Related papers: Non-linear spiral waves in accretion discs
A scroll wave in a very thin layer of excitable medium is similar to a spiral wave, but its behaviour is affected by the layer geometry. We identify the effect of sharp variations of the layer thickness, which is separate from filament…
We simulate the nonlinear hydrodynamical evolution of tidally-excited inertial waves in convective envelopes of rotating stars and giant planets modelled as spherical shells containing incompressible, viscous and adiabatically-stratified…
Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here we report on a novel dispersive hydrodynamics testbed: the…
Collisionless, turbulent plasmas surround the Earth, from the magnetosphere to the intergalactic medium, and the fluctuations within them affect nearly every field in the space sciences, from space weather forecasts to theories of galaxy…
In this paper we address the stability of resonantly forced density waves in dense planetary rings. Already by Goldreich & Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the…
We study the propagation of ultra-short pulses in a cubic nonlinear medium. Using multiple-scale technique, we derive a new wave equation that preserves the nonlocal dispersion present in Maxwell's equations. As a result, we are able to…
This paper continues a series reporting different aspects of the behaviour of disc galaxy simulations that support spiral instabilities. The focus in this paper is to demonstrate how linear spiral instabilities saturate and decay, and how…
A new theory of eccentric accretion discs is presented. Starting from the basic fluid-dynamical equations in three dimensions, I derive the fundamental set of one-dimensional equations that describe how the mass, angular momentum and…
The density-wave theory of galactic spiral-arm structure makes a striking prediction that the pitch angle of spiral arms should vary with the wavelength of the galaxy's image. The reason is that stars are born in the density wave but move…
We investigate models of the Milky Way disc taking into account simultaneously the bar and a two-armed quasi-static spiral pattern. Away from major resonance overlaps, the mean stellar radial motions in the plane are essentially a linear…
After a short review of the principal theories of spiral structure in galaxies, I describe two new developments. First, it now seems clear that linear theory cannot yield a full description for the development of spiral patterns because…
Thin elastic sheets bend easily, leading to mechanical instabilities such as wrinkling. Here, we investigate wrinkles at edges of bi-strips, which consist of two thin sheets, one that swells and one that does not, joined side-by-side. It is…
We consider misaligned accretion discs formed after tidal disruption events occurring when a star encounters a supermassive rotating black hole. We use the linear theory of warped accretion discs to find the disc shape when the stream…
Numerical simulations of global three-dimensional (3D), self-gravitating discs with a gap opened by an embedded planet are presented. The simulations are customised to examine planetary gap stability. Previous results, obtained by Lin &…
Theories of stellar spiral arms in disk galaxies can be grouped into two classes based on the longevity of a spiral arm. Although the quasi-stationary density wave theory supposes that spirals are rigidly-rotating, long-lived patterns, the…
We present a unified theory of linear spiral structure in stellar disks. We begin by identifying the characteristic scales involved in the spiral structure problem and listing some quantitative requirements of a successful theory. We then…
Growing planets interact with their surrounding protoplanetary disk, generating feedback effects that may promote or suppress nearby planet formation. We study how spiral waves launched by planets affect the motion and collisional evolution…
Accretion discs are generally warped. If a warp in a disc is too large, the disc can `break' apart into two or more distinct planes, with only tenuous connections between them. Further if an initially planar disc is subject to a strong…
The nonlinear dynamics of pulses in a two-temperature collisionless plasma with formation of dispersion shock waves is studied. An analytical description is given for arbitrary form of an initial disturbance with smooth enough density…
We present a numerical study of the properties of the stellar velocity distribution in stellar discs which have developed a saturated, two-armed spiral structure. We follow the growth of the spiral structure deeply into the non-linear…