Related papers: Thick Arnold tongues
We illustrate an atomistic periodic two-dimensional stationary shear flow, $u_x = \langle \ \dot x \ \rangle = \dot \epsilon y$, using the simplest possible example, the periodic shear of just two particles ! We use a short-ranged…
Modelling the flow in a thin accretion disc like a dynamical system, we analyse the nature of the critical points of the steady solutions of the flow. For the simple inviscid disc there are two critical points, with the outer one being a…
A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…
We study, by means of extensive direct numerical simulations, the turbulent flow produced by a two-dimensional cellular forcing in a cubic box with periodic boundary conditions. In spite of the strong anisotropy of the forcing, we find that…
It is well known that instabilities of nearly integrable Hamiltonian systems occur around resonances. Dynamics near resonances of these systems is well approximated by the associated averaged system, called slow system. Each resonance is…
The central result about fast rotating-flow structures is the Taylor-Proudman theorem (TPT) which connects various aspects of the dynamics. Taylor's geometrical proof of TPT is reproduced and extended substantially, with Lie's theory for…
We consider the evolution of arbitrarily large perturbations of a prescribed pure hydrodynamical flow of an electrically conducting fluid. We study whether the flow perturbations as well as the generated magnetic fields decay or grow with…
In this work, we discuss the long-time behavior of non-rotating quasi-2D viscous flows over topographies. We develop a novel theoretical and numerical framework for the analysis of these flows, derived as a dimensional reduction of the 3D…
The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is slaved to the forcing. The forcing…
The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they…
Consider a symplectic map which possesses a normally hyperbolic invariant manifold of any even dimension with transverse homoclinic channels. We develop a topological shadowing argument to prove the existence of Arnold diffusion along the…
We study the finite-shear-rate rheology of disordered solids by means of molecular dynamics simulations in two dimensions. By systematically varying the damping magnitude $\zeta$ in the low-temperature limit, we identify two well defined…
The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and…
We study a one-dimensional discrete analog of the von Karman flow, widely investigated in turbulence. A lattice of anharmonic oscillators is excited by both ends in order to create a large scale structure in a highly nonlinear medium, in…
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…
Electron transport in two-dimensional conducting materials such as graphene, with dominant electron-electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
The flow in a cylinder driven by time harmonic oscillations of the rotation rate, called longitudinal librations, is investigated. Using a theoretical approach and axisymmetric numerical simulations, we study two distinct phenomena…
In the present work we consider the behavior of the geodesic flow on the unit tangent bundle of the 2-torus $T^2$ for an arbitrary Riemannian metric. A natural non-negative quantity which measures the complexity of the geodesic flow is the…
Slender objects are commonplace in microscale flow problems, from soft deformable sensors to biological filaments such as flagella and cilia. Whilst much research has focussed on the local translational motion of these slender bodies,…