Related papers: Nonlinear bending waves in Keplerian accretion dis…
A dispersion relation for gravity waves in water covered by disk-like impurities embedded in a viscous matrix is derived. The macroscopic equations are obtained by ensemble-averaging the fluid equations at the disk scale in the asymptotic…
Understanding oscillations and waves in astrophysical fluid bodies helps to elucidate their observed variability and the underlying physical mechanisms. Indeed, global oscillations and bending modes of accretion discs or tori may be…
The propagation of nonlinear waves in one dimensional space, unsteady and compressible flow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagate long the characteristic path using the characteristics…
The effects of ambipolar diffusion on the linear stability of weakly ionised accretion discs are examined. Earlier work on this topic has focused on axial magnetic fields and perturbation wavenumbers. We consider here more general field and…
We study the nonlinear evolution of unstable flux compactifications, applying numerical relativity techniques to solve the Einstein equations in $D$ dimensions coupled to a $q$-form field and positive cosmological constant. We show that…
Dispersive shock waves dominate wave-breaking phenomena in Hamiltonian systems. In the absence of loss, these highly irregular and disordered waves are potentially reversible. However, no experimental evidence has been given about the…
A problem in nonlinear water-wave propagation on the surface of an inviscid, stationary fluid is presented. The primary surface wave, suitably initiated at some radius, is taken to be a slowly evolving nonlinear cylindrical wave (governed…
The effect of the Kerr nonlinearity on linear non-diffractive Bessel beams is investigated analytically and numerically using the nonlinear Schr\"odinger equation. The nonlinearity is shown to primarily affect the central parts of the…
Non-linear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce…
The manner in which warps in accretion disks evolve depends on the magnitude of the viscosity. For small viscosity $(\alpha < H/R)$ the warp evolves in a wave-like manner; for large viscosity $H/R<\alpha \ll 1$ it evolves diffusively. Here…
We are carrying out a programme of non-linear time-dependent numerical calculations to study the evolution of the thermal instability driven by radiation pressure in transonic accretion discs around black holes. In our previous studies we…
A scaling argument is presented that leads to a shallow water theory of non-axisymmetric disturbances in annular sections of thin Keplerian disks. To develop a theoretical construction that will aid in physically understanding the…
We present numerical simulations of misaligned discs around a spinning black hole covering a range of parameters. Previous simulations have shown that discs that are strongly warped by a forced precession -- in this case the Lense-Thirring…
We present results from a suite of three-dimensional global hydrodynamic simulations which show that spiral density waves propagating in circumstellar disks are unstable to the growth of a parametric instability that leads to break-down of…
Accretion disks in binary systems can experience hydrodynamic impact at inner as well as outer edges. The first case is typical for protoplanetary disks around young T Tau stars. The second one is typical for circumstellar disks in close…
We study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1-D Euclidean space. The diffusion coefficient depends on the gradient in analogy with the p-Laplacian and may be degenerate.…
We study the nonlinear wave dynamics of one-dimensional chains of polycatenated rings. These interlocked structures support amplitude-dependent nonlinear wave propagation driven by tensile activation and internal structural flexibility,…
We study the evolution of nonlinear surface gravity water-wave packets developing from modulational instability over an uneven bottom. A nonlinear Schr\"odinger equation (NLSE) with coefficients varying in space along propagation is used as…
Warped accretion discs are expected in many protostellar binary systems. In this paper, we study the long-term evolution of disc warp and precession for discs with dimensionless thickness $H/r$ larger than their viscosity parameter…
We develop several aspects of the theory of gaseous astrophysical discs in which the gravity of the disc makes a significant contribution to its structure and dynamics. We show how the internal gravitational potential can be expanded in…