Numerical and analytical estimates for the structure functions in two-dimensional magnetohydrodynamic flows

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Abstract
In two‐dimensional magnetohydrodynamicturbulence, the Kraichnan–Iroshnikov dimensional analysis suggests a linear scaling law for the exponents ζ p =p/4 of the structure functions for the Elsässer variables z ±=u±B. Numerical simulations are presented and higher order structure functions are calculated using the extended self‐similarity hypothesis of Benzi et al. [Phys. Rev. E 48, R29 (1993)]. In addition, an estimate for the first structure function ζ1≥1/4 is derived using a geometric technique introduced by Constantin and Procaccia [Phys. Rev. E 47, 3307 (1993)] in the the context of the transport of a passive scalar in three‐dimensional Navier–Stokes turbulence.