AbstractN-body simulations of disc galaxies that display recurrent transient spiral patterns are comparatively easy to construct, but are harder to understand. In this paper, I summarise the evidence from such experiments that the spiral patterns result from a recurrent spiral instability cycle. Each wave starts as rapidly growing, small-amplitude instability caused by a deficiency of particles at a particular angular momentum. The resulting largeamplitude wave creates, through resonant scattering, the conditions needed to precipitate a new instability.

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The problem of spiral structure in galaxies has been worked on for many years but progress has been painfully slow. Most effort has been directed towards the development of an analytical (or at least semi-analytical) approach and many aspects of the problem have been discovered (see Sellwood 1989 for a review). Here, I collect the evidence from N-body simulations which indicates that the structure is continuously variable and results from a recurrent cycle of spiral instabilities.

A subsidiary purpose of this paper, is to convince the reader of the advantages of using N-body simulations in tandem with approximate analytic treatments. Without a close comparison of this nature, each separate approach is much less powerful; the limitations of the N-body experiments remain unquantified and the validity of the approximations in the analytic approach cannot be assessed.

The paper is divided into three distinct sections. In §2, I discuss swing-amplified noise in global simulations, and show that the behaviour in the Mestel (V = const.) disc is very similar to that reported by Toomre (e.g. this conference) for simulations in the shearing sheet.