Related papers: Nonlinear Scale Invariance in Local Disk Flows
Hydrodynamic unstratified keplerian flows are known to be linearly stable at all Reynolds numbers, but may nevertheless become turbulent through nonlinear mechanisms. However, in the last ten years, conflicting points of view have appeared…
Thin viscous Keplerian accretion disks are considered asymptotically stable, even though they can show significant dynamic activity on short timescales. In this paper the dynamics of non-axisymmetric hydrodynamical disturbances of disks are…
Many dynamical interactions can induce eccentricities in astrophysical accretion disks. Disk eccentricities in turn seed a variety of instabilities, even in ideal hydrodynamics. We use 3D nonlinear simulations and 2+1D linear calculations…
Turbulent viscosity in cold accretion disks is likely to be hydrodynamic in origin. We investigate the growth of hydrodynamic perturbations in a small region of a disk, which we model as a linear shear flow with Coriolis force, between two…
We analyze the hydrodynamic stability of force-driven parallel shear flows in nonequilibrium molecular simulations with three-dimensional periodic boundary conditions. We show that flows simulated in this way can be linearly unstable, and…
The linear stability of accretion disks is revisited. The governing equations are expanded asymptotically and solved to first order in the expansion parameter $\epsilon$ defined by the ratio of the disk's vertical thickness to its radial…
(Abridged) We analyse the stability and evolution of power-law accretion disc models. These have midplane densities that follow radial power-laws, and have either temperature or entropy distributions that are power-law functions of…
Subcritical transition to turbulence in Keplerian accretion disks is still a controversial issue and some theoretical progress is required in order to determine whether or not this scenario provides a plausible explanation for the origin of…
Direct numerical simulations are performed for the steady flow normal to a circular disk at the Reynolds number of 1000. Numerical simulations are conducted with different levels of simplification procedure by reducing the azimuthal…
The dynamics and stability of a fluid-filled hollow cylindrical shell rolling on an inclined plane are analyzed. We study the motion in two dimensions by analyzing the interaction between the fluid and the cylindrical shell. An analytical…
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 examine long-time properties of the ideal dynamics of three--dimensional flows, in the presence or not of an imposed solid-body rotation and with or without helicity (velocity-vorticity correlation). In all cases the results agree with…
We study the hydrodynamical stability of the laminar flows associated with warped astrophysical discs using numerical simulations of warped shearing boxes. We recover linear growth rates reported previously due to a parametric resonance of…
In this paper, we investigate the nonlinear stability of the Couette flow for the two-dimensional compressible Navier--Stokes equations at high Reynolds numbers ($Re$) regime. It was proved that if the initial data $(\rho_{in},u_{in})$…
Experiments in an extraordinary turbulent boundary layer called the sink flow, displaying a perfect streamwise invariance, show a wide extent of logarithmic scaling for moments of streamwise velocity up to order 12, even at moderate…
A three-layer asymptotic structure for turbulent pipe flow is proposed, revealing in terms of intermediate variables, the existence of a Reynolds-number invariant logarithmic region. It provides a theoretical foundation for addressing…
We report on measurements of self-diffusion coefficients in discrete numerical simulations of steady, homogeneous, collisional shearing flows of nearly identical, frictional, inelastic spheres. We focus on a range of relatively high solid…
Two-dimensional free-surface flow over localised topography is examined with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a…
A viscous instability in shearing laminar axisymmetric hydrodynamic flows around a gravitating center is described. In the linearized hydrodynamic equations written in the Boussinesq approximation with microscopic molecular transport…
The susceptibility of timestepping algorithms to numerical instabilities is an important consideration when simulating partial differential equations (PDEs). Here we identify and analyze a pernicious numerical instability arising in…