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Turbulent energy density in scale space for inhomogeneous turbulence

Published online by Cambridge University Press:  13 March 2018

Fujihiro Hamba Open the ORCID record for Fujihiro Hamba [Opens in a new window]
Fujihiro Hamba*
Affiliation:
Institute of Industrial Science, The University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8505, Japan
*
†Email address for correspondence: hamba@iis.u-tokyo.ac.jp
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Abstract

The energy spectrum is commonly used to describe the scale dependence of the turbulent fluctuations in homogeneous isotropic turbulence. In contrast, one-point statistical quantities, such as the turbulent kinetic energy, are employed for inhomogeneous turbulence modelling. To obtain a better understanding of inhomogeneous turbulence, some attempts have been made to describe its scale dependence by using the second-order structure function and the two-point velocity correlation. However, previous expressions for the energy density in the scale space do not satisfy the requirement that it should be non-negative. In this work, a new expression for the energy density in the scale space is proposed on the basis of the two-point velocity correlation; the integral with a filter function is introduced to satisfy the non-negativity of the energy density. Direct numerical simulation (DNS) data of homogeneous isotropic turbulence were first used to assess the role of the energy density by comparing it with the energy spectrum. DNS data of a turbulent channel flow were then used to investigate the energy density and its transport equation in inhomogeneous turbulence. It was shown that the new energy density is positive in the scale space of the homogeneous direction. The energy transfer was successfully examined in the scale space both in the homogeneous and inhomogeneous directions. The energy cascade from large to small scales was clearly observed. Moreover, the inverse energy cascade from large to very large scales was observed in the scale space of the spanwise direction.

JFM classification

Turbulent Flows: Isotropic turbulence Turbulent Flows: Shear layer turbulence Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 842 , 10 May 2018 , pp. 532 - 553
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Copyright
© 2018 Cambridge University Press 

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