Mixing of strongly diffusive passive scalars like temperature by turbulence

Abstract

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 (1968a) 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 LK. 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 LC > LK; 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 LK. 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 (1968b) that turbulent mixing depends on γ for all Pr.