Abstract
The magneto-rotational-instability (MRI) is considered by many researchers to provide a viable solution to one of the fundamental problems of theoretical astrophysics, namely, how turbulence arises and angular momentum is transported in accretion disks. A novel scenario of weakly nonlinear evolution of the MRI that is based on resonant as well as non-resonant three-wave interactions is introduced and discussed. Such mechanism relies on the energy transfer from the MRI to linearly stable slow and fast Alfvén-Coriolis (AC) as well as Magnetosonic (MS) waves. The dynamical equations that govern the evolution of the amplitudes of the participating waves are derived. In particular, the equation that describes the MRI is shown to be a second order generalized forced Duffing equation. The behavior exhibited by the solutions of the dynamical equations ranges from bounded nonlinear oscillations of the MRI, to nonlinear exponential instability of the linearly stable AC and MS modes, to explosive instability of all three waves. Triads of resonantly interacting waves thus provide the building blocks for a weakly nonlinear turbulence theory.
Coffee and tea will be served 20 minutes prior to the seminar.