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The Beltrami spectrum for incompressible fluid flows

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Abstract

Recently V. Yakhot, S. Orszag, and their co-workers have suggested that turbulent flows in various regions of space organize into a coherent hierarchy of weakly interacting superimposed approximate Beltrami flows. A mathematical framework is developed here to study organized Beltrami hierarchies in a systematic fashion. This framework is applied to several important classes of examples with universal Beltrami hierarchies. An analysis of the persistence of such Beltrami hierarchies is also presented for general solutions of the Navier-Stokes equations.

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Authors and Affiliations

  1. Department of Mathematics, The University of Chicago, 60637, Chicago, IL, USA

    Peter Constantin

  2. Department of Mathematics, and Program in Applied and Computational Mathematics, Princeton University, 08544, Princeton, NJ, USA

    Andrew Majda

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  1. Peter Constantin
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  2. Andrew Majda
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Communicated by A. Jaffe

Research partially supported by grant NSF DMS-860-2031. Sloan research fellowship gratefully acknowledged

This research was partially supported by grants NSF DMS 86-11110 and DARPA — ONR N00014-86-K-0759

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Constantin, P., Majda, A. The Beltrami spectrum for incompressible fluid flows. Commun.Math. Phys. 115, 435–456 (1988). https://doi.org/10.1007/BF01218019

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  • DOI: https://doi.org/10.1007/BF01218019

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