相关论文: On some recent results about inertial manifolds an…
We show that the initial-value problem for the non-relativistic magnetic dynamo equation turns out to be ill-posed when the electromotive force depends linearly on the magnetic field. This result implies that the increasing of magnetic…
A version of extended magnetohydrodynamics (MHD) that incorporates electron inertia is obtained by constructing an action principle. Unlike MHD which freezes in magnetic flux, the present theory freezes in an alternative flux related to the…
Numerical simulations of kinematic dynamo action in steady and 3-d ABC flows are presented with special focus on growth rates and multiple periods of the prescribed velocity field. It is found that the difference in growth rate is due to…
The induction equation of kinematic magnetohydrodynamics is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent…
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…
Magneto-rotational instability (MRI) is an important instability mechanism for rotating flows with magnetic fields. In particular, when the strength of the magnetic field tends to zero, the stability criterion for rotating flows is…
Kinematic dynamo theory is presented here for turbulent conductive fluids. We describe how inhomogeneous magnetic fluctuations are generated below the viscous scale of turbulence where the spatial smoothness of the velocity permits a…
The kinematic dynamo problem is investigated for the flow of a conducting fluid in a cylindrical, periodic tube with conducting walls. The methods used are an eigenvalue analysis of the steady regime, and the three-dimensional solution of…
We investigate why the non-slip boundary condition for the velocity, imposed in the direction of impressed magnetic fields, can contribute to the magnetic inhibition effect based on the nonhomogeneous magnetic Rayleigh--Taylor (abbr. NMRT)…
Recent studies suggest that unstable, non-chaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role…
We supplement the mean field dynamo growth equation with the total magnetic helicity evolution equation. This provides an explicitly time dependent model for alpha quenching in dynamo theory. For dynamos without shear, this approach…
This article considers the ideal 2D magnetohydrodynamic equations on an infinite periodic channel close to a combination of an affine shear flow, called Couette flow, and a constant magnetic field. This setting combines important physical…
In this article, we devote to the existence of an $N$-dimensional inertial manifold for the incompressible Navier-Stokes equations in $\mathbb{T}^{d}$ ($d=2,3$). Our results can be summarized as two aspects: Firstly, we construct an…
Choosing a simple class of flows, with characteristics that may be present in the Earth's core, we study the ability to generate a magnetic field when the flow is permitted to oscillate periodically in time. The flow characteristics are…
Large-scale dynamo action due to turbulence in the presence of a linear shear flow is studied. Our treatment is quasilinear and kinematic but is non perturbative in the shear strength. We derive the integro-differential equation for the…
A kinetic theory of classical particles serves as a unified basis for developing a geometric $3+1$ spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases…
This paper is devoted to analytical solutions for the base flow and temporal stability of a liquid film driven by gravity over an inclined plane when the fluid rheology is given by the Carreau-Yasuda model, a general description that…
This pedagogical note revisits the concept of electromagnetic helicity in classical systems. In particular, magnetic helicity and its role in mean field dynamo theories is briefly discussed highlighting the major mathematical inconsistency…
The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing Inertial Manifolds for such type of problems is suggested…
First we prove a general spectral theorem for the linear Navier-Stokes (NS) operator in both 2D and 3D. The spectral theorem says that the spectrum consists of only eigenvalues which lie in a parabolic region, and the eigenfunctions (and…