Passive scalar turbulence in high dimensions.

Exploiting a Lagrangian strategy we present a numerical study for both perturbative and nonperturbative regions of the Kraichnan advection model. The major result is the numerical assessment of the first-order 1/d expansion by Chertkov, Falkovich, Kolokolov, and Lebedev [Phys. Rev. E 52, 4924 (1995)] for the fourth-order scalar structure function in the limit of high dimension d's. In addition to the perturbative results, the behavior of the anomaly for the sixth-order structure functions versus the velocity scaling exponent, xi, is investigated and the resulting behavior is discussed.