Abstract
In this paper, Lattice Boltzmann Method (LBM) is used to investigate the freely-decaying two-dimensional (2D) turbulence. The main purpose focuses on recent mathematical results about a central assumption in the theory of two-dimensional turbulence proposed by Batchelor. The numerical results found an approximate exponent of energy spectrum E(k) ∼ k−3.5 at the high mesh resolutions and an approximate decaying exponent of enstrophy ‹ω› ∼ T−2/3. In addition, an approximate exponent of integral length scale l ∼ T−1/2 is observed. These results validate the recent new results of 2D turbulence and are different from the results derived by Batchelor's 2D model.
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