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We review statistical methods, such as the DIA and related theories and compare their predictions to direct numerical simulations (DNS) of homogeneous fluid turbulence. After a brief review of the closures, we record some of its successes and failures as revealed in comparisons with DNS. The comparisons included isotropic turbulence, at low and large Reynolds numbers, stably stratified turbulence, and convection. Our discussion also includes the very large scales, for which the computational box may limit the trustworthiness of the DNS. Finally, we shall consider the utility of the statistical methods as an economical way of gaining insights into fluid turbulence. Host: Jian-Zhou Zhu, T-CNLS & T-07 |