Local and Non-local Interactions in the Batchelor Regime of the Passive Scalar

Abstract

Following a suggestion of Yukio Kaneda, Kraichnan’s interpretation of Batchelor’s analysis of high Schmidt number passive scalar turbulence is described in terms of local and non-local interactions. The formulations of Batchelor and Kraichnan are then compared through their predictions of the diffusive range following the Batchelor range and of the reduction of mean-square advection in scalar turbulence. Although comparison based on the diffusive range proves inconclusive, the predictions of reduction of mean-square advection may support Kraichnan’s formulation; however, a definite conclusion is not yet possible.