An analysis of the spectral turbulent kinetic energy budget in a fully developed turbulent plane channel flow is performed. Direct numerical simulation data are evaluated at friction Reynolds numbers Reτ of 180 and 1000. The analysis is focused on the influence of the Reynolds number on the spectral cascade of energy and the corresponding energy cascade in physical space in the presence of inhomogeneity and anisotropy. The turbulent kinetic energy distribution is compared for both Reynolds numbers, and the relevant characteristics of the energy transfer process in a wall-bounded turbulent flow are described. Differences in energy cascade are noted between the Reynolds number at both low and high wavenumbers. The results of the analysis are further assessed with a comparison to an earlier study of spectral energy transfer at Reτ = 180.
REFERENCES
1.
Bolotnov
, Jr., I. A.
, Lahey
, R. T.
, Drew
, D. A.
, and Jansen
, K. E.
, “Turbulent cascade modeling of single and bubbly two-phase turbulent flows
,” Int. J. Multiphase Flow
34
, 1142
–1151
(2008
).2.
Bolotnov
, I. A.
, Lahey
, Jr., R. T.
, Drew
, D. A.
, Jansen
, K. E.
, and Oberai
, A. A.
, “Spectral analysis of turbulence based on the DNS of a channel flow
,” Comput. Fluids
, 39
(4
), 640
–655
(2010
).3.
Chaouat
, B.
and Schiestel
, R.
, “A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows
,” Phys. Fluids
17
, 065106
(2005
).4.
Cimarelli
, A.
and De Angelis
, E.
, “The physics of energy transfer toward improved subgrid-scale models
,” Phys. Fluids
26
(5
), 055103
(2014
).5.
Cimarelli
, A.
, De Angelis
, E.
, and Casciola
, C.
, “Paths of energy in turbulent channel flows
,” J. Fluid Mech.
715
, 436
–451
(2013
).6.
Comte-Bellot
, G.
and Corrsin
, S.
, “The use of a contraction to improve the isotropy of grid-generated turbulence
,” J. Fluid Mech.
25
, 657
(1966
).7.
Del Álamo
, J. C.
and Jiménez
, J.
, “Spectra of the very large anisotropic scales in turbulent channels
,” Phys. Fluids
15
(6
), L41
(2003
).8.
Del Álamo
, J. C.
, Jiménez
, J.
, Zandonade
, P.
, and Moser
, R. D.
, “Scaling of the energy spectra of turbulent channels
,” J. Fluid Mech.
500
, 135
–144
(2004
).9.
Domaradzki
, J. A.
and Rogallo
, R. S.
, “Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence
,” Phys. Fluids
2
(3
), 413
–426
(1990
).10.
Dunn
, D. C.
and Morrison
, J. F.
, “Analysis of the energy budget in turbulent channel flow using orthogonal wavelets
,” Comput. Fluids
34
, 199
(2005
).11.
George
, W. K.
, “The decay of homogeneous isotropic turbulence
,” Phys. Fluids A
4
, 1492
(1992
).12.
Gualtieri
, P.
, Casciola
, C. M.
, Benzi
, R.
, and Piva
, R.
, “Preservation of statistical properties in large-eddy simulation of shear turbulence
,” J. Fluid Mech.
592
, 471
–494
(2007
).13.
Hill
, R. J.
, “Equations relating structure functions of all orders
,” J. Fluid Mech.
434
, 379
–388
(2001
).14.
Hill
, R. J.
, “Exact second-order structure-function relationship
,” J. Fluid Mech.
468
, 317
–326
(2002
).15.
Hoyas
, S.
and Jiménez
, J.
, “Scaling of the velocity fluctuations in turbulent channels up to Reτ = 2003
,” Phys. Fluids
18
(1
), 011702
(2006
).16.
Jiménez
, J.
, “The physics of wall turbulence
,” Phys. A
263
, 252
–262
(1999
).17.
Kolmogorov
, A.
, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers
,” Dokl. Akad. Nauk SSSR
30
(1890
), 301
–305
(1941
).18.
Marati
, N.
, Casciola
, C.
, and Piva
, R.
, “Energy cascade and spatial fluxes in wall turbulence
,” J. Fluid Mech.
