Why, how and when MHD turbulence at low Rm becomes three-dimensional

MHD turbulence at low Magnetic Reynolds number is experimentally investigated by studying a liquid metal flow in a cubic domain. We focus on the mechanisms that determine whether the flow is quasi-2D, 3D or in any intermediate state. To this end, forcing is applied by injecting a DC current $I$ through one wall of the cube only, to drive vortices spinning along the magnetic field. Depending on the intensity of the externally applied magnetic field, these vortices extend part or all of the way through the cube. Driving the flow in this way allows us to precisely control not only the forcing intensity but also its dimensionality. A comparison with the theoretical analysis of this configuration singles out the influences of the walls and of the forcing on the flow dimensionality, which is characterised in several ways. First, when inertia drives three-dimensionality, the velocity near the wall where current is injected scales as $U_b\sim I^{2/3}$. Second, when the distance $l_z$ over which momentum diffuses under the action of the Lorentz force reaches the channel width $h$, the velocity near the opposite wall $U_t$ follows a similar law with a correction factor $(1-h/l_z)$. When $l_z<h$, by contrast, the opposite wall has less influence on the flow and $U_t\sim I^{1/2}$. The central role played by the ratio $l_z/h$ is confirmed by experimentally verifying Sommeria & Moreau (1982)'s scaling $l_z\sim N^{1/2}$ ($N$ is the interaction parameter) and finally, the nature of the three-dimensionality is further clarified by distinguishing weak and strong three-dimensionalities. It is found that both vanish only asymptotically in the limit $N\rightarrow\infty$. This provides evidence that because of the no-slip walls, 1) the transition between quasi-2D and 3D turbulence does not result from a global instability of the flow, and 2) it doesn't occur simultaneously at all scales

Wavelength selection of vortex ripples in an oscillating cylinder: The effect of curvature and background rotation

We present results of laboratory experiments on the formation, evolution, and wavelength selection of vortex ripples. These ripples formed on a sediment bed at the bottom of a water-filled oscillating cylindrical tank mounted on top of a rotating table. The table is made to oscillate sinusoidally in time, while a constant background rotation was added for some experiments. The changes in bed thickness are measured using a light attenuation technique. It was found that the wavelength normalized with the excursion length depends on both a Reynolds number and the Strouhal number. This differs from straight or annular geometries where the wavelength is proportional to the excursion length. The flow in an oscillating cylinder has the peculiarity that it develops a secondary flow in the radial direction that depends on the excursion length. The effect of this secondary circulation is evident in the radial transport for small values of the Strouhal number or in the orientation of the ripples for strong enough background rotation. Additionally, ripples in an oscillating cylinder present a rich dynamic behavior where the number of ripples can oscillate even with constant forcing parameters

Regime transitions in stratified shear flows: the link between horizontal and inclined ducts

We present an analytical model that provides the transition curves between different regimes of stratified shear flows in inclined ducts for high Schmidt number values. These curves are described by constant values of a generalized Reynolds number multiplied by the aspect ratio of the duct, showing good agreement with previous experimental results. The generalized Reynolds number is obtained by extending to inclined ducts the solution of a one-dimensional model of a stratified shear flow in a horizontal duct within a regime where advection is neglected in the momentum equation but included in the density transport equation

Pattern formation of spherical particles in an oscillating flow

We study the self-organization of spherical particles in an oscillating flow through experiments inside an oscillating box. The interactions between the particles and the time-averaged (steady streaming) flow lead to the formation of either one-particle-thick chains or multiple-particle-wide bands, depending on the oscillatory conditions. Both the chains and the bands are oriented perpendicular to the direction of oscillation with a regular spacing between them. For all our experiments, this spacing is only a function of the relative particle-fluid excursion length normalized by the particle diameter, $A_r/D$, implying that it is an intrinsic quantity that is established only by the hydrodynamics. In contrast, the width of the bands depends on both $A_r/D$ and the confinement, characterized by the particle coverage fraction $\phi$. Using the relation for the chain spacing, we accurately predict the transition from one-particle-thick chains to wider bands as a function of $\phi$ and $A_r/D$. Our experimental results are complemented with numerical simulations in which the flow around the particles is fully resolved. These simulations show that the regular chain spacing arises from the balance between long-range attractive and short-range repulsive hydrodynamic interactions, caused by the vortices in the steady streaming flow. We further show that these vortices induce an additional attractive interaction at very short range when $A_r/D\gtrsim0.7$, which stabilizes the multiple-particle-wide bands. Finally, we give a comprehensive overview of the parameter space where we illustrate the different regions using our experimental data.Comment: 20 pages, 16 figures, 1 table, to be submitted to Physical Review

