Explosive Instability in Keplerian Disks

TL;DR

This paper reveals a new nonlinear explosive instability in differentially rotating Keplerian disks with weak magnetic fields, caused by near-resonance three-wave interactions, leading to either explosive growth or irregular oscillations.

Contribution

It introduces the concept of nonlinear explosive instability in Keplerian disks due to three-wave interactions involving magnetorotational and stable modes.

Findings

Explosive instability causes amplitudes to diverge in finite time.

Small frequency mismatch influences the type of dynamical behavior.

Asymptotic solutions match numerical results near explosion time.

Abstract

In this paper it is shown that deferentially rotating disks that are in the presence of weak axial magnetic field are prone to a new nonlinear explosive instability. The latter occurs due to the near-resonance three-wave interactions of a magnetorotational instability with stable Alfven-Coriolis and magnetosonic modes. The dynamical equations that govern the temporal evolution of the amplitudes of the three interacting modes are derived. Numerical solutions of the dynamical equations indicate that small frequency mismatch gives rise to two types of behavior: 1. explosive instability which leads to infinite values of the three amplitudes within a finite time, and 2. bounded irregular oscillations of all three amplitudes. Asymptotic solutions of the dynamical equations are obtained for the explosive instability regimes and are shown to match the numerical solutions near the explosion time.