Related papers: A Weakly Nonlinear Model for the Damping of Resona…
This paper addresses resonantly forced spiral density waves in a dense planetary ring which is close to the threshold for viscous overstability. We solve numerically the hydrodynamical equations for a dense, axisymmetric thin disk in the…
This paper examines the onset of the viscous overstability in dense particulate rings. First, we formulate a dense gas kinetic theory that is applicable to the Saturnian system. Our model is essentially that of Araki and Tremaine (1986),…
We perform axisymmetric hydrodynamical simulations that describe the nonlinear outcome of the viscous overstability in dense planetary rings. These simulations are particularly relevant for Cassini observations of fine-scale structure in…
Irregular structure in planetary rings is often attributed to the intrinsic instabilities of a homogeneous state undergoing Keplerian shear. Previously these have been analysed with simple hydrodynamic models. We instead employ a kinetic…
An exact solution of the collisionless time-dependent Vlasov equation is found for the first time. By means of this solution the behavior of the Langmuir waves in the nonlinear stage is considered. The analysis is restricted by the…
In this paper I develop a nonlinear theory of tightly-wound (highly twisted) eccentric waves in astrophysical discs, based on the averaged Lagrangian method of Whitham. Viscous dissipation is included in the theory by use of a…
This paper discusses new perspectives and approaches to the problem of disk dynamics where, in this study, we focus on the effects of viscous instabilities influenced by boundary effects. The Boussinesq approximation of the viscous large…
We investigate the linear axisymmetric viscous overstability in dense planetary rings with typical values of the dynamical optical depth $\tau\gtrsim 0.5$. We develop a granular flow model which accounts for the particulate nature of a…
We study modulational stability and instability in the Whitham equation, combining the dispersion relation of water waves and a nonlinearity of the shallow water equations, and modified to permit the effects of surface tension and constant…
This paper addresses the fine-scale axisymmetric structure exhibited in Saturn's A and B-rings. We aim to explain both the periodic microstructure on 150-220m, revealed by the Cassini UVIS and RSS instruments, and the irregular variations…
We investigate a higher order nonlinear Schr\"odinger equation with linear damping and weak viscosity, recently proposed as a model for deep water waves exhibiting frequency downshifting. Through analysis and numerical simulations, we…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…
We provide a rigorous justification of various kinetic regimes exhibited by the nonlinear Schr\"{o}dinger equation with an additive stochastic forcing and a viscous dissipation. The importance of such damped-driven models stems from their…
In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is…
Hydrodynamic systems arising in swarming modelling include nonlocal forces in the form of attractive-repulsive potentials as well as pressure terms modelling strong local repulsion. We focus on the case where there is a balance between…
We study the excitation and damping of tides in close binary systems, accounting for the leading order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct effects: three-mode nonlinear interactions…
We study the weakly non-linear development of shear-driven gravity waves, and investigate the mixing properties of the finite amplitude solutions. Calculations to date have been restricted to the linear theory, which predicts that gravity…
We study the nonlinear energy transfer around the peak of the spectrum of surface gravity waves by taking into account nonhomogeneous effects. In the narrow-banded approximation the kinetic equation resulting from a nonhomogeneous wave…
Planets embedded in protoplanetary discs are capable of creating a wide variety of substructures through gravitational interactions. This process is mediated through the excitation and damping of density waves which carry angular momentum…