Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T08:09:48.506Z Has data issue: false hasContentIssue false
  • English
  • Français

The emergence of isolated coherent vortices in turbulent flow

Published online by Cambridge University Press:  20 April 2006

James C. Mcwilliams
James C. Mcwilliams
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307
Get access Rights & Permissions [Opens in a new window]

Abstract

A study is made of some numerical calculations of two-dimensional and geostrophic turbulent flows. The primary result is that, under a broad range of circumstances, the flow structure has its vorticity concentrated in a small fraction of the spatial domain, and these concentrations typically have lifetimes long compared with the characteristic time for nonlinear interactions in turbulent flow (i.e. an eddy turnaround time). When such vorticity concentrations occur, they tend to assume an axisymmetric shape and persist under passive advection by the large-scale flow, except for relatively rare encounters with other centres of concentration. These structures can arise from random initial conditions without vorticity concentration, evolving in the midst of what has been traditionally characterized as the ‘cascade’ of isotropic, homogeneous, large-Reynolds-number turbulence: the systematic elongation of isolines of vorticity associated with the transfer of vorticity to smaller scales, eventually to dissipation scales, and the transfer of energy to larger scales. When the vorticity concentrations are a sufficiently dominant component of the total vorticity field, the cascade processes are suppressed. The demonstration of persistent vorticity concentrations on intermediate scales - smaller than the scale of the peak of the energy spectrum and larger than the dissipation scales - does not invalidate many of the traditional characterizations of two-dimensional and geostrophic turbulence, but I believe it shows them to be substantially incomplete with respect to a fundamental phenomenon in such flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 146 , September 1984 , pp. 21 - 43
Copyright
© 1984 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

