Decay of scalar variance in isotropic turbulence in a bounded domain

TL;DR

This paper investigates how the finite size of a bounded domain affects the decay of scalar variance in isotropic turbulence, revealing a proportional relationship between decay exponent and spectral constants, supported by analytical, closure, and simulation methods.

Contribution

It extends previous work to passive scalars, deriving a relationship between decay exponent and spectral constants, validated through analytical models, closure calculations, and large-eddy simulations.

Findings

Decay exponent proportional to the ratio of Kolmogorov to Corrsin-Obukhov constants

Spectral truncation influences scalar and eddy lengthscales

Simulation results support the analytical predictions

Abstract

The decay of scalar variance in isotropic turbulence in a bounded domain is investigated. Extending the study of Touil, Bertoglio and Shao (2002; Journal of Turbulence, 03, 49) to the case of a passive scalar, the effect of the finite size of the domain on the lengthscales of turbulent eddies and scalar structures is studied by truncating the infrared range of the wavenumber spectra. Analytical arguments based on a simple model for the spectral distributions show that the decay exponent for the variance of scalar fluctuations is proportional to the ratio of the Kolmogorov constant to the Corrsin-Obukhov constant. This result is verified by closure calculations in which the Corrsin-Obukhov constant is artificially varied. Large-eddy simulations provide support to the results and give an estimation of the value of the decay exponent and of the scalar to velocity time scale ratio.