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On steady columnar vortices under local compression

Published online by Cambridge University Press:  26 April 2006

Roberto Verzicco ,
Javier Jiménez  and
Paolo Orlandi
Roberto Verzicco
Affiliation:
Università di Roma “La Sapienza” Dipartimento di Meccanica e Aeronautica, via Eudossiana 18, 00184 Roma, Italy
Javier Jiménez
Affiliation:
School of Aeronautics, U. Politécnica, Pl. Cardenal Cisneros 3, 28040 Madrid, Spain
Paolo Orlandi
Affiliation:
Università di Roma “La Sapienza” Dipartimento di Meccanica e Aeronautica, via Eudossiana 18, 00184 Roma, Italy
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Abstract

Numerical simulations are presented of the long time behaviour of viscous columnar vortices subject to non-uniform axial stretching. The relevant result is that the vortices reach a steady state even when the axial average of the strain is zero, such that they are being compressed during half of their extent. The structure of the flow is analysed and shown to range from local Burgers equilibrium to massive separation. For an intermediate range of Reynolds numbers the vortices are more or less uniform and compact, and it is suggested that this condition is related to the strong vortices observed in turbulent flows. The reason for the survival of the vortices under compression is traced to induced axial pressure gradients and to the viscous cancellation of outgoing vorticity. Theoretical analyses of the linear Burgers’ regime and of the onset of separation are presented and compared to the numerical experiments. The results are related to the observation of intermittency in turbulence, and shown to be consistent both with the observed scaling of vortex diameter, and with the lack of intermittency of the velocity signal.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 299 , 25 September 1995 , pp. 367 - 388
Copyright
© 1995 Cambridge University Press

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References

Anselmet, F., Gagne, Y., Hopfinger, E. J. & Antonia, R. A. 1984 High order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89.Google Scholar
Beran, P. S. & Culick, F. E. C. 1992 The role of non-uniqueness in the development of vortex breakdown in tubes. J. Fluid Mech. 242, 491–527.Google Scholar
Benjamin, T. B. 1962 Theory of vortex breakdown phenomenon. J. Fluid Mech. 14, 593–629.Google Scholar
Bradshaw, P. & Koh, Y. M. 1981 A note on Poisson's equation for pressure in a turbulent flow. Phys. Fluids 24, 777.Google Scholar
Brown, G. L. & López, J. M. 1990 Axisymmetric vortex breakdown. Part 2. Physical mechanisms. J. Fluid Mech. 221, 553–576.Google Scholar
Caflisch, R. E., Li, X. & Shelley, M. J. 1993 The collapse of an axi-symmetric, swirling vortex sheet. Nonlinearity 4, 843–867.Google Scholar
Hosokawa, I. & Yamamoto, K. 1990 Intermittency of dissipation in directly simulated fully developed turbulence. J. Phys. Soc. Japan 59, 401–404.Google Scholar
Jiménez, J. & Wray, A. A. 1994a Columnar vortices in isotropic turbulence. Meccanica 29, 453–464.Google Scholar
Jiménez, J. & Wray, A. A. 1994b The dynamics of intense vorticity in isotropic turbulence. CTR Annual Res. Briefs 1994.
Jiménez, 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
Kelvin, Lord 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.Google Scholar
Keller, J. J, Egli, W. & Exley, J. 1985 Force- and loss-free transitions between flow states. Z. Angew. Math. Phys. 36, 854–889.Google Scholar
Kerr, R. M. 1985 Higher order derivative correlation and the alignment of small-scale structure in isotropic numerical turbulence. J. Fluid Mech. 153, 31–58.Google Scholar
Leibovich, S. 1978 Structure of vortex breakdown. Ann. Rev. Fluid Mech. 10, 221–246.Google Scholar
Leonard, A. 1994 Nonlocal theory of area-varying waves on axisymmetric vortex tubes. Phys. Fluids 6, 765–777.Google Scholar
López, J. M. 1990 Axisymmetric vortex breakdown. Part 1. Confined swirling flows. J. Fluid Mech. 221, 533–552.Google Scholar
Lundgren, T. S. & Ashurst, W. T. 1989 Area-varying waves on curved vortex tubes with application to vortex breakdown. J. Fluid Mech. 200, 283–307.Google Scholar
Melander, M. V. & Hussain, F. 1994 Core dynamics on a vortex column. Fluid Dyn. Res. 13, 1–37.Google Scholar
Moore, D. W. & Saffman, P. G. 1972 The motion of a vortex filament with axial flow. Phil. Trans. R. Soc. Lond. A 272, 407–429.Google Scholar
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA TM-81315.
Ruetsch, G. R. & Maxey, M. R. 1991 Small scales features of vorticity and passive scalar fields in homogeneous isotropic turbulence. Phys. Fluids A 3, 1587–1597.Google Scholar
She, Z.-S., Jackson, E. & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344, 226–228.Google Scholar
Siggia, E. D. 1981 Numerical study of small scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375–406.Google Scholar
Verzicco, R. & Orlandi, P. 1993 A finite-difference scheme for three-dimensional incompressible flows in cylindrical coordinates. J. Comput. Phys. (submitted).Google Scholar
Verzicco, R. & Orlandi, P. 1994 Normal and oblique collisions of a vortex ring with a wall. Meccanica 29, 383–391.Google Scholar
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1–25.Google Scholar