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Dynamics of vortical structures in a homogeneous shear flow

Published online by Cambridge University Press:  26 April 2006

Shigeo Kida  and
Mitsuru Tanaka
Shigeo Kida
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606–01, Japan
Mitsuru Tanaka
Affiliation:
Department of Physics, Faculty of Science, Kyoto University, Kyoto 606–01, Japan
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Abstract

The mechanism of generation, development and interaction of vortical structures, extracted as concentrated-vorticity regions, in homogeneous shear turbulence is investigated by the use of the results of a direct numerical simulation of the Navier-Stokes equation with 1283 grid points. Among others, a few of typical vortical structures are identified as important dynamical elements, namely longitudinal and lateral vortex tubes and vortex layers. They interact strongly with each other. Longitudinal vortex tubes are generated from a random fluctuating vorticity field through stretching of fluid elements caused by the mean linear shear. They are inclined toward the streamwise direction by rotational motion due to the mean shear. There is a small (about 10°) deviation in direction between the longitudinal vortex tubes and vorticity vectors therein, which makes the vorticity vectors turn toward the spanwise direction (against the mean vorticity) until the spanwise components of the fluctuating vorticity become comparable in magnitude with the mean vorticity. These longitudinal vortex tubes induce straining flows perpendicular to themselves which generate vortex layers with spanwise vorticity in planes spanned by the tubes and the spanwise axis. These vortex layers are unstable, and roll up into lateral vortex tubes with concentrated spanwise vorticity through the Kelvin-Helmholtz instability. All of these vortical structures, through strong mutual interactions, break down into a complicated smallscale random vorticity field. Throughout the simulated period an oblique stripe structure dominates the whole flow field: initially it is inclined at about 45° to the downstream and, as the flow develops, the inclination angle decreases but eventually stays at around 10°–20°.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 274 , 10 September 1994 , pp. 43 - 68
Copyright
© 1994 Cambridge University Press

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References

Betchov, R. & Szewczyk, A. 1963 Stability of a shear layer between parallel streams. Phys. Fluids 6, 1391.Google Scholar
Hopfinger, E. J., Browand, F. K. & Gagne, Y. 1982 Turbulence and waves in a rotating tank. J. Fluid Mech. 125, 505.Google Scholar
Hosokawa, I. & Yamamoto, K. 1989 Fine structure of a directly simulated isotropic turbulence. J. Phys. Soc. Japan 58, 20.Google Scholar
Hussain, A. K. M. F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303.Google Scholar
Jiménez, J., Cogollos, M. & Bernal, L. P. 1985 A perspective view of the plane mixing layer. J. Fluid Mech. 152, 125.Google Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213.Google Scholar
Kerr, R. M. 1985 Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence. J. Fluid Mech. 153, 31.Google Scholar
Kida, S. & Takaoka, M. 1994 Vortex reconnection. Ann. Rev. Fluid Mech. 26, 169–189.Google Scholar
Kida, S. & Tanaka, M. 1992 Reynolds stress and vortical structure in a uniformly sheared turbulence. J. Phys. Soc. Japan 61, 4400.Google Scholar
Kida, S. & Tanaka, M. 1993 Evolution of homogeneously sheared turbulence. In Ninth Symp. on Turbulent Shear Flow, p. 17–4–1. Kyoto.
Kim, J. & Moin, P. 1986 The structure of vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields. J. Fluid Mech. 162, 339.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741.Google Scholar
Lee, M. J., Kim, J. & Moin, P. 1990 Structure of turbulence at high shear rate. J. Fluid Mech. 216, 561.Google Scholar
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA TM 81315.Google Scholar
Rogers, M. M. & Moin, P. 1987 The structure of the vorticity field in homogeneous turbulent flows. J. Fluid Mech. 176, 33.Google Scholar
Ruetsch, G. R. & Maxey, M. R. 1992 The evolution of small-scale structures in homogeneous isotropic turbulence. Phys. Fluids A 4, 2747.Google Scholar
Sandham, N. D. & Kleiser, L. 1992 The late stage of transition to turbulence in channel flow. J. Fluid Mech. 245, 319.Google Scholar
She, Z.-S., Jackson, E. & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226.Google Scholar
Siggia, E. D. 1981 Numerical study of small-scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375.Google Scholar
Tanaka, M. & Kida, S. 1993 Characterization of vortex tubes and sheets. Phys. Fluids A 5, 2079.Google Scholar
Tavoularis, S. 1985 Asymptotic laws for transversely homogeneous turbulent shear flows. Phys. Fluids 28, 999.Google Scholar
Tavoularis, S. & Karnik, U. 1989 Further experiments on the evolution of turbulent stresses and scales in uniformly sheared turbulence. J. Fluid Mech. 204, 457.Google Scholar
Townsend, A. A. 1970 Entrainment and the structure of turbulent flow. J. Fluid Mech. 41, 13.Google Scholar
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous isotropic turbulence. J. Fluid Mech. 225, 1.Google Scholar