Related papers: A viscous-convective instability in laminar Kepler…
The stability of toroidal magnetic fields in rotating radiative stellar zones is studied for realistic values of both the Prandtl numbers. The two considered models for the magnetic geometry represent fields with odd and even symmetry with…
We discuss steady viscous Keplerian decretion discs around rapidly rotating stars. We assume that low frequency modes, which may be excited by the opacity bump mechanism, convective motion in the core, or tidal force if the star is in a…
In the classical theory of thin disc accretion discs, the constraints of mass and angular momentum conservation lead to a diffusion-like equation for the turbulent evolution of the surface density. Here, we revisit this problem, extending…
The linear theory for rotating compressible convection in a plane layer geometry is presented for the astrophysically-relevant case of low Prandtl number gases. When the rotation rate of the system is large, the flow remains geostrophically…
In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic…
We present simulations of the non-linear evolution of streaming instabilities in protoplanetary disks. The two components of the disk, gas treated with grid hydrodynamics and solids treated as superparticles, are mutually coupled by drag…
The minimalist approach in the study of perturbations in fluid dynamics and magnetohydrodynamics involves describing their evolution in the linear regime using a single first-order ordinary differential equation, dubbed principal equation.…
The KdV-Burgers equation is a canonical model describing the interplay between nonlinearity, viscosity and dispersion, and it admits viscous-dispersive shocks as traveling wave solutions. In this paper, we establish an $L^2$-contraction…
This thesis investigates phenomena occurring in black-hole accretion discs which are likely to induce high-frequency quasi-periodic variability. Two classes of pseudo-relativistic theoretical models are studied. The first is based on the…
Accretion discs are ubiquitous in the universe and it is a crucial issue to understand how angular momentum and mass are being radially transported in these objects. Here, we study the role played by non-linear spiral patterns within…
We discuss the basic hydrodynamics that determines the density structure of the disks around hot stars. Observational evidence supports the idea that these disks are Keplerian (rotationally supported) gaseous disks. A popular scenario in…
We study quasi-periodic eigenvalue problems that arise in the stability analysis of periodic traveling wave solutions to Hamiltonian PDEs. We establish bounds on regions in the complex plane when the eigenvalues may deviate from the…
Linear stability of solid body rotating flows with axisymmetric density variations is addressed analytically. Considering inviscid disturbances, a non trivial dispersion relation is obtained and it is shown that the instability is of…
Magnetized disk winds and wind-driven accretion are an essential and intensively studied dispersion mechanism of protoplanetary disks. However, the stability of these mechanisms has yet to be adequately examined. This paper employs…
We consider discs that orbit a central object and are tidally perturbed by a circular orbit companion. Such discs are sometimes subject to an eccentric instability due to the effects of certain resonances. Eccentric instabilities may be…
Here, the perturbation equation for a dissipative medium is derived from the first principle from the linearized compressible Navier-Stokes equation without Stokes's hypothesis. The dispersion relations of this generic governing equation…
Magnetic buoyancy instability plays an important role in the evolution of astrophysical magnetic fields. Here we revisit the problem introduced by \citet{Gilman_1970} of the short wavelength linear stability of a plane layer of compressible…
In low-mass disks, turbulent torques are probably the most important way of redistributing angular momentum. Here we present the theory of turbulent accretion disks. We show the molecular viscosity is far too small to account for the…
In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature…
We review our current knowledge of thermal and viscous instabilities in accretion discs around compact objects. We begin with classical disc models based on analytic viscosity prescriptions, discussing physical uncertainties and exploring…