Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T22:40:20.075Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bolotnov, I. A., Lahey, R. T. Jr., Drew, D. A., Jansen, K. E. & Oberai, A. A. 2010 Spectral analysis of turbulence based on the DNS of a channel flow. Comput. Fluids 39, 640–655.CrossRefGoogle Scholar
Chaouat, B. & Schiestel, R. 2005 A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows. Phys. Fluids 17, 065106.Google Scholar
Cimarelli, A., De Angelis, E. & Casciola, C. M. 2013 Paths of energy in turbulent channel flows. J. Fluid Mech. 715, 436–451.Google Scholar
Cimarelli, A., De Angelis, E., Jiménez, J. & Casciola, C. M. 2016 Cascades and wall-normal fluxes in turbulent channel flows. J. Fluid Mech. 796, 417–436.CrossRefGoogle Scholar
Danaila, L., Anselmet, F., Zhou, T. & Antonia, R. A. 2001 Turbulent energy scale budget equations in a fully developed channel flow. J. Fluid Mech. 430, 87–109.Google Scholar
Danaila, L., Krawczynski, J. F., Thiesset, F. & Renou, B. 2012 Yaglom-like equation in axisymmetric anisotropic turbulence. Physica D 241, 216–223.Google Scholar
Davidson, P. A. 2004 Turbulence. Oxford University Press.Google Scholar
Davidson, P. A. & Pearson, B. R. 2005 Identifying turbulent energy distributions in real, rather than Fourier, space. Phys. Rev. Lett. 95, 214501.Google Scholar
Davidson, P. A., Nickels, T. B. & Krogstad, P.-A. 2006 The logarithmic structure function law in wall-layer turbulence. J. Fluid Mech. 550, 51–60.CrossRefGoogle Scholar
Domaradzki, J. A., Liu, W., Härtel, C. & Kleiser, L. 1994 Energy transfer in numerically simulated wall-bounded turbulent flows. Phys. Fluids 6, 1583–1599.Google Scholar
Donzis, D. A. & Sreenivasan, K. R. 2010 The bottleneck effect and the Kolmogorov constant in isotropic turbulence. J. Fluid Mech. 657, 171–188.CrossRefGoogle Scholar
Dunn, D. C. & Morrison, J. F. 2003 Anisotropy and energy flux in wall turbulence. J. Fluid Mech. 491, 353–378.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence. Cambridge University Press.CrossRefGoogle Scholar
Hamba, F. 2015 Turbulent energy density and its transport equation in scale space. Phys. Fluids 27, 085108.Google Scholar
Hill, R. J. 2002 Exact second-order structure-function relationships. J. Fluid Mech. 468, 317–326.Google Scholar
Jiménez, J., Wray, A. A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.Google Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497–543.Google Scholar
Lee, M. & Moser, R. D. 2015 Spectral analysis on Reynolds stress transport equation in high Re wall-bounded turbulence. In Ninth International Symposium on Turbulence and Shear Flow Phenomena, Melbourne, pp. 4A-3.Google Scholar
Leslie, D. C. 1973 Developments in the Theory of Turbulence. Clarendon Press.Google Scholar
Marati, N., Casciola, C. M. & Piva, R. 2004 Energy cascade and spatial fluxes in wall turbulence. J. Fluid Mech. 521, 191–215.CrossRefGoogle Scholar
Mizuno, Y. 2016 Spectra of energy transport in turbulent channel flows for moderate Reynolds numbers. J. Fluid Mech. 805, 171–187.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Schiestel, R. & Dejoan, A. 2005 Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations. Theor. Comput. Fluid Dyn. 18, 443–468.Google Scholar
Schiestel, R. 1987 Multiple-time-scale modeling of turbulent flows in one point closures. Phys. Fluids 30, 722–731.Google Scholar
Yamazaki, Y., Ishihara, T. & Kaneda, Y. 2002 Effects of wavenumber truncation on high-resolution direct numerical simulation of turbulence. J. Phys. Soc. Jpn. 71, 777–781.Google Scholar
Yoshizawa, A. 1984 Statistical analysis of the deviation of the Reynolds stress from its eddy-viscosity representation. Phys. Fluids 27, 1377–1387.Google Scholar
Yoshizawa, A. 1998 Hydrodynamic and Magnetohydrodynamic Turbulent Flows: Modelling and Statistical Theory. Kluwer.CrossRefGoogle Scholar