Statistics and geometry in high-Schmidt number scalar mixing

The mixing of substances is present in various turbulent systems. Examples arise in reacting flows and combustion, mixing of salt and plankton in oceans and of chemical pollutants in the stratosphere [1]. The physics of scalar mixing depends strongly on the ratio of the kinematic viscosity ν of the fluid to the diffusivity κ of the scalar. It is given by the Schmidt number Sc = ν/κ. For the following, we focus to the so-called Batchelor regime of scalar mixing [2], i.e. Sc > 1. High-resolution simulations are used to explore some geometrical and statistical properties of the gradients of passive scalar fields, ∇θ(x, t) (for more details, see also [3, 4]). The strong resolution requirements that significantly exceed usually adopted conditions result in rather low Taylor microscale Reynolds numbers (Rλ ≤ 63) of the advecting flow. The Schmidt numbers are 8 and 32. Large scalar gradients are associated with regions of locally intensive mixing and can be quantified by the scalar dissipation rate. This field will be of interest for the following and is defined as