Mixing of strongly diffusive passive scalars like temperature by turbulence

Mechanisms of turbulent mixing are explored by numerical simulations of one-dimensional and two-dimensional mixing with Pr < 1. The simulations suggest that the local rate of strain γ mixes the scalar field by at least two interacting mechanisms: the mechanism of generation, pinching and splitting of extrema proposed by Gibson (1968 a ) which acts along lines where the scalar-gradient magnitude is small; and a new mechanism of alignment, pinching and amplification of the gradients which acts along lines where the scalar-gradient magnitude is large. After extrema are generated, they split to form new extrema of the same sign, and saddle points. These zero-gradient points are connected by minimal-scalar-gradient lines which continuously stretch at rates of order γ, becoming longer than the viscous scale L K . For Pr < 1, this extends the influence of the local rate of strain to lengths of at least the order of the inertial-diffusive scale L C > L K ; that is, larger than the maximum assumed possible by Batchelor, Howells & Townsend (1959). Roughly orthogonal maximal-scalar-gradient lines are also embedded in the fluid, and compressive mixing along these lines also reflects the magnitude and direction of the local rate of strain over distances larger than L K . Because the two rate-of-strain mixing mechanisms act along lines, they can be modelled by one-dimensional numerical simulation. Both are Prandtl-number independent and together they provide a plausible physical basis for the universal scalar similarity hypothesis of Gibson (1968 b ) that turbulent mixing depends on γ for all Pr .