Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-02-03T22:05:19.447Z Has data issue: false hasContentIssue false
  • English
  • Français

Decay of two-dimensional homogeneous turbulence

Published online by Cambridge University Press:  29 March 2006

J. R. Herring ,
S. A. Orszag ,
R. H. Kraichnan  and
D. G. Fox
J. R. Herring
Affiliation:
Advanced Study Program, National Center for Atmospheric Research, Boulder, Colorado 80303 Present address: U.S.D.A. Forest Service, Rocky Mountain Forest and Range Experimrnt Station, Fort Collins, Colorado 80521
S. A. Orszag
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge
R. H. Kraichnan
Affiliation:
Dublin, New Hampshire 03444
D. G. Fox
Affiliation:
Meteorological Laboratory, National Environmental Research Center, Environmental Protection Agency, Research Triangle Park, North Carolina
Get access Rights & Permissions [Opens in a new window]

Abstract

The decay of two-dimensional, homogeneous, isotropic, incompressible turbulence is investigated both by means of numerical simulation (in spectral as well as in grid-point form), and theoretically by use of the direct-interaction approximation and the test-field model. The calculations cover the range of Reynolds numbers 50 ≤ RL ≤ 100. Comparison of spectral methods with finite-difference methods shows that one of the former with a given resolution is equivalent in accuracy to one of the latter with twice the resolution. The numerical simulations at the larger Reynolds numbers suggest that earlier reported simulations cannot be used in testing inertial-range theories. However, the large-scale features of the flow field appear to be remarkably independent of Reynolds number.

The direct-interaction approximation is in satisfactory agreement with simulations in the energy-containing range, but grossly underestimates enstrophy transfer at high wavenumbers. The latter failing is traced to an inability to distinguish between convection and intrinsic distortion of small parcels of fluid. The test-field model on the other hand appears to be in excellent agreement with simulations at all wavenumbers, and for all Reynolds numbers investigated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 66 , Issue 3 , 25 November 1974 , pp. 417 - 444
Copyright
© 1974 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

Arakawa, A. 1966 Computational design for long-term integration of the equations of motion: two-dimensional incompressible flow. Part 1. J. Comp. Phys. 1, 119–143.Google Scholar
Batchelor, G. K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence. High-speed computing in fluid dynamics. Phys. Fluids Suppl. II, 12, II233–239.Google Scholar
Charney, J. G. 1971 Geostrophic turbulence J. Atmos. Sci. 28, 1087–1095.Google Scholar
Deem, G. S. & Zabusky, N. J. 1971 Ergodic boundary in numerical simulations of two-dimensional turbulence Phys. Rev. Lett. 27, 396–399.Google Scholar
Fox, D. G. & Orszag, S. A. 1973a Pseudospectral approximation to two-dimensional turbulence J. Comp. Phys. 11, 612–619.Google Scholar
Fox, D. G. & Orszag, S. A. 1973b Inviscid dynamics of two-dimensional turbulence Phys. Fluids, 16, 169–171.Google Scholar
Heisenberg, W. 1948 On the theory of statistical and isotropic turbulence. Proc. Roy. Soc A 195, 402–406.Google Scholar
Herring, J. R. & Kraichnan, R. H. 1972 Comparison of some approximations for isotropic turbulence. In Lecture Notes in Physics, vol. 12. Statistical Models and Turbulence, pp. 148–194. Springer.
Herring, J. R., Riley, J. J., Patterson, G. S. & Kraichnan, R. H. 1973 Growth of uncertainty in decaying isotropic turbulence J. Atmos. Sci. 30, 997–1006.Google Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers J. Fluid Mech. 5, 497–543.Google Scholar
Kraichnan, R. H. 1964 Kolmogorov's hypothesis and Eulerian turbulence theory Phys. Fluids, 7, 1723–1734.Google Scholar
Kraichnan, R. H. 1966 Isotropic turbulence and inertial-range structure Phys. Fluids, 9, 1728–1752.Google Scholar
Kraichnan, R. H. 1967 Inertial range in two-dimensional turbulence Phys. Fluids, 10, 1417–1423.Google Scholar
Kraichnan, R. H. 1971a An almost-Markovian Galilean-invariant turbulence model J. Fluid Mech. 47, 513–524.Google Scholar
Kraichnan, R. H. 1971b Inertial-range transfer in two- and three-dimensional turbulence J. Fluid Mech. 47, 525–535.Google Scholar
Kraichnan, R. H. 1973 Test-field model for inhomogeneous turbulence J. Fluid Mech. 56, 287–304.Google Scholar
Leith, C. E. 1971 Atmospheric predictability and two-dimensional turbulence J. Atmos. Sci. 28, 145–161.Google Scholar
Leith, C. E. & Kraichnan, R. H. 1972 Predictability of turbulent flows J. Atmos. Sci. 29, 1041–1058.Google Scholar
Lilly, D. K. 1971 Numerical simulation of developing and decaying two-dimensional turbulence J. Fluid Mech. 45, 395–415.Google Scholar
Lilly, D. K. 1972a Numerical simulation studies of two-dimensional turbulence: I. Models of statistically steady turbulence. Geophys. Fluid Dyn. 3, 289–319.Google Scholar
Lilly, D. K. 1972b Numerical simulation studies of two-dimensional turbulence: II. Stability and predictability studies. Geophys. Fluid Dyn. 4, 1–28.Google Scholar
Orszag, S. A. 1970 Analytical theories of turbulence J. Fluid Mech. 41, 363–386.Google Scholar
Orszag, S. A. 1971 Numerical simulation of incompressible flows within simple boundaries. I. Galerkin (spectral) representations Studies in Appl. Math. 50, 293–327.Google Scholar
Orszag, S. A. 1974 Statistical Theory of Turbulence, Les Houches Summer School on Physics. Gordon & Breach.
Orszag, S. A. & Patterson, G. S. 1972 Numerical simulation of three-dimensional homogeneous isotropic turbulence Phys. Rev. Lett. 28, 76–79. (See also ‘Numerical simulation of turbulence.’ In Lecture Notes in Physics, vol. 12, Statistical Models and Turbulence, pp. 127–147. Springer.)Google Scholar