Turbulent mixing with chemical reaction and collection of inertialess particles on cylinders and spheroids with electrical forces and gravitation

By numerically integrating the Fourier transformed exact conservation equations of reactants over time using a numerical simulation of a homogeneous isotropic turbulent velocity field for the convection velocity, O'Brien's and Toor's statistical independence hypotheses were tested. Two simulated turbulent velocity fields that obey continuity were used. The first had a constant specified energy spectrum but lacked interaction between Fourier modes. The second velocity field, which was generated using a modified form of the Navier-Stokes equation, had interaction and conserved energy but the energy-spectrum was transient.