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Volume 3 Issue 3
Jul.  2016

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2016  >  3(3): 257-260
Bruce J. West and Malgorzata Turalska, "The Fractional Landau Model," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 3, pp. 257-260, 2016.
Citation: Bruce J. West and Malgorzata Turalska, "The Fractional Landau Model," IEEE/CAA J. of Autom. Sinica, vol. 3, no. 3, pp. 257-260, 2016.
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The Fractional Landau Model

  • 1. Information Science Directorate, Army Research Office, Research Triangle Park, NC 27708, USA;

  • 2. Department of Physics, Duke University, Durham, NC 27708, USA

    Abstract
  • Herein the Landau model of the transition from laminar to turbulent fluid flow is generalized to include the effect of memory. The original Landau model is quadratically nonlinear and memoryless, with turbulent fluctuations decaying exponentially. However, recent experiments show a dependence of the decay of fluctuations on memory, with the exponential being replaced by an inverse power law. This transition is explained herein as being due to critical slowing down. The fractional calculus is used to model this memory and to relate the index of the inverse power law decay to that of the fractional derivative in time.

     

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