Abstract

Thin discs of gas in orbital motion around a massive central body, such as a star or black hole, are found throughout the Universe. They include the discs of dusty gas around young stars, in which planetary systems are born, and high-energy plasma accretion discs around black holes, both in the centres of galaxies and around stellar remnants within our own Galaxy.

Astrophysical discs are (Rayleigh-stable) rotating shear flows of extremely high Reynolds number and support a variety of oscillations, waves and instabilities. Fluid-mechanical processes (which may also involve magnetic fields or solid particles, not discussed in this talk) govern not only the evolution of discs, by regulating the transport of angular momentum, but also the structures that are increasingly observed within them, including rings, arcs, spirals and warps.

This talk explores a variety of problems of nonlinear gas dynamics in discs in which a non-circular or non-planar orbital geometry drives oscillatory flows within the disc. I will survey a range of physical models, as well as asymptotic and variational methods, that can capture the relevant degrees of freedom and the (often resonant) couplings between them, as seen in numerical simulations. A recurring feature is that internal waves can be destabilized by the oscillatory flows.

If time allows, I will also introduce a novel approach to gravitational instability in discs (a mechanism capable of forming either bound objects or long-lived spiral structure), in which the nonlinear gas dynamics gives rise to subcritical behaviour that may help to explain a self-sustaining process for gravitational turbulence.