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The kinematics of stretching and alignment of material elements in general flow fields

Published online by Cambridge University Press:  26 April 2006

Eliot Dresselhaus  and
M. Tabor
Eliot Dresselhaus
Affiliation:
Division of Applied Mathematics, Department of Applied Physics, Columbia University, New York, NY 10027, USA
M. Tabor
Affiliation:
Division of Applied Mathematics, Department of Applied Physics, Columbia University, New York, NY 10027, USA
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Abstract

A rigorous, kinematic description of the stretching and alignment of infinitesimal material elements in general flow fields is presented. An evolution equation is derived, in the Lagrangian frame, for the alignment angles between a material element and the principal axes of strain. The equation identifies the precise roles played by the local angular velocity and the rotation of the strain axes in the alignment process and provides the framework in which to investigate the extent to which the straining field is ‘persistent’. This general kinematical picture is specialized to study line and vortex stretching in fluid flows and analytically predicts the numerically observed alignment of the vorticity vector with the intermediate strain axis. The alignment equations are solved exactly for a number of special flow fields and investigated numerically for the ABC and STF flows. The kinematic formalism and numerical phenomenology suggests the use of new criteria to analyse the material element stretching properties of large-scale numerical simulations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 236 , March 1992 , pp. 415 - 444
Copyright
© 1992 Cambridge University Press

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References

Ashurst, W. T., Kerstein, A. R., Kerr, R. M. & Gibson, C. H. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier—Stokes turbulence. Phys. Fluids 30, 2343–2353.Google Scholar
Bajer, K. & Moffatt, H. K. 1990 On a class of steady confined Stokes flows with chaotic streamlines. J. Fluid Mech. 212, 337–363.Google Scholar
Batchelor, G. K. 1952 The effect of homogeneous turbulence on material lines and surfaces. Proc. R. Soc. Lond. A 213, 349–366.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1956 Turbulent diffusion. In Surveys in Mechanics (ed. G. K. Batchelor & R. M. Davies), pp. 352–399. Cambridge University Press.
Betchov, R. 1956 An inequality concerning the production of vorticity in isotropic turbulence. J. Fluid Mech. 1, 497–504.Google Scholar
Cocke, W. J. 1969 Turbulent hydrodynamic line stretching: consequences of isotropy. Phys. Fluids 12, 2488–2492.Google Scholar
Cocke, W. J. 1971 Turbulent hydrodynamic line stretching: the random walk limit. Phys. Fluids 14, 1624–1628.Google Scholar
Dombre, T., Frisch, U., Greene, J. M., Hénon, M., Mehr, A. & Soward, A. M. 1986 Chaotic streamlines in the ABC flows. J. Fluid Mech. 167, 353–391.Google Scholar
Drummond, I. T. & Münch, W. 1990 Turbulent stretching of line and surface elements. J. Fluid Mech. 215, 45–59.Google Scholar
Girimaji, S. S. & Pope, S. B. 1990 Material element deformation in isotropic turbulence. J. Fluid Mech. 220, 427–458.Google Scholar
Kraichnan, R. H. 1970 Diffusion by a random velocity field. Phys. Fluids 13, 22–31.Google Scholar
Kraichnan, R. H. 1974 Convection of a passive scalar by a quasi-uniform random straining field. J. Fluid Mech. 64, 737–762.Google Scholar
Majda, A. J. 1991 Vorticity, turbulence, and acoustics in fluid flow. SIAM Rev. 33, 349–388.Google Scholar
Monin, A. M. & Yaglom, I. 1975 Statistical Fluid Mechanics, vol. 2. MIT Press.
Orszag, S. A. 1970 Comments on ‘Turbulent hydrodynamic line stretching: consequences of isotropy’. Phys. Fluids 13, 2203–2204.Google Scholar
Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. 1986 Numerical Recipes. Cambridge University Press.
She, Z.-S., Jackson, E. & Orszag, S. A. 1991 Structure and dynamics of homogeneous turbulence: models and simulations. Proc. R. Soc. Lond. A 434, 101–124.Google Scholar
Tabor, M. & Gennes, P. G. de 1986 A cascade theory of drag reduction. Europhys. Lett. 2, 519–522.Google Scholar
Townsend, A. A. 1951 The diffusion of heat spots in isotropic turbulence. Proc. R. Soc. Lond. A 209, 418–430.Google Scholar
Vieillefosse, P. 1982 Local interaction between vorticity and shear in a perfect incompressible fluid. J. Phys. Paris 43, 837–842.Google Scholar
Vieillefosse, P. 1984 Internal motion of small element of fluid in an inviscid flow. Physica 125A, 150.Google Scholar