Soumyajit Bose, Anindya Sengupta, Arnab K. Ray
Stationary solutions of an inviscid and rotational accretion process have been subjected to a time-dependent radial perturbation, whose equation includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of the perturbation bears a form that is remarkably similar to the metric equation of an analogue acoustic black hole. Casting the perturbation as a standing wave and maintaining nonlinearity in it up to the second order, brings out the time-dependence of the perturbation in the form of a Lienard system. A dynamical systems analysis of this Lienard system reveals a saddle point in real time, with the implication that instabilities will develop in the accreting system when the perturbation is extended into the nonlinear regime. The instability of initial sub-critical states may also adversely affect the non-perturbative drive of the flow towards a final and stable critical state.
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http://arxiv.org/abs/1207.1895
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