Dynamo Enhancement and Mode Selection Triggered by High Magnetic Permeability.

We present results from consistent dynamo simulations, where the electrically conducting and incompressible flow inside a cylinder vessel is forced by moving impellers numerically implemented by a penalization method. The numerical scheme models jumps of magnetic permeability for the solid impellers, resembling various configurations tested experimentally in the von Kármán sodium experiment. The most striking experimental observations are reproduced in our set of simulations. In particular, we report on the existence of a time-averaged axisymmetric dynamo mode, self-consistently generated when the magnetic permeability of the impellers exceeds a threshold. We describe a possible scenario involving both the turbulent flow in the vicinity of the impellers and the high magnetic permeability of the impellers.

Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations.

It is shown how suitably scaled, order-m moments, D_{m}^{±}, of the Elsässer vorticity fields in three-dimensional magnetohydrodynamics (MHD) can be used to identify three possible regimes for solutions of the MHD equations with magnetic Prandtl number P_{M}=1. These vorticity fields are defined by ω^{±}=curlz^{±}=ω±j, where z^{±} are Elsässer variables, and where ω and j are, respectively, the fluid vorticity and current density. This study follows recent developments in the study of three-dimensional Navier-Stokes fluid turbulence [Gibbon et al., Nonlinearity 27, 2605 (2014)NONLE50951-771510.1088/0951-7715/27/10/2605]. Our mathematical results are then compared with those from a variety of direct numerical simulations, which demonstrate that all solutions that have been investigated remain in only one of these regimes which has depleted nonlinearity. The exponents q^{±} that characterize the inertial range power-law dependencies of the z^{±} energy spectra, E^{±}(k), are then examined, and bounds are obtained. Comments are also made on  (a) the generalization of our results to the case P_{M}≠1 and (b) the relation between D_{m}^{±} and the order-m moments of gradients of magnetohydrodynamic fields, which are used to characterize intermittency in turbulent flows.

Transition from large-scale to small-scale dynamo.

The dynamo equations are solved numerically with a helical forcing corresponding to the Roberts flow. In the fully turbulent regime the flow behaves as a Roberts flow on long time scales, plus turbulent fluctuations at short time scales. The dynamo onset is controlled by the long time scales of the flow, in agreement with the former Karlsruhe experimental results. The dynamo mechanism is governed by a generalized α effect, which includes both the usual α effect and turbulent diffusion, plus all higher order effects. Beyond the onset we find that this generalized α effect scales as O(Rm(-1)), suggesting the takeover of small-scale dynamo action. This is confirmed by simulations in which dynamo occurs even if the large-scale field is artificially suppressed.

Spectral modeling of magnetohydrodynamic turbulent flows.

We present a dynamical spectral model for large-eddy simulation of the incompressible magnetohydrodynamic (MHD) equations based on the eddy damped quasinormal Markovian approximation. This model extends classical spectral large-eddy simulations for the Navier-Stokes equations to incorporate general (non-Kolmogorovian) spectra as well as eddy noise. We derive the model for MHD flows and show that the introduction of an eddy damping time for the dynamics of spectral tensors, in the absence of equipartition between the velocity and magnetic fields, leads to better agreement with direct numerical simulations, an important point for dynamo computations.

Spectral modeling of turbulent flows and the role of helicity.

We present a version of a dynamical spectral model for large eddy simulation based on the eddy damped quasinormal Markovian approximation [S. A. Orszag, in, edited by R. Balian, Proceedings of Les Houches Summer School, 1973 (Gordon and Breach, New York, 1977), p. 237; J. P. Chollet and M. Lesievr, J. Atmos. Sci. 38, 2747 (1981)]. Three distinct modifications are implemented and tested. On the one hand, whereas in current approaches, a Kolmogorov-like energy spectrum is usually assumed in order to evaluate the non-local transfer, in our method the energy spectrum of the subgrid scales adapts itself dynamically to the large-scale resolved spectrum; this first modification allows in particular for a better treatment of transient phases and instabilities, as shown on one specific example. Moreover, the model takes into account the phase relationships of the small scales, embodied, for example, in strongly localized structures such as vortex filaments. To that effect, phase information is implemented in the treatment of the so-called eddy noise in the closure model. Finally, we also consider the role that helical small scales may play in the evaluation of the transfer of energy and helicity, the two invariants of the primitive equations in the inviscid case; this leads as well to intrinsic variations in the development of helicity spectra. Therefore, our model allows for simulations of flows for a variety of circumstances and a priori at any given Reynolds number. Comparisons with direct numerical simulations of the three-dimensional Navier-Stokes equation are performed on fluids driven by an Arnold-Beltrami-Childress (ABC) flow which is a prototype of fully helical flows (velocity and vorticity fields are parallel). Good agreements are obtained for physical and spectral behavior of the large scales.

