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Nonlinear dynamical systems and bistability in linearly forced isotropic turbulence

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Abstract

In this paper, we present an extensive study of the linearly forced isotropic turbulence. By using analytical method, we identify two parametric choices, of which they seem to be new as far as our knowledge goes. We prove that the underlying nonlinear dynamical system for linearly forced isotropic turbulence is the general case of a cubic Lienard equation with linear damping. We also discuss a Fokker-Planck approach to this new dynamical system, which is bistable and exhibits two asymmetric and asymptotically stable stationary probability densities.

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 200072, Shanghai, China

    Zheng Ran & Xing-Jie Yuan

Authors
  1. Zheng Ran
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  2. Xing-Jie Yuan
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Correspondence to Zheng Ran.

Additional information

The project was supported by the National Natural Science Foundation of China (11172162, 10572083).

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Ran, Z., Yuan, XJ. Nonlinear dynamical systems and bistability in linearly forced isotropic turbulence. Acta Mech Sin 29, 823–826 (2013). https://doi.org/10.1007/s10409-013-0085-3

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  • DOI: https://doi.org/10.1007/s10409-013-0085-3

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