1996/02/23 by Erik Aurell, Aurell, Erik, С. Н. Гурбатов +3
Earth and Planetary Sciences · Engineering · Environmental Science · #Climate variability and models #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.patt-sol/9602005
openalex publication_date 1996/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the statistical properties of solutions to Burgers' equation, vt + vvx = νvxx, for large times, when the initial velocity and its potential are stationary Gaussian processes. The initial power spectral density at small wave numbers follows a steep power-law E0(k) ∼ |k|n where the exponent n is greater than two. We compare results of numerical simulations with dimensional predictions, and with asymptotic analytical theory. The theory predicts self-similarity of statistical characteristics of the turbulence, and also leads to a logarithmic correction to the law of energy decay in comparison with dimensional analysis. We confirm numerically the existence of self-similarity for the power spectral density, and the existence of a logarithmic correction to the dimensional predictions.