Related papers: Density waves in the shearing sheet V. Feedback cy…
The shearing sheet model of a galactic disk is studied anew. The theoretical description of its dynamics is based on three building blocks: Stellar orbits, which are described here in epicyclic approximation, the collisionless Boltzmann…
The problem of dynamical heating of galactic discs by spiral density waves is discussed using the shearing sheet model. The secular evolution of the disc is described quantitatively by a diffusion equation for the distribution function of…
We develop an analytic theory to describe spiral density waves propagating in a shearing disc in the weakly nonlinear regime. Such waves are generically found to be excited in simulations of turbulent accretion disks, in particular if said…
The nonlinear dynamics of a warped accretion disc is investigated in the important case of a thin Keplerian disc with negligible viscosity and self-gravity. A one-dimensional evolutionary equation is formally derived that describes the…
We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we…
We present the results of two-dimensional numerical simulations of stellar galactic disks, aimed at studying the non-linear coupling between bar and spiral waves and modes, in disks with realistically peaked rotation profiles. The power…
The generation and evolution of nonlinear waves in microwave amplifiers such as travelling wave tubes, free electron lasers and klystrons have been studied. The analysis is based on the hydrodynamic and field equations for the…
The principal results of the classic analysis of the shearing sheet and swing amplification by Julian & Toomre (1966) are re-derived in a more accessible way and then used to gain a better quantitative understanding of the dynamics of…
Gravitational coupling between protoplanetary discs and planets embedded in them leads to the emergence of spiral density waves, which evolve into shocks as they propagate through the disc. We explore the performance of a semi-analytical…
We examine the development of a transient spiral arm in a disk galaxy made up of both gas and stars. To this end we have performed numerical simulations in a shearing sheet (basically a rectangular patch of a disc) that contains gas in the…
In this paper, we study the evolution of intensive light pulses in nonlinear single-mode fibers. The dynamics of light in such fibers is described by the nonlinear Schr\"odinger equation with the Raman term, due to stimulated Raman…
Based on the nonlinear equations of the density wave theory, the evolutionary direction and the observable conditions on spiral galaxies may be derived by the qualitative analysis theory.
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
In this paper we continue investigations of the Parker-shearing instability performing numerical simulations of the magnetic flux tube dynamics in the thin flux-tube approximation. We show that evolution of flux tubes resulting from…
We explore the interplay between in-plane and vertical dynamics in stellar discs within the framework of the shearing box approximation. Julian and Toomre used the shearing sheet to show that leading density waves are amplified as they…
A numerical shearing box is used to perform three-dimensional simulations of a 1 kpc stratified cubic box of turbulent and self-gravitating interstellar medium (in a rotating frame) with supernovae and HII feedback. We vary the value of the…
We investigate numerically the propagation of density waves excited by a low-mass planet in a protoplanetary disk in the nonlinear regime, using 2D local shearing box simulations with the grid-based code Athena at high spatial resolution…
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…
Most prior works studying tidal interactions in tight star/planet or star/star binary systems have employed linear theory of a viscous fluid in a uniformly-rotating two-dimensional spherical shell. However, compact systems may have…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…