Dynamics and structure of decaying shallow dipolar vortices

The current work reports on a numerical and experimental study of the evolution of decaying dipolar vortices in a shallow fluid layer. The dynamics and the structure of such vortices are investigated as a function of both their Reynolds number Re and the aspect ratio of vertical and horizontal length scales δ. By quantifying the strength of the secondary motions (vertical motions and nonzero horizontal divergence) with respect to the swirling motions of the primary vortex cores, it was found that the three-dimensionality of a shallow (δ << 1) dipolar vortex only depends on a single parameter: δ²Re. Depending on the value of this parameter, three flow regimes are observed for shallow dipolar vortices: (1) a quasi-two-dimensional regime where the structure of the dipolar vortex remains almost unchanged throughout its lifetime, (2) a transitional regime where the structure presents some three-dimensional characteristics but remains coherent, and (3) a three-dimensional regime where the structure of the dipolar vortex acquires a complicated three-dimensional shape with a persistent spanwise vortex at its front

The break-up of Ekman theory in a flow subjected to background rotation and driven by a non-conservative body force

We present an experimental/numerical study of a dipolar flow structure in a shallow layer of electrolyte driven by electromagnetic forcing and subjected to background rotation. The aim of this study is to determine the influence of a non-conservative body force on the range of applicability of the classical Ekman boundary layer theory in rapidly rotating systems. To address this question, we study the response of the flow to the three control parameters: the magnitude of the forcing, the rotation rate of the system, and the shallowness of the layer. This response is quantified taking into account the magnitude of the flow velocity (represented by the Reynolds number), the symmetry between both vortex cores, and the vertical profile of the horizontal velocity. As in the case without background rotation, the response of the flow exhibits two scaling regimes (a linear and a nonlinear regime) in which the flow exhibits different vertical profiles of velocity. The transition between the two regimes occurs when the convective acceleration becomes of the same order as the viscous damping. This suggests that the applicability of the Ekman theory depends on the existence of a balance between the forcing and the damping due to the Ekman layers and does not depend solely on the value of the Rossby number as for decaying flows. On the other hand, the cyclone/anticyclone asymmetry is governed exclusively by the Rossby number. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4766818

Inertial oscillations in a confined vortex subjected to background rotation

No abstract

Inertial oscillations in a confined monopolar vortex subjected to background rotation

We study the axisymmetric inertial oscillations in a confined monopolar vortex under the influence of background rotation. By first focusing on the inviscid linear dynamics, and later studying the effects of viscosity and of a no-slip bottom, we characterize the effects of rotation and confinement. It was found that background rotation allows for oscillations outside the vortex core even with frequencies larger than 2O, with O the background rotation rate. However, confinement is necessary for the system to sustain oscillations with frequencies smaller than 2O. Through the analytical solution for a small perturbation of a Rankine vortex, we obtain five regimes where the oscillations are qualitatively different, depending on their frequency. Numerical results for the linear inviscid waves sustained by a Lamb–Oseen vortex show a similar behavior. The effects of viscosity are twofold: the oscillations are damped and the vortex sustaining the oscillations is modified. When a no-slip bottom is considered, a boundary layer drives a secondary motion superimposed on the inertial oscillations. In this case, the vortex is quickly damped, but the oscillations persist due to the background rotation

Educational level, socioeconomic status and aphasia research: A comment on Connor et al. (2001) - Effect of socioeconomic status on aphasia severity and recovery

Is there a relation between socioeconomic factors and aphasia severity and recovery? Connor, Obler, Tocco, Fitzpatrick, and Albert (2001) describe correlations between the educational level and socioeconomic status of aphasic subjects with aphasia severity and subsequent recovery. As stated in the introduction by Connor et al. (2001), studies of the influence of educational level and literacy (or illiteracy) on aphasia severity have yielded conflicting results, while no significant link between socioeconomic status and aphasia severity and recovery has been established. In this brief note, we will comment on their findings and conclusions, beginning first with a brief review of literacy and aphasia research, and complexities encountered in these fields of investigation. This serves as a general background to our specific comments on Connor et al. (2001), which will be focusing on methodological issues and the importance of taking normative values in consideration when subjects with different socio-cultural or socio-economic backgrounds are assessed. (C) 2003 Elsevier Science (USA). All rights reserved