Focusing of non-linear eccentric waves in astrophysical discs. Issue 1 (25th June 2019)

• Record Type: Journal Article
• Authors: Lynch, Elliot M; Ogilvie, Gordon I
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 488:Issue 1(2019)
• Page Start: 1127
• Page End: 1140
• Publication Date: 2019-06-25
• Subjects: accretion, accretion discs -- hydrodynamics -- celestial mechanics; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/stz1731
• Languages: English
• ISSNs: 0035-8711

Abstract

ABSTRACT: We develop a fully non-linear approximation to the short-wavelength limit of eccentric waves in astrophysical discs, based on the averaged Lagrangian method of Whitham. In this limit there is a separation of scales between the rapidly varying eccentric wave and the background disc. Despite having small eccentricities, such rapidly varying waves can be highly non-linear, potentially approaching orbital intersection, and this can result in strong pressure gradients in the disc. We derive conditions for the steepening of non-linearity and eccentricity as the waves propagate in a radially structured disc in this short-wavelength limit and show that the behaviour of the solution can be bounded by the behaviour of the WKB solution to the linearized equations.