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Spectral theory of passive scalar with mean scalar gradient

Published online by Cambridge University Press:  02 August 2021

Takuya Kitamura Open the ORCID record for Takuya Kitamura [Opens in a new window]
Takuya Kitamura*
Affiliation:
Graduate School of Engineering, Nagasaki University, Nagasaki 852-8521, Japan
*
†Email address for correspondence: t.kitamura@nagasaki-u.ac.jp
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Abstract

A single-time two-point spectral closure is developed by approximation of the Lagrangian direct interaction approximation (LDIA) for a passive scalar in the presence of a mean scalar gradient in homogeneous isotropic turbulence. In the derivation of a single-time two-point spectral closure, the two assumptions, Markovianisation and the exponential form of Lagrangian velocity response function, are made for the LDIA, and angle dependence of the passive-scalar field is expressed by the second-order truncation of Legendre polynomials, in which such a truncation is justified by the linear theory. The resulting closure equations are derived in a straightforward way except for the above assumptions and further simplifications. The closures studied agree qualitatively with direct numerical simulation for one- and two-point statistics of a passive-scalar field in the case of unity Schmidt number. For both direct numerical simulation and closures, we show that the dependence of one-point passive-scalar statistics on the Péclet number based on scalar Taylor microscales collapses properly compared with that based on velocity microscales. We also propose universal scaling laws for second-order scalar structure functions and demonstrate their validity.

JFM classification

Mixing: Turbulent mixing Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory

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JFM Papers
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Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , A28
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© The Author(s), 2021. Published by Cambridge University Press

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