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A simple model of a passive scalar quantity advected by a Gaussiannon-solenoidal ("compressible") velocity field is considered. Large orderasymptotes of quantum-field expansions are investigated by instanton approach.The existence of finite convergence radius of the series is proved, a positionand a type of the corresponding singularity of the series in the regularizationparameter are determined. Anomalous exponents of the main contributions to thestructural functions are resummed using new information about the seriesconvergence and two known orders of the expansion.Comment: 21 page

Large-order asymptotes of the quantum-field expansions for the Kraichnan model of passive scalar advection