Revisiting two-dimensional turbulence by lattice boltzmann method

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 «ω²» ∼ 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.