Factorized cumulant expansion for homogeneous turbulence |
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| Institution: | 1. Physical Sciences and Computational Division, Pacific Northwest National Laboratory, Richland, WA, United States;2. Computational Science Division, Argonne National Laboratory, Lemont, IL, United States;1. LOCEAN Laboratory, Sorbonne Université-CNRS-IRD-MNHN, Paris F-75005, France;2. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia;3. Department of Meteorology (MISU), Stockholm University, 114 18 Stockholm, Sweden;4. Department of Marine Sciences, University of Gothenburg, S-405 30 Gothenburg, Sweden;5. University of Southampton, National Oceanography Centre, Southampton, United Kingdom |
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| Abstract: | A factorization approximation is introduced to the cumulant expansion of the characteristic functional for homogeneous turbulence. Under this approximation, an arbitrary nth order cumulant C(itn) is expressed in terms of the cumulants C(2),C(3) and C(n−1), and thus we obtain a closed but untruncated system of equations for the cumulants. Using the factorized fourth-cumulant approximation, a closed set of equations for the energy spectrum function E(k,t) and the energy transfer function T(k,t) is derived. These equations are solved numerically and the similarity laws of the solutions are derived analytically. The statistical quantities such as the energy, the enstrophy, Taylor's microscale and the skewness of the velocity derivative are calculated numerically and the statistical laws of these quantities are discussed. |
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