Fine structure characteristics of large Schmidt number molecular mixing in turbulent flows

Molecular mixing in fluid flows plays a central role in an enormous range of practical problems, and especially those in which some sort of chemical reaction or phase change occurs between two or more reactants. Often in engineering practice, the particular objective involves achieving relatively rapid rates of mixing, and for this reason practical problems tend to focus on mixing in turbulent flows. Many such problems in which molecular mixing in turbulent shear flows is a key factor can be formulated, either directly or in certain limiting cases, in terms of the mixing of an appropriately defined, dynamically passive, conserved scalar quantity ζ This denotes any scalar variable that is strictly advected by the fluid and diffuses relative to the fluid, but which is neither created nor destroyed within the flow and which does not directly affect the flow field. The scalar fields ζ(x, t) considered here thus satisfy conservative advection-diffusion equations of the form 1 https://www.w3.org/1998/Math/MathML" display="block"> [ ∂ ∂ t + u ⋅ ∇ – 1 R e S c ∇ 2 ] ζ ( x, t ) = 0 where all variables have been made nondimensional by normalization with reference length and velocity scales, l* and u*, and reference scalar value ζ*. In Equation (1) , the only parameter appearing explicitly is the dimensionless scalar diffusivity ( 1 /ReSc), with ReSc the product of the Reynolds number Re = (u*l*/ν) and the Schmidt number Sc = (ν/D), where ν and D are the vorticity and scalar diffusivities. However, the velocity field u(x , t ) in Equation (1) is governed by its own transport equa- tions which introduce the Reynolds number separately, namely 2 https://www.w3.org/1998/Math/MathML" display="block"> ∇ ⋅ u(x, t ) = 0 and [ ∂ ∂ t + u ⋅ ∇ – 1 R e ∇ 2 ] u(x, t ) = − ∇ p ρ