Search Results (12 total)

We discuss the importance of phase information and coherence times in determining the dynamo properties of turbulent flows. We compare the kinematic dynamo properties of three flows with the same energy spectrum. The first flow is dominated by coherent structures with nontrivial phase information and long eddy coherence times, the second has random phases and long-coherence time, the third has nontrivial phase information, but short coherence time. We demonstrate that the first flow is the most efficient kinematic dynamo, owing to the presence of sustained stretching and constructive folding. We argue that these results place limitations on the possible inferences of the dynamo properties of flows from the use of spectra alone, and that the role of coherent structures must always be accounted for.

We report the results of an extensive set of direct numerical simulations of forced, incompressible, magnetohydrodynamic (MHD) turbulence with a strong guide field. The aim is to resolve the controversy regarding the power-law exponent (α, say) of the field-perpendicular energy spectrum E(k_⊥)∝k_⊥^α. The two main theoretical predictions α=−3/2 and α=−5/3 have both received some support from differently designed numerical simulations. Our calculations have a resolution of 512³ mesh points, a strong guide field, and an anisotropic simulation domain and implement a broad range of large-scale forcing routines, including those previously reported in the literature. Our findings indicate that the spectrum of well-developed, strong incompressible MHD turbulence with a strong guide field is E(k_⊥)∝k_⊥^−3/2.

Motivated by recent analytic predictions, we report numerical evidence showing that in driven incompressible magnetohydrodynamic turbulence the magnetic- and velocity-field fluctuations locally tend to align the directions of their polarizations. This dynamic alignment is stronger at smaller scales with the angular mismatch between the polarizations decreasing with the scale λ approximately as θ_λ∝λ^1/4. This can naturally lead to a weakening of the nonlinear interactions and provide an explanation for the energy spectrum E(k)∝k^-3/2 that is observed in numerical experiments of strongly magnetized turbulence.

We report time-of-flight experiments on photonic-crystal waveguide structures using optical Kerr gating of a femtosecond white-light supercontinuum. These photonic-crystal structures, based on engineered silicon-nitride slab waveguides, possess broadband low-loss guiding properties, allowing the group velocity dispersion of optical pulses to be directly tracked as a function of wavelength. This dispersion is shown to be radically disrupted by the spectral band gaps associated with the photonic-crystal periodicity. Increased time-of-flight effects, or “slowed light,” are clearly observed at the edges of band gaps in agreement with two-dimensional plane-wave theoretical models of group velocity dispersion. A universal model for slow light in such photonic crystals is proposed, which shows that slow light is controlled predominantly by the detuning from, and the size of, the photonic band gaps. Slowed light observed up to time delays of ∼1  ps, corresponds to anomalous dispersion of ∼3.5  ps∕nm per mm of the photonic crystal structure. From the decreasing intensity of time-gated slow light as a function of time delay, we estimate the characteristic losses of modes which are guided in the spectral proximity of the photonic band gaps.

We investigate analytically the amplification of a weak magnetic field in a homogeneous and isotropic turbulent flow lacking reflectional symmetry (helical turbulence). We propose that the spectral distributions of magnetic energy and magnetic helicity can be found as eigenmodes of a self-adjoint, Schrödinger-type system of evolution equations. We argue that large-scale and small-scale magnetic fluctuations cannot be effectively separated, and that the conventional α model is, in general, not an adequate description of the large-scale dynamo mechanism. As a consequence, the correct numerical modeling of such processes should resolve magnetic fluctuations down to the very small, resistive scales.

We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, v(l)∼l^α, α<1. This regime is relevant to the problem of magnetic field generation in fluids with small magnetic Prandtl number, i.e., with Ohmic resistivity much larger than viscosity. We propose that the smaller the roughness exponent α, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.

We study the saturation of the turbulent α effect in the nonlinear regime. A numerical experiment is constructed based on the full nonlinear magnetohydrodynamics equations that allows the α effect to be measured for different values of the mean magnetic field. The object is to distinguish between two possible theories of nonlinear saturation. It is found that the results are in close agreement with the theories that predict strong suppression and are incompatible with those that predict that the turbulent α effect persists up to mean fields of order of the equipartition energy.

A simplified nonlinear dynamo model is constructed that allows the transition from the kinematic to the dynamic regime to be studied in detail. We apply this construction to a chaotic flow recently studied in the context of fast dynamo action. It is found that the structure of the magnetic field in the two regimes is markedly different. Furthermore, the saturation of the exponential growth of the magnetic field is achieved by a drastic suppression of the chaotic properties of the flow.

The ratio R₁ between the average magnetic energy and the square-averaged flux plays an important role in the study of nonlinear dynamos, as a measure of the efficiency of a dynamo at generating flux. For large values of R_m, R₁ displays a scaling behavior of the type R₁∼R_m ⁿ, where R_m is the magnetic Reynolds number. We show by direct numerical evaluation that n depends sensitively on the flow complexity for small-scale dynamos. Furthermore, by relating n to the cancellation exponent and the correlation dimension of the magnetic field, we argue that n is not likely to be close to zero in general.

New numerical evidence for a transition to hard turbulence in 2D Boussinesq convection is presented. These 2D simulations agree with some, but not all, experimental results for the scaling properties of 3D hard turbulence. The transition to 2D hard turbulence, as measured by a change in the Nusselt-Rayleigh scaling law, coincides with a gradual change in the velocity probability distribution from Gaussian to exponential form and with the development of a ‘‘well-mixed’’ central region.

We report results on the transition from soft to hard turbulence in simulations of 2D Boussinesq convection. The computed probability densities for temperature fluctuations are exponential in form in both soft and hard turbulence, unlike what is observed in experiments; in contrast, we obtain a change in the Nusselt number scaling on Rayleigh number in good agreement with the 3D experiments.

The recovery of quenched-in extra resistivity has been studied in thin gold wires, to which atomic concentrations of silver equal to 1.2×10^-3 or 1.4×10^-4 have been added. Recovery occurs at higher temperatures than for pure specimens, the effective activation energy being larger than 1 ev. The interpretation is that vacancy-impurity complexes are formed, whose binding energy is about 0.3 ev. Evidence of motion of defects at low temperature is also obtained in the case of impure specimens.