Transport of toroidal magnetic field by the meridional flow at the base of the solar convection zone

In this paper we discuss the transport of toroidal magnetic field by a weak meridional flow at the base of the convection zone. We utilize the differential rotation and meridional flow model developed by Rempel and incorporate feedback of a purely toroidal magnetic field in two ways: directly through the Lorentz force (magnetic tension) and indirectly through quenching of the turbulent viscosity, which affects the parametrized turbulent angular momentum transport in the model. In the case of direct Lorentz force feedback we find that a meridional flow with an amplitude of around 2 m/s can transport a magnetic field with a strength of 20 to 30 kG. Quenching of turbulent viscosity leads to deflection of the meridional flow from the magnetized region and a significant reduction of the transport velocity if the magnetic field is above equipartition strength.Comment: 8 pages, 6 figure

On-off intermittency and amplitude-phase synchronization in Keplerian shear flows

We study the development of coherent structures in local simulations of the magnetorotational instability in accretion discs in regimes of on-off intermittency. In a previous paper [Chian et al., Phys. Rev. Lett. 104, 254102 (2010)], we have shown that the laminar and bursty states due to the on-off spatiotemporal intermittency in a one-dimensional model of nonlinear waves correspond, respectively, to nonattracting coherent structures with higher and lower degrees of amplitude-phase synchronization. In this paper we extend these results to a three-dimensional model of magnetized Keplerian shear flows. Keeping the kinetic Reynolds number and the magnetic Prandtl number fixed, we investigate two different intermittent regimes by varying the plasma beta parameter. The first regime is characterized by turbulent patterns interrupted by the recurrent emergence of a large-scale coherent structure known as two-channel flow, where the state of the system can be described by a single Fourier mode. The second regime is dominated by the turbulence with sporadic emergence of coherent structures with shapes that are reminiscent of a perturbed channel flow. By computing the Fourier power and phase spectral entropies in three-dimensions, we show that the large-scale coherent structures are characterized by a high degree of amplitude-phase synchronization.Comment: 17 pages, 10 figure

Route to hyperchaos in Rayleigh-Benard convection

Transition to hyperchaotic regimes in Rayleigh-Benard convection in a square periodicity cell is studied by three-dimensional numerical simulations. By fixing the Prandtl number at P=0.3 and varying the Rayleigh number as a control parameter, a bifurcation diagram is constructed where a route to hyperchaos involving quasiperiodic regimes with two and three incommensurate frequencies, multistability, chaotic intermittent attractors and a sequence of boundary and interior crises is shown. The three largest Lyapunov exponents exhibit a linear scaling with the Rayleigh number and are positive in the final hyperchaotic attractor. Thus, a route to weak turbulence is found

Solar differential rotation and meridional flow: The role of a subadiabatic tachocline for the Taylor-Proudman balance

We present a simple model for the solar differential rotation and meridional circulation based on a mean field parameterization of the Reynolds stresses that drive the differential rotation. We include the subadiabatic part of the tachocline and show that this, in conjunction with turbulent heat conductivity within the convection zone and overshoot region, provides the key physics to break the Taylor-Proudman constraint, which dictates differential rotation with contour lines parallel to the axis of rotation in case of an isentropic stratification. We show that differential rotation with contour lines inclined by 10 - 30 degrees with respect to the axis of rotation is a robust result of the model, which does not depend on the details of the Reynolds stress and the assumed viscosity, as long as the Reynolds stress transports angular momentum toward the equator. The meridional flow is more sensitive with respect to the details of the assumed Reynolds stress, but a flow cell, equatorward at the base of the convection zone and poleward in the upper half of the convection zone, is the preferred flow pattern.Comment: 15 pages, 7 figure

Edge of Chaos and Genesis of Turbulence

The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As a control parameter is varied, the chaotic transient evolves to well-developed transient turbulence via a cascade of fractal-fractal metamorphoses. The edge state responsible for the edge of chaos and the genesis of turbulence is an unstable travelling wave in the laboratory frame, corresponding to a saddle point lying at the basin boundary in the Fourier space

Existence, uniqueness and analyticity of space-periodic solutions to the regularised long-wave equation

We consider space-periodic evolutionary and travelling-wave solutions to the regularised long-wave equation (RLWE) with damping and forcing. We establish existence, uniqueness and smoothness of the evolutionary solutions for smooth initial conditions, and global in time spatial analyticity of such solutions for analytical initial conditions. The width of the analyticity strip decays at most polynomially. We prove existence of travelling-wave solutions and uniqueness of travelling waves of a sufficiently small norm. The importance of damping is demonstrated by showing that the problem of finding travelling-wave solutions to the undamped RLWE is not well-posed. Finally, we demonstrate the asymptotic convergence of the power series expansion of travelling waves for a weak forcing.Comment: 29 pp., 4 figures, 44 reference

Waves as the source of apparent twisting motions in sunspot penumbrae

The motion of dark striations across bright filaments in a sunspot penumbra has become an important new diagnostic of convective gas flows in penumbral filaments. The nature of these striations has, however, remained unclear. Here we present an analysis of small scale motions in penumbral filaments in both simulations and observations. The simulations, when viewed from above, show fine structure with dark lanes running outwards from the dark core of the penumbral filaments. The dark lanes either occur preferentially on one side or alternate between both sides of the filament. We identify this fine structure with transverse (kink) oscillations of the filament, corresponding to a sideways swaying of the filament. These oscillations have periods in the range of 5-7 min and propagate outward and downward along the filament. Similar features are found in observed G-band intensity time series of penumbral filaments in a sunspot located near disk center obtained by the Broadband Filter Imager (BFI) on board {\it Hinode}. We also find that some filaments show dark striations moving to both sides of the filaments. Based on the agreement between simulations and observations we conclude that the motions of these striations are caused by transverse oscillations of the underlying bright filaments.Comment: Accepted for publication in Astrophysical Journal on 8th April 201

Origin of solar torsional oscillations

Helioseismology has revealed many details of solar differential rotation and also its time variation, known as torsional oscillations. So far there is no generally accepted theoretical explanation for torsional oscillations, even though a close relation to the solar activity cycle is evident. On the theoretical side non-kinematic dynamo models (including the Lorentz force feedback on differential rotation) have been used to explain torsional oscillations. In this paper we use a slightly different approach by forcing torsional oscillations in a mean field differential rotation model. Our aim is not a fully self-consistent model but rather to point out a few general properties of torsional oscillations and their possible origin that are independent from a particular dynamo model. We find that the poleward propagating high latitude branch of the torsional oscillations can be explained as a response of the coupled differential rotation / meridional flow system to periodic forcing in mid-latitudes, of either mechanical (Lorentz force) or thermal nature. The speed of the poleward propagation sets constraints on the value of the turbulent viscosity in the solar convection zone to be less than 3x10^8 m^2/s. We also show that the equatorward propagating low latitude branch is very unlikely a consequence of mechanical forcing (Lorentz force) alone, but rather of thermal origin due to the Taylor-Proudman theorem.Comment: 11 pages, 7 figures. accepted by Astrophys.