Spatial dependence of correlation functions in the decay problem for a passive scalar in a large-scale velocity field

Statistical characteristics of a passive scalar advected by a turbulent velocity field are considered in the decay problem with a low scalar diffusivity κ (large Prandtl number v/κ, where v is kinematic viscosity). A regime in which the scalar correlation length remains smaller than the velocity correlation length is analyzed. The equal-time correlation functions of the scalar field are found to vary according to power laws and have angular singularities reflecting locally layered distribution of the scalar in space.