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On inertial-range scaling laws

Published online by Cambridge University Press:  26 April 2006

John C. Bowman
John C. Bowman
Affiliation:
Institute for Fusion Studies, The University of Texas, Austin, TX 78712, USA
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Abstract

Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's k−5/3 scaling is derived for the energy inertial range. A related modification is found to Kraichnan's logarithmically corrected two-dimensional enstrophy-range law that removes its unexpected divergence at the injection wavenumber. The significance of these corrections is illustrated with steady-state energy spectra from recent high-resolution closure computations. Implications for conventional numerical simulations are discussed. These results underscore the asymptotic nature of inertial-range scaling laws.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 306 , 10 January 1996 , pp. 167 - 181
Copyright
© 1996 Cambridge University Press

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References

Benzi, R., Paladin, G. & Vulpiani, A. 1990 Power spectra in two-dimensional turbulence. Phys. Rev. A 42, 3654–3656.
Boer, G. J. & Shepherd, T. G. 1983 Large-scale two-dimensional turbulence in the atmosphere. J. Atmos. Sci. 40, 164–184.Google Scholar
Borue, V. 1993 Spectral exponents of enstrophy cascade in stationary two-dimensional homogeneous turbulence. Phys. Rev. Lett. 71, 3967–3970.
Bowman, J. C. 1992 Realizable Markovian statistical closures: general theory and application to drift-wave turbulence. PhD thesis, Princeton University, Princeton, NJ.
Bowman, J. C. 1995 A wavenumber partitioning scheme for two-dimensional statistical closures. Submitted to J. Sci. Comput.
Bowman, J. C. & Krommes, J. A. 1996 The realizable Markovian closure and realizable test-field model. II: Application to anisotropic drift-wave turbulence. To be submitted to Phys. Plasmas.
Bowman, J. C., Krommes, J. A. & Ottaviani, M. 1993 The realizable Markovian closure. I: General theory, with application to three-wave dynamics. Phys. Fluids B 5, 3558–3589.Google Scholar
Ellison, T. H. 1962 The universal small-scale spectrum of turbulence at high reynolds number. In Mécanique de la Turbulence, Intl Colloq., Marseille, 1961, pp. 113–121. Paris: CNRS.
Falkovich, G. & Lebedev, V. 1994 Universal direct cascade in two-dimensional turbulence. Phys. Rev. E 50, 3883–3899.Google Scholar
Fjørtoft, R. 1953 On the changes in the spectral distribution of kinetic energy for two dimensional, nondivergent flow. Tellus 5, 225–230.Google Scholar
Herring, J. R. 1985 Comparison of direct numerical simulation of two-dimensional turbulence with two-point closure: the effects of intermittency. J. Fluid Mech. 153, 229–242.Google Scholar
Herring, J. R., Orszag, S. A., Kraichnan, R. H. & Fox, D. G. 1974 Decay of two-dimensional homogenous turbulence. J. Fluid Mech. 66, 417–444.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C. R. Acad. Sci. USSR 30, 301–306.Google Scholar
Kraichnan, R. H. 1958 Irreversible statistical mechanics of incompressible hydromagnetic turbulence. Phys. Rev. 109, 1407–1422.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. 1961 Dynamics of nonlinear stochastic systems. J. math. phys. 2, 124–148.Google Scholar
Kraichnan, R. H. 1964 Decay of isotropic turbulence in the direct-interaction approximation. Phys. Fluids 7, 1030–1047.Google Scholar
Kraichnan, R. H. 1967 Inertial ranges 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. 1991 Turbulent cascade and intermittency growth. Proc. R. Soc. Lond. A 434, 65–78.Google Scholar
Leslie, D. C. 1973 Developments in the Theory of Turbulence. Clarendon Press.
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.Google Scholar
Orszag, S. A. 1977 Lectures on the statistical theory of turbulence. In Fluid Dynamics, (ed. R. Balian, & J.-L. Peube), pp. 236–373. Gordon and Breach.
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 self-similarity. Phys. Fluids A 1, 1027–1034.Google Scholar