Focusing of non-linear eccentric waves in astrophysical discs – II. Excitation and damping of tightly wound waves

ABSTRACT In this paper, I develop a non-linear theory of tightly wound (highly twisted) eccentric waves in astrophysical discs, based on the averaged Lagrangian method Whitham. Viscous dissipation is included by use pseudo-Lagrangian. This work an extension developed Lee & Goodman to 3D with addition viscosity. confirm that linear are overstable and excited presence shear viscosity show persists for weakly waves. find damped when wave become sufficiently non-linear, result previously found particulate discs. Additionally, compare results model recent simulations propagating inner regions black hole discs ingoing can be strongly near marginally stable orbit, resulting nearly circular disc, strong azimuthal variation disc density.