Spectrum of passive scalar carried by particles in isotropic turbulence

We conducted numerical simulations of passive scalar carried by noninertial particles convected by the isotropic turbulence at low to high Reynolds number up to $R_{\lambda }=550$ with infinitely large Schmidt numbers. In the numerical method, each particle has a scalar value ${\theta }_p$ that relaxes with a relaxation time ${\tau }_{\theta }$ independent of the turbulence and its evolution is computed along the Lagrangian trajectory, and the scalar is mapped onto the Eulerian grid points. In the limit of large ${\tau }_{\theta }$, the evolution equation for the mapped field $\theta$ converges to that in the Batchelor regime with an infinite Schmidt number. We investigated the two point statistics including the variance spectrum of the field $\theta$ and confirmed their consistency with the turbulence theory, such as the Batchelor spectrum, constancy of the transfer flux, and the Yaglom 4/3 law for the third-order structure function by parameter sweep simulations with various values of ${\tau }_{\theta }$. An explanation of the present numerical method from the view point of the turbulence physics is presented. The visualized scalar field shows features commonly seen in passive scalar turbulence, such as plateaus, fronts, and sheetlike structures.