LocalMove: computing on-lattice fits for biopolymers.

Given an input Protein Data Bank file (PDB) for a protein or RNA molecule, LocalMove is a web server that determines an on-lattice representation for the input biomolecule. The web server implements a Markov Chain Monte-Carlo algorithm with simulated annealing to compute an approximate fit for either the coarse-grain model or backbone model on either the cubic or face-centered cubic lattice. LocalMove returns a PDB file as output, as well as dynamic movie of 3D images of intermediate conformations during the computation. The LocalMove server is publicly available at http://bioinformatics.bc.edu/clotelab/localmove/.

Asymptotics of RNA shapes.

RNA shapes, introduced by Giegerich et al. (2004), provide a useful classification of the branching complexity for RNA secondary structures. In this paper, we derive an exact value for the asymptotic number of RNA shapes, by relying on an elegant relation between non-ambiguous, context-free grammars, and generating functions. Our results provide a theoretical upper bound on the length of RNA sequences amenable to probabilistic shape analysis (Steffen et al., 2006; Voss et al., 2006), under the assumption that any base can basepair with any other base. Since the relation between context-free grammars and asymptotic enumeration is simple, yet not well-known in bioinformatics, we give a self-contained presentation with illustrative examples. Additionally, we prove a surprising 1-to-1 correspondence between pi-shapes and Motzkin numbers.

DIAL: a web server for the pairwise alignment of two RNA three-dimensional structures using nucleotide, dihedral angle and base-pairing similarities.

DIAL (dihedral alignment) is a web server that provides public access to a new dynamic programming algorithm for pairwise 3D structural alignment of RNA. DIAL achieves quadratic time by performing an alignment that accounts for (i) pseudo-dihedral and/or dihedral angle similarity, (ii) nucleotide sequence similarity and (iii) nucleotide base-pairing similarity. DIAL provides access to three alignment algorithms: global (Needleman-Wunsch), local (Smith-Waterman) and semiglobal (modified to yield motif search). Suboptimal alignments are optionally returned, and also Boltzmann pair probabilities Pr(a(i),b(j)) for aligned positions a(i) , b(j) from the optimal alignment. If a non-zero suboptimal alignment score ratio is entered, then the semiglobal alignment algorithm may be used to detect structurally similar occurrences of a user-specified 3D motif. The query motif may be contiguous in the linear chain or fragmented in a number of noncontiguous regions. The DIAL web server provides graphical output which allows the user to view, rotate and enlarge the 3D superposition for the optimal (and suboptimal) alignment of query to target. Although graphical output is available for all three algorithms, the semiglobal motif search may be of most interest in attempts to identify RNA motifs. DIAL is available at http://bioinformatics.bc.edu/clotelab/DIAL.

Subcritical dynamo bifurcation in the Taylor-Green flow.

We report direct numerical simulations of dynamo generation for flow generated using a Taylor-Green forcing. We find that the bifurcation is subcritical and show its bifurcation diagram. We connect the associated hysteretic behavior with hydrodynamics changes induced by the action of the Lorentz force. We show the geometry of the dynamo magnetic field and discuss how the dynamo transition can be induced when an external field is applied to the flow.

Numerical study of dynamo action at low magnetic Prandtl numbers.

We present a three-pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers P(M). The difficulty of resolving a large range of scales is circumvented by combining direct numerical simulations, a Lagrangian-averaged model and large-eddy simulations. The flow is generated by the Taylor-Green forcing; it combines a well defined structure at large scales and turbulent fluctuations at small scales. Our main findings are (i) dynamos are observed from P(M)=1 down to P(M)=10(-2), (ii) the critical magnetic Reynolds number increases sharply with P(M)(-1) as turbulence sets in and then it saturates, and (iii) in the linear growth phase, unstable magnetic modes move to smaller scales as P(M) is decreased. Then the dynamo grows at large scales and modifies the turbulent velocity fluctuations.

Effect of a random noise on scaling laws of finite Prandtl number rotating convection near threshold.

A generalized Swift-Hohenberg model including a weak random forcing, viewed as mimicking the intrinsic source of noise due to boundary defects, is used to reproduce the experimentally observed power-law variation of the correlation length of rotating convection patterns as a function of the stress parameter near threshold, and to demonstrate the sensitivity of the exponent to the amplitude of the superimposed random noise. The scaling properties of rotating convection near threshold are thus conjectured to be nonuniversal.