Nonlinear evolution of the dynamical instability in a Keplerian disk  Resonant excitation of higher modes
Abstract
The second order perturbations induced by linearly unstable perturbations were computed in order to study the nonlinear evolution of the dynamical instabilities. When the linearly most unstable mode with azimuthal wavenumber, m, is excited, the second order perturbation with azimuthal wavenumber, 2m, is also excited with a large amplitude. Even when the first order density fluctuation is 0.01, the second order fluctuation has an amplitude of the same order. This large amplitude is ascribed to the resonance of the radial wavenumber of the second order perturbation to that of the cross term of the firstorder perturbations. The third and higher modes are also expected to be highly excited. The excitation of these shorter wavelength modes makes the wave profile steep and may lead to a shock wave. The angular momentum transfer associated with the dynamical instability is discussed, based on the secondorder change in the angular momentum.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 November 1988
 Bibcode:
 1988A&A...206...79H
 Keywords:

 Accretion Disks;
 Dynamic Stability;
 Nonlinear Evolution Equations;
 Perturbation Theory;
 Rotating Fluids;
 Corotation;
 Eigenvalues;
 Radial Velocity;
 Shock Waves;
 Astrophysics