Using velocity fields obtained in direct numerical simulations of turbulent convection and of turbulent channel flow, the energy transfer process among lateral scales of motion in these low Reynolds number flows is analyzed. In all cases the energy is transferred most effectively between scales of similar size. As a result, the subgrid‐scale energy transfer is caused almost exclusively by interactions between resolved scales and subgrid scales characterized by wave numbers not greater than twice the cutoff wave number. The scale dependence of forward and inverse energy transfers contributing to the total subgrid‐scale eddy viscosity is discussed. The local energy transfer between small scales is strongly affected by the nonlocal interactions characterized by a scale separation greater than a factor of 2 in wave number. However, the direct energy transfer between scales satisfying this condition is one order of magnitude less than the local energy transfer between scales of similar size.
REFERENCES
1.
. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, 1979).
2.
M. Lesieur, Turbulence in Fluids, 2nd ed. (Martinus Nijhoff, Dordrecht, 1990).
3.
W. D. McComb, The Physics of Fluid Turbulence (Clarendon, Oxford, 1990).
4.
R. S.
Rogallo
and P.
Moin
, “Numerical simulation of turbulent flows
,” Annu. Rev. Fluid Mech.
16
, 99
(1984
).5.
C.
Meneveau
, “Statistics of turbulence subgrid-scale stresses: Necessary conditions and experimental tests
,” Phys. Fluids
6
, 815
(1994
).6.
J. A.
Domaradzki
and R. S.
Rogallo
, “Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence
,” Phys. Fluids A
2
, 413
(1990
).7.
P. K.
Yeung
and J. G.
Brasseur
, “The response of isotropic turbulence to isotropic and anisotropic forcing at the large scales
,” Phys. Fluids A
3
, 413
(1991
).8.
K.
Ohkitani
and S.
Kida
, “Triad interactions in a forced turbulence
,” Phys. Fluids A
4
, 794
(1992
).9.
J. A. Domaradzki, R. S. Rogallo, and A. A. Wray, “Interscale energy transfer in numerically simulated homogeneous turbulence,” in Proceedings of the 1990 Summer Program (Center for Turbulence Research, NASA Ames/Stanford University, Stanford, CA, 1990), p. 319.
10.
J. A.
Domaradzki
, “Nonlocal triad interactions and the dissipation range of isotropic turbulence
,” Phys. Fluids A
4
, 2037
(1992
).11.
Y.
Zhou
, “Degrees of locality of energy transfer in the inertial range
,” Phys. Fluids A
5
, 1092
(1993
).12.
J. A.
Domaradzki
, R. W.
Metcalfe
, R. S.
Rogallo
, and J. J.
Riley
, “Analysis of subgrid-scale eddy viscosity with the use of results from direct numerical simulations
,” Phys. Rev. Lett.
58
, 547
(1987
).13.
J. A.
Domaradzki
, W.
Liu
, and M. E.
Brachet
, “An analysis of subgrid-scale interactions in numerically simulated isotropic turbulence
,” Phys. Fluids A
5
, 1747
(1993
).14.
J. R.
Chasnov
, “Simulation of the Kolmogorov inertial subrange using an improved subgrid model
,” Phys. Fluids A
3
, 188
(1991
).15.
M.
Lesieur
and R. S.
Rogallo
, “Large-eddy simulation of passive scalar diffusion in isotropic turbulence
,” Phys. Fluids A
1
, 718
(1989
).16.
Y.
Zhou
and G.
Vahala
, “Reformulation of recursive-renormalization-group-based subgrid modeling of turbulence
,” Phys. Rev. E
47
, 2503
(1993
).17.
W. D.
Smyth
, “Spectral transfers in two-dimensional anisotropic flow
,” Phys. Fluids A
4
, 340
(1992
).18.
S. L.
Christie
and J. A.
Domaradzki
, “Numerical evidence for nonuniversality of the soft/hard turbulence classification for thermal convection
,” Phys. Fluids A
5
, 412
(1993
).19.
N. Gilbert, “Numerische Simulation der Transition von der Laminaren in die Turbulente Kanalstromung,” DFVLR-Forschungsbericht 88–55, DLR Gattingen, Germany, 1988.
20.
Gilbert and L. Kleiser, “Turbulence model testing with the aid of direct numerical simulation results,” in Proceedings of the 8th Symposium on Turbulent Shear Flows (Springer-Verlag, Munich, 1991).
21.
C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics, (Springer, New York, 1988).
22.
J. A.
Domaradzki
and R. W.
Metcalfe
, “Direct numerical simulations of the effects of shear on turbulent Rayleigh-Bénard convection
,” J. Fluid Mech.
193
, 499
(1988
).23.
J.
Kim
, P.
Moin
, and R. D.
Moser
, “Turbulence statistics in fully developed channel flow at low Reynolds number
,” J. Fluid Mech.
177
, 133
(1987
).24.
K. Nishino and N. Kasagi, “Turbulence statistics measurements in a two-dimensional channel flow using a three-dimensional particle tracing velocimeter,” in Proceedings of the 7th Symposium on Turbulent Shear Flows (Stanford University Press, Stanford, CA, 1989).
25.
A. A. Townsend, The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1967).
26.
J. O. Hinze, Turbulence, 2nd ed. (McGraw-Hill, New York, 1987).
27.
M.
Germano
, U.
Piomelli
, P.
Moin
, and W. H.
Cabot
, “A dynamic subgrid-scale eddy viscosity model
,” Phys. Fluids A
3
, 1760
(1991
).28.
Härtel, L. Kleiser, F. Unger, and R. Friedrich, “Subgrid-scale energy transfer in the near-wall region of turbulent flows,” submitted to Phys. Fluids (1993).
29.
J. W.
Deardorff
and G. E.
Willis
, “Investigation of turbulent thermal convection between horizontal plates
,” J. Fluid Mech.
28
, 675
(1967
).30.
J. L.
Lumley
, “Spectral energy budget in wall turbulence
,” Phys. Fluids
7
, 190
(1964
).31.
J. L. Lumley and H. A. Panofsky, The Structure of Atmospheric Turbulence (Wiley, New York, 1964).
32.
S. Kida, R. H. Kraichnan, R. S. Rogallo, F. Waleffe, and Y. Zhou, “Triad interactions in the dissipation range,” in Proceedings of the 1992 Summer Program (Center for Turbulence Research, NASA Ames/ Stanford University, Stanford, CA, 1992), p. 83.
33.
S.
Chen
, G.
Doolen
, J. R.
Herring
, R. H.
Kraichnan
, S. A.
Orszag
, and Z. S.
She
, “Far dissipations range of turbulence
,” Phys. Rev. Lett.
70
, 3051
(1993
).34.
J. G.
Brasseur
and C. H.
Wei
, “Interscale dynamics and local isotropy in high Reynolds number turbulence within triadic interactions
,” Phys. Fluids
6
, 842
(1994
).35.
U.
Piomelli
, W. H.
Cabot
, P.
Moin
, and S.
Lee
, “Subgrid-scale back-scatter in turbulent and transitional flows
,” Phys. Fluids A
3
, 1766
(1991
).36.
R. H.
Kraichnan
, “Eddy viscosity in two and three dimensions
,” J. Atmos. Sci.
33
, 1521
(1976
).
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