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We discuss cross-field diffusion of energetic particles using compressional and noncompressional two-dimensional turbulence models by performing test particle simulations. For both models, the diffusion coefficient, defined in the classical way, exhibits a timescale dependence, suggesting that the underlining physical process should be described by Lévy statistics. The diffusion coefficient for long timescales is classified in terms of the Kubo number, K = bL ⊥ /ρ, where b is the standarddoi:10.1088/0004-637x/697/1/886 fatcat:cvgcyllqdvdu3kvs2ekfxvpcc4