Related papers: A self-sustaining nonlinear dynamo process in Kepl…
A 3-dimensional non-commutative oscillator with no mass term but with a certain momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The latter corresponds to a Dirac…
In this paper, we provide a classification of steady solutions to two-dimensional incompressible Euler equations in terms of the set of flow angles. The first main result asserts that the set of flow angles of any bounded steady flow in the…
A conducting Taylor-Couette flow with quasi-Keplerian rotation law containing a toroidal magnetic field serves as a mean-field dynamo model of the Tayler-Spruit-type. The flows are unstable against nonaxisymmetric perturbations which form…
In the paper we study the Boltzmann equation in the diffusive limit in a channel domain $\mathbb{T}^2\times (-1,1)$ for the 3D kinetic Couette flow. Our results demonstrate that the first-order approximation of the solutions is governed by…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that…
Streamwise and quasi-streamwise elongated structures have been shown to play a significant role in turbulent shear flows. We model the mean behavior of fully turbulent plane Couette flow using a streamwise constant projection of the Navier…
Laminar shear flows can display large non-modal perturbation growth, often through the lift-up mechansm, and can undergo subcritical transition to turbulence. The process is three-dimensional. Two-dimensional (2D) spanwise-independent…
Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the Navier-Stokes equations. We construct a…
The non-modal kinetic theory of the kinetic drift instability of plasma shear flows [Phys.Plasmas, 18, 062103 (2011)] is extended to the investigation of the long-time evolution of the hydrodynamic ion temperature gradient and resistive…
We numerically solve the magnetic induction equation in a spherical shell geometry, with a kinematically prescribed axisymmetric flow that consists of a superposition of a small-scale helical flow and a large-scale shear flow. The…
This paper deals with the problem of hydrodynamic shear turbulence in non-magnetized Keplerian disks. We wish to draw attention to a route to hydrodynamic turbulence which seems to be little known by the astrophysical community, but which…
We have performed numerical simulations of boundary-driven dynamos using a three-dimensional non-linear magnetohydrodynamical model in a spherical shell geometry. A conducting fluid of magnetic Prandtl number Pm=0.01 is driven into motion…
We present axisymmetric numerical calculations of the fluid flow induced in a spherical shell with inner sphere rotating and outer sphere stationary. A magnetic field is also imposed, consisting of particular linear combinations of axial…
We study the unsteady incompressible Navier-Stokes equations in three dimensions interacting with a non-linear flexible shell of Koiter type. This leads to a coupled system of non-linear PDEs where the moving part of the boundary is an…
We report 3D numerical simulations of the flow of an electrically conducting fluid in a spherical shell when a magnetic field is applied. Different spherical Couette configurations are investigated, by varying the rotation ratio between the…
We prove the asymptotic stability of shear flows close to the Couette flow for the 2-D inhomogeneous incompressible Euler equations on $\mathbb{T}\times \mathbb{R}$. More precisely, if the initial velocity is close to the Couette flow and…
Quasi-Keplerian flow, a special regime of Taylor-Couette co-rotating flow, is of great astrophysical interest for studying angular momentum transport in accretion disks. The well-known magnetorotational instability (MRI) successfully…
In this paper we argue that differential rotation can possibly sustain hydrodynamic turbulence in the absence of magnetic field. We explain why the non-linearities of the hydrodynamic equations (i.e. turbulent diffusion) should not be…
We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes…
A three-dimensional numerical computation of magnetohydrodynamic dynamo behavior is described. The dynamo is mechanically forced with a driving term of the Taylor-Green type. The magnetic field development is followed from negligibly small…