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Spatial structure of spectral transport in two-dimensional flow

Published online by Cambridge University Press:  14 May 2013

Yang Liao  and
Nicholas T. Ouellette
Yang Liao
Affiliation:
Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT 06520, USA
Nicholas T. Ouellette*
Affiliation:
Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT 06520, USA
*
†Email address for correspondence: nicholas.ouellette@yale.edu
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Abstract

Using filter-space techniques (FSTs), we study the spatial structure of the scale-to-scale flux of energy in two-dimensional flow. Analysing data from a weakly turbulent, experimental quasi-two-dimensional flow, we find rotationally symmetric patterns consisting of lobes of spectral flux of alternating sign that are associated with vortical motion in the flow field. Such patterns also occur in a simple analytical model, even though the single-scale model flow should have no scale-to-scale energy transfer. Thus, the interpretation of these alternating patterns must be handled with care. By decomposing the spectral flux into three distinct components, we show that these lobe patterns are entirely associated with the Leonard and, to a lesser extent, cross terms. In addition, we show that the contributions from these two terms are localized around the energy injection scale, and that the bulk of the inverse energy transfer in our flow is carried by the subgrid term alone.

JFM classification

Turbulent Flows: Isotropic turbulence Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 725 , 25 June 2013 , pp. 281 - 298
Copyright
©2013 Cambridge University Press 

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References

Batchelor, G. K. 1969 Computation of the energy spectrum in homegeneous two-dimensional turbulence. Phys. Fluids 12, II233–II239.CrossRefGoogle Scholar
Boffetta, G. 2007 Energy and enstrophy fluxes in the double cascade of two-dimensional turbulence. J. Fluid Mech. 589, 253–260.CrossRefGoogle Scholar
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Annu. Rev. Fluid Mech. 44, 427–451.Google Scholar
Boffetta, G. & Musacchio, S. 2010 Evidence for the double cascade scenario in two-dimensional turbulence. Phys. Rev. E 82, 016307.Google Scholar
Chen, S., Ecke, R. E., Eyink, G. L., Rivera, M., Wan, M. & Xiao, Z. 2006 Physical mechanism of the two-dimensional inverse energy cascade. Phys. Rev. Lett. 96, 084502.CrossRefGoogle ScholarPubMed
Chen, S., Ecke, R. E., Eyink, G. L., Wang, X. & Xiao, Z. 2003 Physical mechanism of the two-dimensional enstrophy cascade. Phys. Rev. Lett. 91, 214501.Google Scholar
Eyink, G. L. 1995 Local energy flux and the refined similarity hypothesis. J. Stat. Phys. 78, 335–351.Google Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.CrossRefGoogle Scholar
Hussain, A. K. M. F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303–356.Google Scholar
Kelley, D. H. & Ouellette, N. T. 2011a Onset of three-dimensionality in electromagnetically forced thin-layer flows. Phys. Fluids 23, 045103.Google Scholar
Kelley, D. H. & Ouellette, N. T. 2011b Spatiotemporal persistence of spectral fluxes in two-dimensional weak turbulence. Phys. Fluids 23, 115101.Google Scholar
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423.Google Scholar
Leith, C. E. 1967 Diffusion approximation for two-dimensional turbulence. Phys. Fluids 11, 671–673.Google Scholar
Liao, Y., Kelley, D. H. & Ouellette, N. T. 2012 Effects of forcing geometry on two-dimensional weak turbulence. Phys. Rev. E 86, 036306.Google Scholar
Liu, S., Meneveau, C. & Katz, J. 1994 On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83–119.Google Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1–32.Google Scholar
Mordant, N., Crawford, A. M. & Bodenschatz, E. 2004 Experimental Lagrangian probability density function measurement. Physica D 193, 245–251.Google Scholar
Ouellette, N. T. 2012 On the dynamical role of coherent structures in turbulence. C. R. Physique 13, 866–877.Google Scholar
Ouellette, N. T., O’Malley, P. J. J. & Gollub, J. P. 2008 Transport of finite-sized particles in chaotic flow. Phys. Rev. Lett. 101, 174504.CrossRefGoogle ScholarPubMed
Ouellette, N. T., Xu, H. & Bodenschatz, E. 2006 A quantitative study of three-dimensional Lagrangian particle tracking algorithms. Exp. Fluids 40, 301–313.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Rivera, M. K., Daniel, W. B., Chen, S. Y. & Ecke, R. E. 2003 Energy and enstrophy transfer in decaying two-dimensional turbulence. Phys. Rev. Lett. 90, 104502.CrossRefGoogle ScholarPubMed
Solomon, T. H. & Gollub, J. P. 1988 Chaotic particle transport in time-dependent Rayleigh–Bénard convection. Phys. Rev. A 38, 6280–6286.CrossRefGoogle ScholarPubMed
Wan, M., Xiao, Z., Meneveau, C., Eyink, G. L. & Chen, S. 2010 Dissipation-energy flux correlations as evidence for the Lagrangian energy cascade in turbulence. Phys. Fluids 22, 061702.Google Scholar
Xiao, Z., Wan, M., Chen, S. & Eyink, G. L. 2009 Physical mechanism of the inverse energy cascade of two-dimensional turbulence: a numerical investigation. J. Fluid Mech. 619, 1–44.Google Scholar