Related papers: A self-sustaining nonlinear dynamo process in Kepl…
We describe a special class of steady Couette flows in dilute granular gases admitting a non-Newtonian hydrodynamic description for strong dissipation. The class occurs when viscous heating exactly balances inelastic cooling, resulting in a…
In this paper, we consider the Boussinesq equations with magnetohydrodynamics convection in the domain $\mathbb{T} \times \mathbb{R}$ and establishes the nonlinear stability of the Couette flow $(\mathbf{u}_{sh} = (y,0), \mathbf{b}_{sh} =…
The emergence of turbulence in shear flows is a well-investigated field. Yet, one of major issues is the apparent contradiction between linear stability analysis quoting a flow to be stable and results from experiments and simulations…
It is widely accepted that astrophysical magnetic fields are generated by dynamo action. In many cases these fields exhibit organisation on a scale larger than that of the underlying turbulent flow (e.g., the eleven-year solar cycle). The…
We establish the nonlinear stability threshold $O(\nu^{3/2})$ for the three-dimensional Couette flow governed by the compressible Navier--Stokes equations. While stability thresholds are well understood in two dimensions for both…
We investigate numerically kinematic dynamos driven by flow of electrically conducting fluid in the shell between two concentric differentially rotating spheres, a configuration normally referred to as spherical Couette flow. We compare…
The no-slip boundary condition results in a velocity shear forming in fluid flow near a solid surface. This shear flow supports the turbulence characteristic of fluid flow near boundaries at Reynolds numbers above $\approx1000$ by making…
Equilibrium, traveling wave, and periodic orbit solutions of pipe, channel, and plane Couette flows can now be computed precisely at Reynolds numbers above the onset of turbulence. These invariant solutions capture the complex dynamics of…
Stationary flows of an inviscid and incompressible fluid of constant density in the region $D=(0, L)\times \mathbb R^2$, periodic in the second and third variables, are considered. The flux and the Bernoulli function are prescribed at each…
It is numerically demonstrated by means of a magnetohydrodynamics code that a short Taylor-Couette setup with a body force can sustain dynamo action. The magnetic threshold is comparable to what is usually obtained in spherical geometries.…
It is shown that the physical interpretation of Elie Cartan three-dimensional space torsion as couple asymmetric stress, has the effect of damping, previously Riemannian unstable Couette planar shear flow, leading to stability of the flow…
A concise review is given of astrophysically motivated experimental and theoretical research on Taylor-Couette flow. The flows of interest rotate differentially with inner cylinder faster than outer one but are linearly stable against…
Cold accretion disks such as those in star-forming systems, quiescent cataclysmic variables, and some active galactic nuclei, are expected to have neutral gas which does not couple well to magnetic fields. The turbulent viscosity in such…
According to Rayleigh's criterion, rotating flows are linearly stable when their specific angular momentum increases radially outward. The celebrated magnetorotational instability opens a way to destabilize those flows, as long as the…
We attempt to address the old problem of plane shear flows: the origin of turbulence and hence transport of angular momentum in accretion flows as well as laboratory flows, such as plane Couette flow. We undertake the problem by introducing…
Three-dimensional direct numerical simulations of an incompressible open square cavity flow are conducted. Features of the permanent (non-linear) regime together with the linear stability analysis of a two-dimensional steady base flow are…
This paper examines the linearized stability of plane Couette flow for stress-power law fluids, which exhibit non-monotonic stress-strain rate behavior. The constitutive model is derived from a thermodynamic framework using a non-convex…
We prove that, in a two-dimensional strip, a steady flow of an ideal incompressible fluid with no stationary point and tangential boundary conditions is a shear flow. The same conclusion holds for a bounded steady flow in a half-plane. The…
The origin of hydrodynamic turbulence in rotating shear flow is a long standing puzzle. Resolving it is especially important in astrophysics when the flow angular momentum profile is Keplerian which forms an accretion disk having negligible…
The origin of hydrodynamical instability and turbulence in the Keplerian accretion disk is a long-standing puzzle. The flow therein is linearly stable. Here we explore the evolution of perturbation in this flow in the presence of an…