521
, 191
–215
(2004
).19.
Moin
, P.
and Mahesh
, K.
, “Direct numerical simulation: A tool in turbulent research
,” Annu. Rev. Fluid Mech.
30
, 539
–578
(1998
).20.
Mollicone
, J.-P.
, Battista
, F.
, Gualtieri
, P.
, and Casciola
, C. M.
, “Effect of geometry and Reynolds number on the turbulent separated flow behind a bulge in a channel
,” J. Fluid Mech.
823
, 100
–133
(2017
).21.
Mollicone
, J.-P.
, Battista
, F.
, Gualtieri
, P.
, and Casciola
, C. M.
, “Turbulence dynamics in separated flows: The generalised Kolmogorov equation for inhomogeneous anisotropic conditions
,” J. Fluid Mech.
841
, 1012
–1039
(2018
).22.
Moser
, R. D.
, Kim
, J.
, and Mansour
, N. N.
, “Direct numerical simulation of turbulent channel flow up to Reτ = 590
,” Phys. Fluids
11
, 943
–945
(1999
).23.
Oliver
, T. A.
, Malaya
, N.
, Ulerich
, R.
, and Moser
, R. D.
, “Estimating uncertainties in statistical category computed from direct numerical simulation
,” Phys. Fluids
26
, 035101
(2014
).24.
Piomelli
, U.
, Cabot
, W. H.
, Moin
, P.
, and Lee
, S.
, “Subgrid-scale backscatter in turbulent and transitional flows
,” Phys. Fluids A
3
(7
), 1766
(1991
).25.
Piomelli
, U.
, Yu
, Y.
, and Adrian
, R. J.
, “Subgrid-scale energy transfer and near-wall turbulence structure
,” Phys. Fluids
8
, 215
(1996
).26.
Pope
, S. B.
, “A more general effective-viscosity hypothesis
,” J. Fluid Mech.
72
, 331
–334
(1975
).27.
28.
Richardson
, L. F.
, Weather Prediction by Numerical Process
(Cambridge University Press
, 1922
).29.
Sagaut
, P.
, in Large Eddy Simulation for Incompressible Flows: An Introduction
, Scientific Computation, edited by Sagaut
, P.
and Meneveau
, C.
(Amazon.com: Books
, 2005
), ISBN: 9783540263449.30.
Schiavo
, L. A. C. A.
, Wolf
, W. R.
, and Azevedo
, J. L. F.
, “Turbulent kinetic energy budgets in wall bounded flows with pressure gradients and separation
,” Phys. Fluids
29
(11
), 115108
(2017
).31.
Skrbek
, L.
and Stalp
, S. R.
, “On the decay of homogeneous isotropic turbulence
,” Phys. Fluids
12
, 1997
(2000
).32.
Tennekes
, H.
and Lumley
, J. L.
, A First Course in Turbulence
(The MIT Press
, Cambridge, Massachusetts, London, England
, 1972
).33.
Thais
, L.
, Tejada-Martnez
, A. E.
, Gatski
, T. B.
, and Mompean
, G.
, “A massively parallel hybrid scheme for direct numerical simulation of turbulent viscoelastic channel flow
,” Comput. Fluids
43
(1
), 134
–142
(2011
).34.
Thais
, L.
, Mompean
, G.
, and Gatski
, T. B.
, “Spectral analysis of turbulent viscoelastic and Newtonian channel flows
,” J. Non-Newtonian Fluid Mech.
200
, 165
–176
(2013
).35.
Trofimova
, A.
, Tejada-Martinez
, A. E.
, Jansen
, K. E.
, and Lahey
, Jr., R. T.
, “Direct numerical simulation of turbulent channel flows using a stabilized finite element method
,” Comput. Fluids
, 38
(4
), 924
–938
(2009
).36.
Zhou
, Y.
, “Degrees of locality of energy transfer in the inertial range
,” Phys. Fluids
5
(5
), 1092
–1094
(1993a
).37.
Zhou
, Y.
, “Interacting scales and energy transfer in isotropic turbulence
,” Phys. Fluids
5
(10
), 2511
–2524
(1993b
).© 2018 Author(s).
2018
Author(s)
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