2007/01/11 by Elena Kartashova, Alexey Kartashov · 24 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Diophantine equation #Discrete mathematics #Dispersion (optics) #Function (biology) #Mathematical analysis #Mathematics #Meteorological Phenomena and Simulations #Meteorology #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes #Optics #Physics #Rational function #Statistical physics #Turbulence #Wave turbulence #math-ph #math.MP
paper · pdf · doi:10.1016/j.physa.2007.02.098
published in Physica A Statistical Mechanics and its Applications 380, 66-74 (Elsevier BV) · submitted to IJMPC
arxiv created 2007/01/11 · openalex publication_date 2007/03/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Model of laminated wave turbulence allows to study statistical and discrete layers of turbulence in the frame of the same model. Statistical layer is described by Zakharov-Kolmogorov energy spectra in the case of irrational enough dispersion function. Discrete layer is covered by some system(s) of Diophantine equations while their form is determined by wave dispersion function. This presents a very special computational challenge - to solve Diophantine equations in many variables, usually 6 to 8, in high degrees, say 16, in integers of order 1016 and more. Generic algorithms for solving this problem in the case of \it irrational dispersion function have been presented in our previous papers. In this paper we present a new generic algorithm for the case of \it rational dispersion functions. Special importance of this case is due to the fact that in wave systems with rational dispersion the statistical layer does not exist and the general energy transport is governed by the discrete layer alone.