Magnetic spherical Couette flow in linear combinations of axial and dipolar fields

We present axisymmetric numerical calculations of the fluid flow induced in a spherical shell with inner sphere rotating and outer sphere stationary. A magnetic field is also imposed, consisting of particular linear combinations of axial and dipolar fields, chosen to make $B_r=0$ at either the outer sphere, or the inner, or in between. This leads to the formation of Shercliff shear layers at these particular locations. We then consider the effect of increasingly large inertial effects, and show that an outer Shercliff layer is eventually de-stabilized, an inner Shercliff layer appears to remain stable, and an in-between Shercliff layer is almost completely disrupted even before the onset of time-dependence, which does eventually occur though

Tidally driven dynamos in a rotating sphere

Large-scale planetary or stellar magnetic fields generated by a dynamo effect are mostly attributed to flows forced by buoyancy forces in electrically conducting fluid layers. However, these large-scale fields may also be controlled by tides, as previously suggested for the star $\tau$-boo, Mars or the Early Moon. By simulating a small local patch of a rotating fluid, \cite{Barker2014} have recently shown that tides can drive small-scale dynamos by exciting a hydrodynamic instability, the so-called elliptical (or tidal) instability. By performing global magnetohydrodynamic simulations of a rotating spherical fluid body, we investigate if this instability can also drive the observed large-scale magnetic fields. We are thus interested by the dynamo threshold and the generated magnetic field in order to test if such a mechanism is relevant for planets and stars. Rather than solving the problem in a geometry deformed by tides, we consider a spherical fluid body and add a body force to mimic the tidal deformation in the bulk of the fluid. This allows us to use an efficient spectral code to solve the magnetohydrodynamic problem. We first compare the hydrodynamic results with theoretical asymptotic results, and numerical results obtained in a truely deformed ellipsoid, which confirms the presence of the elliptical instability. We then perform magnetohydrodynamic simulations, and investigate the dynamo capability of the flow. Kinematic and self-consistent dynamos are finally simulated, showing that the elliptical instability is capable of generating dipole dominated large-scale magnetic field in global simulations of a fluid rotating sphere.Comment: Astrophysical Journal Letters In press, (accepted) (2014) (accepted

Information length as a new diagnostic of stochastic resonance

Stochastic resonance is a subtle, yet powerful phenomenon in which noise plays an interesting role of amplifying a signal instead of attenuating it. It has attracted great attention with a vast number of applications in physics, chemistry, biology, etc. Popular measures to study stochastic resonance include signal-to-noise ratios, residence time distributions, and different information theoretic measures. Here, we show that the information length provides a novel method to capture stochastic resonance. The information length measures the total number of statistically different states along the path of a system. Specifically, we consider the classical double-well model of stochastic resonance in which a particle in a potential V ( x , t ) = [ - x 2 / 2 + x 4 / 4 - A sin ( ω t ) x ] is subject to an additional stochastic forcing that causes it to occasionally jump between the two wells at x ≈ ± 1 . We present direct numerical solutions of the Fokker–Planck equation for the probability density function p ( x , t ) for ω = 10 - 2 to 10 - 6 , and A ∈ [ 0 , 0 . 2 ] and show that the information length shows a very clear signal of the resonance. That is, stochastic resonance is reflected in the total number of different statistical states that a system passes through

On the necessary conditions for bursts of convection within the rapidly rotating cylindrical annulus

Zonal flows are often found in rotating convective systems. Not only are these jet-flows driven by the convection, they can also have a profound effect on the nature of the convection. In this work the cylindrical annulus geometry is exploited in order to perform nonlinear simulations seeking to produce strong zonal flows and multiple jets. The parameter regime is extended to Prandtl numbers that are not unity. Multiple jets are found to be spaced according to a Rhines scaling based on the zonal flow speed, not the convective velocity speed. Under certain conditions the nonlinear convection appears in quasi-periodic bursts. A mean field stability analysis is performed around a basic state containing both the zonal flow and the mean temperature gradient found from the nonlinear simulations. The convective growth rates are found to fluctuate with both of these mean quantities suggesting that both are necessary in order for the bursting phenomenon to occur

Similarity solutions of the thermocline equations

We apply symmetry group methods to find the group of transformations of the dependent and independent variables that leave the thermocline equations unchanged, These transformations lead to an optimal subset of sixteen forms of similarity solution, Each form obeys an equation with one fewer dependent variable than the original thermocline equations. Previously obtained similarity solutions, which are based solely upon scaling symmetries, are special cases of just three of these forms. Two of the sixteen forms lead to linear, two-dimensional, advection-diffusion equations for the temperature, Bernoulli functional or potential vorticity. Simple exact solutions contain internal boundary layers that resemble the thermocline in subtropical gyres

Time-dependent probability density functions and information geometry of the low-to-high confinement transition in fusion plasma

We report a first study of time-dependent Probability Density Functions (PDFs) in the Low-to- High confinement mode (L-H) transition by extending the previous prey-predator-type model (Kim & Diamond, Phys. Rev. Lett. 91, 185006, 2003) to a stochastic model. We highlight the limited utility of mean value and variance in understanding the L-H transition by showing strongly non-Gaussian PDFs, with the number of peaks changing in time. We also propose a new information geometric method by using information length, dynamical time scale, and information phase portrait, and show their utility in forecasting transitions and self-regulation between turbulence and zonal flows. In particular, we demonstrate the importance of intermittency (rare events of large amplitude) of zonal flows that can play an important role in promoting the L-H transition.Comment: 5 figures, 6 page