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Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Space Time Mode ♦ Two-dimensional Turbulence ♦ Spatial Mode ♦ Adaptive Numerical Simulation ♦ Coherent Vortex ♦ Reduced Mathematical Model ♦ Specific Time ♦ Adaptive Multi-scale Wavelet Collocation Method ♦ Reynolds Number ♦ High Compression ♦ Spatial Fractal Dimension ♦ Space Time Computational Mode ♦ Usual Estimate ♦ Active Region ♦ Spatial Intermittency ♦ Usual Computational Estimate ♦ Temporal Fractal Dimension ♦ First Time ♦ Temporal Intermittency ♦ Two-dimensional Turbulent Flow ♦ Many Eddy Turn-over Time
Abstract It has been estimated that the number of spatial modes (or nodal values) required to uniquely determine a two-dimensional turbulent flow at a specific time is finite, and is bounded by Re 4/3 for forced turbulence and Re for decaying turbulence. The usual computational estimate of the number of space–time modes required to calculated decaying two-dimensional turbulence is N∼Re 3/2. These bounds neglect intermittency, and it is not known how sharp they are. In this paper we use an adaptive multi-scale wavelet collocation method to estimate for the first time the number of space–time computational modes N necessary to represent two-dimensional decaying turbulence as a function of Reynolds number. We find that N∼Re 0.9 for 1260 � Re � 40 400 over many eddy turn-over times, and that temporal intermittency is stronger than spatial intermittency. The spatial modes alone scale like Re 0.7.Theβ-model then implies that the spatial fractal dimension of the active regions is 1.2, and the temporal fractal dimension is 0.3. These results suggest that the usual estimates are not sharp for adaptive numerical simulations. The relatively high compression confirms the importance of intermittency and encourages the search for reduced mathematical models of two-dimensional turbulence (e.g. in terms of coherent vortices). 1.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 2006-01-01