Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-20T20:40:28.995Z Has data issue: false hasContentIssue false
  • English
  • Français

Multi-scalar triadic interactions in differential diffusion with and without mean scalar gradients

Published online by Cambridge University Press:  26 April 2006

P. K. Yeung
P. K. Yeung
Affiliation:
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The spectral mechanisms of the differential diffusion of pairs of passive scalars with different molecular diffusivities are studied in stationary isotropic turbulence, using direct numerical simulation data at Taylor-scale Reynolds number up to 160 on 1283 and 2563 grids. Of greatest interest are the roles of nonlinear triadic interactions between different scale ranges of the velocity and scalar fields in the evolution of spectral coherency between the scalars, and the effects of mean scalar gradients.

Analysis of single-scalar spectral transfer (extending the results of a previous study) indicates a robust local forward cascade behaviour at high wavenumbers, which is strengthened by both high diffusivity and mean gradients. This cascade is driven primarily by moderately non-local interactions in which two small-scale scalar modes are coupled via a lower-wavenumber velocity mode near the peak of the energy dissipation spectrum. This forward cascade is coherent, tending to increase the coherency between different scalars at high wavenumbers but to decrease it at lower wavenumbers. However, at early times coherency evolution at high wavenumbers is dominated by de-correlating effects due to a different type of non-local triad consisting of two scalar modes with a moderate scale separation and a relatively high-wavenumber velocity mode. Consequently, although the small-scale motions play little role in spectral transfer, they are responsible for the rapid de-correlation observed at early times. At later times both types of competing triadic interactions become important over a wider wavenumber range, with increased relative strength of the coherent cascade, so that the coherency becomes slow-changing. When uniform mean scalar gradients are present, a stationary state develops in the coherency spectrum as a result of a balance between a coherent mean gradient contribution (felt within about 1 eddy-turnover time) and the net contribution from scale interactions. The latter is made less de-correlating because of a strengthened coherent forward cascade, which is in turn caused by uniform mean gradients acting as a primarily low-wavenumber source of scalar fluctuations with the same spectral content as the velocity field.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 321 , 25 August 1996 , pp. 235 - 278
Copyright
© 1996 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

