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Symmetry justification of Lorenz’ maximum simplification

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Abstract

In 1960 Edward Lorenz (1917–2008) published a pioneering work on the ‘maximum simplification’ of the barotropic vorticity equation. He derived a coupled three-mode system and interpreted it as the minimum core of large-scale fluid mechanics on a ‘finite but unbounded’ domain. The model was obtained in a heuristic way, without giving a rigorous justification for the chosen selection of modes. In this paper, it is shown that one can legitimate Lorenz’ choice by using symmetry transformations of the spectral form of the vorticity equation. The Lorenz three-mode model arises as the final step in a hierarchy of models constructed via the component reduction by means of symmetries. In this sense, the Lorenz model is indeed the ‘maximum simplification’ of the vorticity equation.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Nordbergstraße 15, 1090, Vienna, Austria

    Alexander Bihlo & Roman O. Popovych

  2. Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivska Str., 01601, Kyiv, Ukraine

    Roman O. Popovych

Authors
  1. Alexander Bihlo
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  2. Roman O. Popovych
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Correspondence to Alexander Bihlo.

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Bihlo, A., Popovych, R.O. Symmetry justification of Lorenz’ maximum simplification. Nonlinear Dyn 61, 101–107 (2010). https://doi.org/10.1007/s11071-009-9634-5

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  • DOI: https://doi.org/10.1007/s11071-009-9634-5

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