Crisis and unstable dimension variability in the bailout embedding map
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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 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 gives rise to a power law with the exponent $β=-1/3$. 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.
7 pages, 4 figures, appeared in the Proceeding of the conference Perspectives in Nonlinear Dynamics 2007, a special issue of the Journal Pramana
7 pages, 4 figures, appeared in the Proceeding of the conference Perspectives in Nonlinear Dynamics 2007, a special issue of the Journal Pramana