Batchelor, G. K. 1959 Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.Google Scholar
Bilger, R. W. & Dibble, R. W. 1982 Differential molecular diffusion effects in turbulent mixing. Combust. Sci. Tech. 28, 161–172.Google Scholar
Brasseur, J. G. & Wei, C.-H. 1994 Interscale dynamics and local isotropy in high, Reynolds number turbulence within triadic interactions. Phys. Fluids 6, 842–870.Google Scholar
Chasnov, J. R. 1994 Similarity states of passive scalar transport in isotropic turbulence. Phys. Fluids 6, 1036–1051.Google Scholar
Corrsin, S. 1951 On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J. Appl. Phys. 22, 469–473.Google Scholar
Domaradzki, J. A. & Rogallo, R. S. 1990 Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence. Phys. Fluids A 2, 413–426.Google Scholar
Eswaran, V. & Pope, S. B. 1988a An examination of forcing in direct numerical simulations of turbulence. Comput. & Fluids 16, 257–278.Google Scholar
Eswaran, V. & Pope, S. B. 1988b Direct numerical simulations of the turbulent mixing of a passive scalar. Phys. Fluids 31, 506–520.Google Scholar
Jaberi, F. A., Miller, R. S., Madnia, C. K. & Givi, P. 1995 Non-Gaussian scalar statistics in homogeneous turbulence. Proc. Tenth Symp. on Turbulent Shear Flows, pp. 31-13–31-18. University Park, PA.
Jayesh & Warhaft, Z. 1992 Probability distribution, conditional dissipation, and transport of passive temperature fluctuations in grid-generated turbulence. Phys. Fluids A 4, 2292–2307.Google Scholar
Jimenez, 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
Kerstein, A. R., Cremer, M. A. & McMurtry, P. A. 1995 Scaling properties of differential molecular diffusion effects in turbulence. Phys. Fluids 7, 1999–2007.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluids for very large Reynolds numbers. C. R. Acad. Sci. URSS 30, 301–305.Google Scholar
Komori, S., Hunt, J. C. R., Kanzaki, K. & Murakami, Y. 1991 The effects of turbulent mixing on the correlation between two species and on concentration fluctuations in non-premixed reacting flows. J. Fluid Mech. 228, 629–659.Google Scholar
Kosály, G. 1993 Frequency spectra of reactant fluctuations in turbulent flows. J. Fluid Mech. 246, 489–502.Google Scholar
Li, J. D., Brown, R. J. & Bilger, R. W. 1993 Spectral measurement of reactive and passive scalars in a turbulent reactive-scalar mixing layer. Proc. Ninth Symp. on Turbulent Shear Flows, paper 28–3. Kyoto, Japan.
Nilsen, V. & Kosály, G. 1996 Differentially diffusing scalars in turbulence. Submitted to Phys. Fluids.Google Scholar
Obukhov, A. M. 1949 Structure of the temperature field in a turbulent flow. Izv. Akad. Nauk SSSR Geogr. Geofiz. 13, 58–69.Google Scholar
Pope, S. B. 1990 Computations of turbulent combustion: progress and challenges. Twenty-Third Symposium (International) on Combustion, pp. 591–612. The Combustion Institute (invited plenary lecture).
Pumir, A. 1994 A numerical study of the mixing of a passive scalar in three-dimensions in the presence of a mean gradient. Phys. Fluids 6, 2118–2132.Google Scholar
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. Tech. Memo. 81315. NASA Ames Research Center.
Rogers, M. M., Moin, P. & Reynolds, W. C. 1986 The structure and modeling of the hydrodynamic and passive scalar fields in homogeneous turbulent shear flow. Rep. TF-25. Dept of Mech. Engng, Stanford University.
Saylor, J. R. & Sreenivasan, K. R. 1993 Differential diffusion in low Reynolds number water jets. J. Fluid Mech. (submitted).Google Scholar
Sirivat, A. & Warhaft 1982 The mixing of passive helium and temperature fluctuations in grid turbulence. J. Fluid Mech. 120, 475–504.Google Scholar
Smith, L. L. 1994 Differential molecular diffusion in reacting and non-reacting turbulent jets of H2CO2 mixing with air. PhD dissertation, Department of Mechanical Engineering, University of California at Berkeley.
Sreenivasan, K. R. 1991 On the local isotropy of passive scalars in turbulent shear flows. In Turbulence and Stochastic Processes: Kolmogorov's ideas 50 years on (ed. J. C. R. Hunt, O. M. Phillips & D. Williams), pp. 165–182. Royal Society, London.
Tong, C. & Warhaft, Z. 1995 Passive scalar dispersion and mixing in a turbulent jet. J. Fluid Mech. 292, 1–38.Google Scholar
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1–20.Google Scholar
Wang, L. P., Chen, S., Brasseur, J. G. & Wyngaard, J. C. 1996 Examination of fundamental hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulation. J. Fluid Mech. 309, 113–156.Google Scholar
Warhaft, Z. & Lumley, J. L. 1978 An experimental study of the decay of temperature fluctuations in grid-generated turbulence. J. Fluid Mech. 88, 659–684.Google Scholar
Yeh, T. T. & Van Atta, C. W. 1973 Spectral transfer of scalar and velocity fields in heated-grid turbulence. J. Fluid Mech. 58, 233–261.Google Scholar
Yeung, P. K. 1994 Spectral transfer of self-similar passive scalar fields in isotropic turbulence. Phys. Fluids 6, 2245–2247.Google Scholar
Yeung, P. K. & Brasseur, J. G. 1991 The response of isotropic turbulence to isotropic and anisotropic forcing at the large scales. Phys. Fluids A 3, 884–897.Google Scholar
Yeung, P. K., Brasseur, J. G. & Wang, Q. 1995 Dynamics of large-to-small scale couplings in coherently forced turbulence: concurrent physical and Fourier space views. J. Fluid Mech. 283, 43–95.Google Scholar
Yeung, P. K. & Luo, B. 1995 Simulation and modeling of differential diffusion in homogeneous turbulence. Proc. Tenth Symp. on Turbulent Shear Flows, pp. 31-7–31-12. University Park, PA.
Yeung, P. K. & Moseley, C. A. 1995a Effects of mean scalar gradients on differential diffusion in isotropic turbulence. AIAA Paper 95-0866.Google Scholar
Yeung, P. K. & Moseley, C. A. 1995b A message-passing, distributed memory parallel algorithm for direct numerical simulation of turbulence with particle tracking. In Parallel Computational Fluid Dynamics: Implementations and Results Using Parallel Computers (ed. A. Ecer, J. Periaux, N. Satofuka & S. Taylor). Elsevier.
Yeung, P. K. & Pope, S. B. 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531–586.Google Scholar
Yeung, P. K. & Pope, S. B. 1993 Differential diffusion of passive scalars in isotropic turbulence. Phys. Fluids A 5, 2467–2478.Google Scholar
Zhou, Y. 1993a Degrees of locality of energy transfer in the inertial range. Phys. Fluids A 5, 1092–1094.Google Scholar
Zhou, Y. 1993b Interacting scales and energy transfer in isotropic turbulence. Phys. Fluids A 5, 2511–2524.Google Scholar
Zhou, Y., Yeung, P. K. & Brasseur, J. G. 1996 Scale disparity and spectral transfer in anisotropic numerical turbulence. Phys. Rev. E 53, 1261–1264.Google Scholar