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Casimir cascades in two-dimensional turbulence

Published online by Cambridge University Press:  19 July 2013

John C. Bowman
John C. Bowman*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
*
†Email address for correspondence: [email protected]
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Abstract

In addition to conserving energy and enstrophy, the nonlinear terms of the two-dimensional incompressible Navier–Stokes equation are well known to conserve the global integral of any continuously differentiable function of the scalar vorticity field. However, the phenomenological role of these additional inviscid invariants, including the issue as to whether they cascade to large or small scales, is an open question. In this work, well-resolved implicitly dealiased pseudospectral simulations suggest that the fourth power of the vorticity cascades to small scales.

JFM classification

Mathematical Foundations: Computational methods Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 729 , 25 August 2013 , pp. 364 - 376
Copyright
©2013 Cambridge University Press 

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References

Batchelor, G. K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids 12 (II), 233–239.CrossRefGoogle Scholar
Bowman, J. C. 1996 On inertial-range scaling laws. J. Fluid Mech. 306, 167–181.Google Scholar
Bowman, J. C. & Roberts, M. 2010 FFTW ++: a fast Fourier transform C++ header class for the FFTW3 library. http://fftwpp.sourceforge.net.Google Scholar
Bowman, J. C. & Roberts, M. 2011 Efficient dealiased convolutions without padding. SIAM J. Sci. Comput. 33 (1), 386–406.CrossRefGoogle Scholar
Cateau, H., Matsuo, Y. & Umeki, M. 1993 Predictions on two-dimensional turbulence by conformal field theory. arXiv: hep-th/9310056.Google Scholar
Eyink, G. L. 1996 Exact results on stationary turbulence in 2D: consequences of vorticity. Physica D 91, 97–142.Google Scholar
Falkovich, G. & Hanany, A. 1993 Is 2D turbulence a conformal turbulence? Phys. Rev. Lett. 71, 3454–3457.Google Scholar
Falkovich, G. & Lebedev, V. 1994 Universal direct cascade in two-dimensional turbulence. Phys. Rev. E 50 (5), 3883–3899.Google Scholar
Kraichnan, R. H. 1959 The structure of isotropic turbulence at very high Reynolds numbers. J. Fluid Mech. 5, 497–543.CrossRefGoogle Scholar
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10 (7), 1417–1423.Google Scholar
Kraichnan, R. H. 1971 Inertial-range transfer in two- and three-dimensional turbulence. J. Fluid Mech. 47, 525–535.Google Scholar
Leith, C. E. 1968 Diffusion approximation for two-dimensional turbulence. Phys. Fluids 11, 671–673.Google Scholar
Novikov, E. A. 1964 Functionals and the random-force method in turbulence theory. J. Exp. Theor. Phys. (USSR) 47, 1919–1926.Google Scholar
Polyakov, A. M. 1993 The theory of turbulence in two dimensions. Nucl. Phys. B 396, 367–385.Google Scholar
Roberts, M. & Bowman, J. C. 2011 Dealiased convolutions for pseudospectral simulations. J. Phys.: Conf. Ser. 318 (7), 072037.Google Scholar
Roberts, M. & Bowman, J. C. 2012 Multithreaded implicitly dealiased pseudospectral convolutions. In Proceedings of the 20th Annual Conference of the CFD Society of Canada (ed. R. Martinuzzi & C. Lange), Canmore, Alberta.Google Scholar
Vallgren, A. & Lindborg, E. 2011 The enstrophy cascade in forced two-dimensional turbulence. J. Fluid Mech. 671, 168–183.CrossRefGoogle Scholar