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Single-time Markovianized spectral closure in fluid turbulence

Published online by Cambridge University Press:  25 June 2020

Takuya Kitamura Open the ORCID record for Takuya Kitamura [Opens in a new window]
Takuya Kitamura*
Affiliation:
Graduate School of Engineering, Nagasaki University, Nagasaki852-8521, Japan
*
†Email address for correspondence: t.kitamura@nagasaki-u.ac.jp
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Abstract

Kaneda’s (J. Fluid Mech., vol. 107, 1981, pp. 131–145) Lagrangian renormalized approximation was extended to single-time spectral closure under two assumptions: (i) Markovianization and (ii) the Lagrangian velocity response function is expressed by $G(k,\unicode[STIX]{x1D70F})=\exp (-C_{1}(k)\unicode[STIX]{x1D70F}-C_{2}(k)\unicode[STIX]{x1D70F}^{2}/2)$. The unknown functions $C_{1}(k)$ and $C_{2}(k)$ are theoretically derived to be consistent with the exact short-time behaviour of $G(k,\unicode[STIX]{x1D70F})$ and the asymptotic short-time behaviour of assumed exponential form of $G(k,\unicode[STIX]{x1D70F})$, i.e. the present closure is derived from the Navier–Stokes equation without introduction of any adjustable parameters and it can calculate the statistical quantities by theory. The results show that the present closure has good agreement with direct numerical simulation for single- and two-point statistics.

JFM classification

Turbulent Flows: Turbulence theory Turbulent Flows: Isotropic turbulence Turbulent Flows: Homogeneous turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 898 , 10 September 2020 , A8
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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