018, background): “Intermittency is also present in other hydrodynamical systems as in Burgers’ equations [500], in MHD turbulence [359, 375, 501–507], in rotating and stratified turbulence [43, 292], quantum turbulence [508, 509], in shell models [510, 511] (see Sec.”
- Beyond Kolmogorov cascades (2019, methodology): “…inertial dissipation by a shock A simple illustration of the concept of inertial dissipation can be given using a a shock, the singularity appearing in inviscid Burgers equation, sometimes regarding as the ”1D equivalent of Navier-Stokes equations” (see Bec & Khanin (2007) for a complete review).”