Mixing of strongly diffusive passive scalars like temperature by turbulence
- 1 September 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Fluid Mechanics
- Vol. 194 (-1) , 261-293
- https://doi.org/10.1017/s0022112088002988
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.Keywords
This publication has 18 references indexed in Scilit:
- The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbersProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1991
- Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulenceJournal of Fluid Mechanics, 1985
- Models of the scalar spectrum for turbulent advectionJournal of Fluid Mechanics, 1978
- The effect of velocity sensitivity on temperature derivative statistics in isotropic turbulenceJournal of Fluid Mechanics, 1971
- Growth of Turbulent Magnetic FieldsPhysics of Fluids, 1967
- Fluctuation Spectrum of a Plasma Additive in a Turbulent GasPhysical Review Letters, 1966
- The universal equilibrium spectra of turbulent velocity and scalar fieldsJournal of Fluid Mechanics, 1963
- A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds numberJournal of Fluid Mechanics, 1962
- The amplification of a weak applied magnetic field by turbulence in fluids of moderate conductivityJournal of Fluid Mechanics, 1961
- Small-scale variation of convected quantities like temperature in turbulent fluid Part 2. The case of large conductivityJournal of Fluid Mechanics, 1959