• Crisis and unstable dimension variability in the bailout embedding map

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      https://www.ias.ac.in/article/fulltext/pram/070/06/1031-1037

    • Keywords

       

      Bailout embedding map; crisis; unstable dimension variability; Lyapunov exponents.

    • Abstract

       

      The dynamics of inertial particles in 2-d incompressible flows can be modeled by 4-d bailout embedding maps. The density of the inertial particles, relative to the density of the fluid, is a crucial parameter which controls the dynamical behaviour of the particles. We study here the dynamical behaviour of aerosols, i.e. particles heavier than the flow. An attractor widening and merging crisis is seen in the phase space in the aerosol case. Crisis-induced intermittency is seen in the time series and the laminar length distribution of times before bursts give rise to a power law with the exponent $\beta = -1/3$. The maximum Lyapunov exponent near the crisis fluctuates around zero indicating unstable dimension variability (UDV) in the system. The presence of unstable dimension variability is confirmed by the behaviour of the probability distributions of the finite time Lyapunov exponents.

    • Author Affiliations

       

      N Nirmal Thyagu1 Neelima Gupta1

      1. Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India
    • Dates

       
  • Pramana – Journal of Physics | News

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