2011/04/26 by Pierre Le Doussal, Alberto Rosso, Kay Jörg Wiese · 7 citations
Earth and Planetary Sciences · Engineering · Environmental Science · Mathematics · Physics and Astronomy · #Brownian motion #Burgers' equation #Classical mechanics #Climate variability and models #Conjecture #Differential equation #Field (mathematics) #Fluid Dynamics and Turbulent Flows #Inviscid flow #Mathematical analysis #Mathematics #Mechanics #Meteorological Phenomena and Simulations #Physics #Pure mathematics #Shock (circulatory) #Statistical physics #Statistics #Turbulence #Uncorrelated #cond-mat.stat-mech
paper · pdf · doi:10.1209/0295-5075/96/14005
published in Europhysics Letters (EPL) 96(1), 14005 (Institute of Physics) · 4 pages, 8 figures
arxiv created 2011/04/26 · openalex publication_date 2011/09/20 · arxiv updated 2015/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We conjecture the exact shock statistics in the inviscid decaying Burgers equation in D >1 dimensions, with a special class of correlated initial velocities, which reduce to Brownian for D =1. The prediction is based on a field theory argument, and receives support from our numerical calculations. We find that, along any given direction, shock sizes and locations are uncorrelated.