Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-18T04:47:44.009Z Has data issue: false hasContentIssue false
  • English
  • Français

The structure of the vorticity field in homogeneous turbulent flows

Published online by Cambridge University Press:  21 April 2006

Michael M. Rogers  and
Parviz Moin
Michael M. Rogers
Affiliation:
Stanford University, Stanford, CA 94305, USA Present address: NASA Ames Research Center, Moffet Field, CA 94035, USA.
Parviz Moin
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The structure of the vorticity fields in homogeneous turbulent shear flow and various irrotational straining flows is examined using results from direct numerical simulations of the unsteady, incompressible Navier-Stokes equations with up to 128 × 128 × 128 grid points. In homogeneous shear flow, the distribution of the inclination angle of the vorticity vectors and contour plots of two-point correlations of both velocity and vorticity are consistent with the existence of persistent vortical structures inclined with respect to the flow direction. Early in the development of these shear flows, the angle of inclination at which most of these structures are found is near 45°; after the flow develops, this angle lies between 35°–40°. Instantaneous vorticity-vector and vortex-line plots confirm the presence of hairpin vortices in this flow at the two Reynolds numbers simulated. These vortices are formed by the roll-up of sheets of mean spanwise vorticity. The average hairpin leg spacing decreases with increasing Reynolds number but increases relative to the Taylor microscale for developed shear flows. Examination of irrotational axisymmetric contraction, axisymmetric expansion, and plane strain flows shows, as expected, that the vorticity tends to be aligned with the direction of positive strain. For example, the axisymmetric contraction flow is dominated by coherent longitudinal vortices. Without the presence of mean shear, however, hairpin structures do not develop. The simulations strongly indicate that the vorticity occurs in coherent filaments that are stretched and strengthened by the mean strain. When compressed, these filaments appear to buckle rather than to decrease in strength.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 176 , March 1987 , pp. 33 - 66
Copyright
© 1987 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

Burgers, J. M. 1948 A mathematical model illustrating the theory of turbulence. In Advances in Applied Mechanics, Vol. 1 (ed R. von Mises & T. von Kármán). p. 171. Academic Press.
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 Experiments on nearly homogeneous shear flow. J. Fluid Mech. 41, 81.Google Scholar
Hama, F. R. 1962 Progressive deformation of a curved vortex filament by its own induction. Phys. Fluids 5, 1156.Google Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary layer structure. J. Fluid Mech. 107, 297.Google Scholar
Harris, V. G., Graham, A. H. & Corrsin, S. 1977 Further experiments in nearly homogeneous turbulent shear flow. J. Fluid Mech. 81, 657.Google Scholar
Hopfinger, E. J., Browand, F. K. & Gagne, Y. 1962 Turbulence and waves in a rotating tank. J. Fluid Mech. 125, 505.Google Scholar
Kim, J. & Moin, P. 1986 The structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields. J. Fluid Mech. 162, 339.Google Scholar
Lee, M. J. & Reynolds, W. C. 1985 On the structure of homogeneous turbulence. In Proc. of the Fifth Symp. Turbulent Shear Flows, Cornell University, Ithaca, New York, August 7–9, 1985.
Moin, P. 1985 High Reynolds shear stress motions in the wall region. Bull. Am. Phys. Soc. 30, 1723.Google Scholar
Moin, P. & Kim, J. 1985 The structure of the vorticity field in turbulent channel flow. Part 1. Analysis of the vorticity fields and statistical correlations. J. Fluid Mech. 155, 441.Google Scholar
Moin, P., Leonard, A. & Kim, J. 1986 Evolution of a curved vortex filament into a vortex ring. Phys. Fluids 29, 955.Google Scholar
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA TM 81315.
Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 1. J. Fluid Mech. 104, 311.Google Scholar
Theodorsen, T. 1952 Mechanism of turbulence. In Proc. 2nd Midwestern Conf. on Fluid Mech. Ohio State University, Columbus, Ohio.
Townsend, A. A. 1970 Entrainment and the structure of turbulent flow. J. Fluid Mech. 41, 13.Google Scholar