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Hyperviscous vortices

Published online by Cambridge University Press:  26 April 2006

Javier Jiménez
Javier Jiménez
Affiliation:
School of Aeronautics, Pl. Cardenal Cisneros 3, 28040 Madrid, Spain
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Abstract

The structure of diffusing planar and axisymmetric vortices of the hyperviscous Navier-Stokes equations is studied for different orders of the dissipative operator. It is found that, except for the classical Newtonian case, the vorticity decays at large distances by means of oscillatory tails, containing circulation of alternating signs. This oscillation becomes stronger for large hyperviscosity orders, and the limit of infinite order is studied. It is argued that these solutions would become unstable for large enough Reynolds numbers, and may contribute non-trivial spurious dynamics to flow simulations using hyperviscosity.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 279 , 25 November 1994, pp. 169 - 176
Copyright
© 1994 Cambridge University Press

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References

Babiano, A., Basdevant, C., Legras, B. & Sadourny, R. 1987 Vorticity and passive scalar dynamics in two-dimensional turbulence. J. Fluid Mech. 183, 379–397.Google Scholar
Batchelor, G. K. 1967 An introduction to Fluid Dynamics. Cambridge University Press.
Bender, C. M. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw Hill.
Borue, V. 1993 Spectral exponents of enstrophy cascade in stationary two-dimensional homogeneous turbulence. Phys. Rev. Lett. 71, 3967–3970.Google Scholar
Carrier, C. F., Krook, M. & Pearson, C. E. 1966 Functions of Complex Variables. McGraw-Hill.
Dritschel, D. G. 1993 Vortex properties of two-dimensional turbulence. Phys. Fluids A 5, 984–997.Google Scholar
Fornberg, B. 1977 A numerical study of 2-D turbulence. J. Comput. Phys. 25, 1–31.Google Scholar
Jiménez, J., Wray, A., Saffman, P. G. & Rogallo, R. S. 1993 The structure of intense vorticity in isotropic turbulence. J. Fluid Mech. 255, 65–90.Google Scholar
Kuo, A. Y. & Corrsin, S. 1972 Experiments on the geometry of the fine-structure regions in fully turbulent fluid. J. Fluid Mech. 56, 447–479.Google Scholar
Maltrud, M. E. & Vallis, G. K. 1993 Energy and enstrophy transfer in numerical simulations of two-dimensional turbulence. Phys. Fluids A 5, 984–997.Google Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flows. J. Fluid Mech. 146, 21–43.Google Scholar
McWilliams, J. C. 1990 The vortices of two-dimensional turbulence. J. Fluid Mech. 219, 361–385.Google Scholar
Nakamura, K., Takahashi, T. & Nakano, T. 1993 Statistical properties of decaying two-dimensional turbulence. J. Phys. Soc. Japan 62, 1193–1202.Google Scholar
Ohkitani, K. 1991 Wave number space dynamics of enstrophy cascade in a forced two-dimensional turbulence. Phys. Fluids A 3, 1598–1611.Google Scholar
Rayleigh, Lord 1880 On the stability, or instability, of certain fluid motions. Proc. Lond. Math. Soc. 11, 57–70.Google Scholar
Santangelo, P., Benzi, R. & Legras, B. 1989 The generation of vortices in high-resolution, two-dimensional decaying turbulence and the influence of initial conditions on the breaking of similarity. Phys. Fluids A 1, 1027–1034.Google Scholar
Siggia, E. D. 1981 Numerical study of small scale intermittency in three dimensional turbulence. J. Fluid Mech. 107, 375–406.Google Scholar
Smith, L. E. & Yakhot, V. 1993 Bose condensation and small-scale structure generation in a random force driven two dimensional turbulence. Phys. Rev. Lett. 71, 352–355.Google Scholar