Aref, H. 1980 Coherent features by the method of point vortices. WHOI Tech. Rep. 80-53, pp. 233–249.Google Scholar
Aref, H. 1983 Integrable chaotic and turbulent vortex motion in two-dimensional flows. Ann. Rev. Fluid Mech. 15, 345–389.Google Scholar
Aref, H. & Siggia, E. 1980 Vortex dynamics of the two-dimensional turbulent shear layer. J. Fluid Mech. 100, 705–737.Google Scholar
Arnold, V. I. 1980 Mathematical Methods of Classical Mechanics. Springer.
Basdevant, C., Legras, B., Sadourny, R. & Beland, M. 1981 A study of barotropic model flows: intermittency, waves and predictability. J. Atmos. Sci. 38, 2305–2326.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Batchelor, G. K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids Suppl. 12, II-233–II-239.Google Scholar
Bennett, A. F. & Haidvogel, D. B. 1983 Low resolution numerical simulation of decaying two-dimensional turbulence. J. Atmos. Sci. 40, 738–748.Google Scholar
Charney, J. G. 1971 Geostrophic turbulence. J. Atmos. Sci. 28, 1087–1095.Google Scholar
Christiansen, J. P. 1973 Numerical simulation of hydrodynamics by the method of point vortices. J. Comp. Phys. 13, 363–379.Google Scholar
Christiansen, J. P. & Zabusky, N. J. 1973 Instability, coalescence and fission of finite-area vortex structures. J. Fluid Mech. 61, 219–243.Google Scholar
Davey, M. K. 1980 Numerical calculation of the spectral representation of u·∇x for doubly periodic flow. Univ. Washington Special Rep. 93.Google Scholar
Deem, G. S. & Zabusky, N. J. 1978 Vortex waves: stationary V-states, interactions, recurrence and breaking. Phys. Rev. Lett. 40, 859–862.Google Scholar
Fornberg, B. 1977 A numerical study of 2-D turbulence. J. Comp. Phys. 25, 1–31.Google Scholar
Haidvogel, D. B. 1983 Particle dispersal and Lagrangian vorticity conservation in models of β-plane turbulence. In preparation.
Herring, J. & McWilliams, J. C. 1984 Comparison of direct numerical simulation of two-dimensional turbulence with two-point closure. Submitted.
Holloway, G. 1983 Contrary roles of planetary wave advection in atmospheric predictability. In Proc. La Jolla Conf. on Predictability (ed. G. Holloway & B. West). AIP Conf. Proc. no. 106, pp. 593–599.
Hopfinger, E., Browand, F. & Gagne, Y. 1982 J. Fluid Mech. 125, 505–534.
Kraichnan, R. H. 1971 An almost-Markovian Galilean-invariant turbulence model. J. Fluid Mech. 47, 513–524.Google Scholar
Kraichnan, R. H. & Montgomery, D. 1980 Two-dimensional turbulence. Rep. Prog. Phys. 00, 000–000.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn, § 159. Dover.
Larichev, V. & Reznik, G. 1982 Numerical experimental studies of interactions between dimensional elongated Rossby waves. Rep. Acad. Sci. USSR, Oceanologie 264, 229–233.Google Scholar
Leith, C. E. 1971 Atmospheric predictability and two-dimensional turbulence. J. Atmos. Sci. 28, 145–161.Google Scholar
Leith, C. E. 1984 Minimum enstrophy vortices. Phys. Fluids in press.Google Scholar
Leith, C. E. & Kraichnan, R. 1972 Pedictability of turbulent flows. J. Atmos. Sci. 29, 1041–1058.Google Scholar
McEwan, A. 1976 Angular momentum diffusion and the initiation of cyclones. Nature 260, 126–128.Google Scholar
McWilliams, J. C. 1983a Interactions of isolated vortices. II. Modon generation by monopole collision. Geophys. Astrophys. Fluid Dyn. 24, 1–22.Google Scholar
McWilliams, J. C. 1983b On the emergence of isolated, coherent vortices in turbulent flow. In Proc. La Jolla Conf. on Predictability (ed. G. Holloway & B. West). AIP Conf. Proc. no. 106, pp. 205–221.
McWilliams, J. C. et al. 1983 The local dynamics of eddies in the Western North Atlantic. In Eddies and Marine Science (ed. A. Robinson), pp. 92–113. Springer.
McWilliams, J. C. & Flierl, G. R. 1979 On the evolution of isolated, nonlinear vortices. J. Phys. Oceanogr. 9, 1155–1182.Google Scholar
McWilliams, J. C., Flierl, G. R., Larichev, V. D. & Reznik, G. M. 1981 Numerical studies of barotropic modons. Dyn. Atmos. Oceans 5, 219–238.Google Scholar
McWilliams, J. C. & Zabusky, N. J. 1982 Interactions of isolated vortices. I. Modons colliding with modons. Geophys. Astrophys. Fluid Dyn. 19, 207.Google Scholar
Makino, M., Kamimura, T. & Taniuiti, T. 1981 Dynamics of two-dimensional solitary vortices in a low-β plasma with convective motion. J. Phys. Soc. Japan 50, 980–989.Google Scholar
Malanotti-Rizzoli, P. 1982 Planetary waves in geophysical flows. Adv. Geophys. 24, 147–224.Google Scholar
Moore, D. W. & Saffman, P. G. 1971 In Aircraft Wake Turbulence (ed. J. H. Olsen A. Goldberg & M. Rogers), pp. 339–000. Plenum.
Overman, E. A. & Zabusky, N. J. 1982 Evolution and merger of isolated vortex structures. Phys. Fluids 25, 1297–1305.Google Scholar
Rhines, P. B. 1975 Waves and turbulence on a beta-plane. J. Fluid Mech. 69, 417–443.Google Scholar
Rhines, P. B. 1979 Geostrophic turbulence. Ann. Rev. Fluid Mech. 11, 401–441.Google Scholar
Saffman, P. G. 1980 In Transition and Turbulence (ed. J. H. Olsen, A. Goldberg & M. Rogers), pp. 339–000. Plenum.
Weiss, J. 1981 The dynamics of enstrophy transfer in two-dimensional hydrodynamics. La Jolla Inst. LJI-TN-81-121.Google Scholar