Related papers: A viscous-convective instability in laminar Kepler…
Using hydrodynamic approach, it is shown that the properties of a marginally stable collisionless stellar disc resemble those of a thermodynamic system undergoing a gas--liquid phase transition. The maximum in Toomre's stability diagram,…
Gravitational stability of a disc consisting of the gaseous and the stellar components are studied in the linear regime when the gaseous component is turbulent. A phenomenological approach is adopted to describe the turbulence, in which not…
It is well-known that at the high Reynolds number, the linearized Navier-Stokes equations around the inviscid stable shear profile admit growing mode solutions due to the destabilizing effect of the viscosity. This phenomenon, called…
This article discusses the modeling of perturbed potential temperature in an atmospheric boundary layer. We adopt a convection-diffusion model with specified initial and boundary conditions that resulted from simplifying the linearized…
We study the equations obtained from linearizing the compressible Navier-Stokes equations around a steady-state profile with a heavier fluid lying above a lighter fluid along a planar interface, i.e. a Rayleigh-Taylor instability. We…
We use well-established observational evidence to draw conclusions about the fundamental nature of the viscosity in accretion discs. To do this, we first summarise the observational evidence for the value of the dimensionless accretion disc…
In this article, a perturbation theory of the compressible Navier-Stokes equations in $\mathbb{R}^n$ $(n \geq 3)$ is studied to investigate decay estimate of solutions around a non-constant state. As a concrete problem, stability is…
Many accretion discs are thought to be warped. Recent hydrodynamical simulations show that (i) discs can break into distinct planes when the amplitude of an imposed warp is sufficiently high and the viscosity sufficiently low, and that (ii)…
We derive expressions for the local ideal magnetohydrodynamic (MHD) equations for a warped astrophysical disc using a warped shearing box formalism. A perturbation expansion of these equations to first order in the warping amplitude leads…
We present a model for the transport of anisotropic turbulence in an accretion disc. The model uses the Reynolds stress tensor approach in the mean field approximation. To study the role of convection in a protoplanetary disc, we combine…
Sharp density features in protoplanetary discs, for instance at the edge of a magnetically dead zone, have recently been proposed as effective barriers to slow down or even stop the problematically fast migration of planetary cores into…
The viscous evolution of a thin disc around a central object is considered. Such discs are described by self-similar solutions in which either all or none of the inflowing mass accretes. An approximate solution for the partial accretion…
In this paper we examine the issue of characterising the transport associated with gravitational instabilities in relatively cold discs, discussing in particular the conditions under which it can be described within a local, viscous…
The local gravitational instability of rotating discs is believed to be an important mechanism in different astrophysical processes, including the formation of gas and stellar clumps in galaxies. We aim to study in three dimensions the…
We review results on the dynamics of warped gaseous discs. We consider tidal perturbation of a Keplerian disc by a companion star orbiting in a plane inclined to the disc. The perturbation induces the precession of the disc, and thus of any…
Hydromagnetic stresses in accretion discs have been the subject of intense theoretical research over the past one and a half decades. Most of the disc simulations have assumed a small initial magnetic field and studied the turbulence that…
We consider the effects of varying dispersion and nonlinearity on the stability of periodic traveling wave solutions of nonlinear PDE of KdV-type, including generalized KdV and Benjamin-Ono equations. In this investigation, we consider the…
We employ numerical simulations to understand the evolution of elastic standing waves in disordered frictional disk systems, where the dispersion relations of rotational sound modes are analyzed in detail. As in the case of frictional…
Axisymmetric accretion disks in vicinity of a central compact body are studied. For the simple models such as vertically isothermal disks as well as adiabatic ones the exact solutions to the steady-state MHD (magneto-hydrodynamic) system…
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…