Iso-scalar surfaces, mixing and reaction in turbulent flows

Turbulent scalar mixing with chemical reaction is investigated in terms of the local geometrical features of the iso-scalar surfaces- 'scalar field topologies'-, using Direct Numerical Simulation data. Two scalars with identical initial distribution, one inert and the other obeying a prescribed Arrhenius-like chemical reaction, evolve in homogeneous isotropic turbulence with a mesh size 256(3). The two local principal curvatures, k(1) and k(2), of the iso-scalar surface at each point are straightforwardly obtained from the curvature tensor, n(i,j), whose elements are the spatial derivatives of the unit vector normal to the iso-surface. The scalar diffusive flux is decomposed into a 'flat-front' contribution plus a curvature induced molecular transport. Expressions for the normal propagating velocity relative to the fluid of iso-surfaces, of both the inert and the reactive scalar fields, are provided making use of the previous decomposition. The 'flat-front' and the curvature induced contributions to the diffusive fluxes, beside to the chemical reaction rate, are correlated with the principal curvatures. Results, including the joint statistics of the principal curvatures and their correlations with the scalar dissipation, are also presented.