Role of helicity for large- and small-scale turbulent fluctuations

The effect of the helicity on the dynamics of the turbulent flows is investigated. The aim is to disentangle the role of helicity in fixing the direction, the intensity and the fluctuations of the energy transfer across the inertial range of scales. We introduce an external parameter, $\alpha$, that controls the mismatch between the number of positive and negative helically polarized Fourier modes. We present the first set of direct numerical simulations of Navier-Stokes equations from the fully symmetrical case, $\alpha=0$, to the fully asymmetrical case, $\alpha=1$, when only helical modes of one sign survive. We found a singular dependency of the direction of the energy cascade on $\alpha$, measuring a positive forward flux as soon as only a few modes with different helical polarities are present. On the other hand, small-scales fluctuations are sensitive only to the degree of mode-reduction, leading to a vanishing intermittency already for values of $\alpha \sim 0.1$ and independently of the degree of mirror symmetry-breaking. Our findings suggest that intermittency is the result of a global mode-coupling in Fourier space.Comment: 4 Fig

Multiscaling in Hall-Magnetohydrodynamic Turbulence: Insights from a Shell Model

We show that a shell-model version of the three-dimensional Hall-magnetohydrodynamic (3D Hall-MHD) equations provides a natural theoretical model for investigating the multiscaling behaviors of velocity and magnetic structure functions. We carry out extensive numerical studies of this shell model, obtain the scaling exponents for its structure functions, in both the low-$k$ and high-$k$ power-law ranges of 3D Hall-MHD, and find that the extended-self-similarity (ESS) procedure is helpful in extracting the multiscaling nature of structure functions in the high-$k$ regime, which otherwise appears to display simple scaling. Our results shed light on intriguing solar-wind measurements.Comment: 7 pages, 6 figure

Real-space Manifestations of Bottlenecks in Turbulence Spectra

An energy-spectrum bottleneck, a bump in the turbulence spectrum between the inertial and dissipation ranges, is shown to occur in the non-turbulent, one-dimensional, hyperviscous Burgers equation and found to be the Fourier-space signature of oscillations in the real-space velocity, which are explained by boundary-layer-expansion techniques. Pseudospectral simulations are used to show that such oscillations occur in velocity correlation functions in one- and three-dimensional hyperviscous hydrodynamical equations that display genuine turbulence.Comment: 5 pages, 2 figure

Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence

We present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to $1024^3$ collocation points, of incompressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number ${\rm Pr_M}$ over a large range, namely, $0.01 \leq {\rm Pr_M} \leq 10$. We obtain data for a wide variety of statistical measures such as probability distribution functions (PDFs) of moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure functions, which we use to characterise intermittency, isosurfaces of quantities such as the moduli of the vorticity and current, and joint PDFs such as those of fluid and magnetic dissipation rates. Our systematic study uncovers interesting results that have not been noted hitherto. In particular, we find a crossover from larger intermittency in the magnetic field than in the velocity field, at large ${\rm Pr_M}$, to smaller intermittency in the magnetic field than in the velocity field, at low ${\rm Pr_M}$. Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of ${\rm Pr_M}$, multiscaling exponent ratios agree, at least within our errorbars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence.Comment: 49 pages,33 figure

Dynamic multiscaling in magnetohydrodynamic turbulence

We present a study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents

On the development of improved adaptive models for efficient prediction of stock indices using clonal-PSO (CPSO) and PSO techniques

The present paper introduces a new clonal particle swarm optimisation (CPSO) and PSO techniques to develop efficient adaptive forecasting models for short and long-term prediction of S&P 500 and DJIA stock indices. The basic structure of the models is an adaptive linear combiner whose weights are iteratively updated by PSO and CPSO-based learning rules. The technical indicators are computed from past stock indices and are used as input to the models. Using simulation study the prediction performances in terms of the convergence rate, the minimum mean square error (MSE), training time and the mean average percentage error (MAPE) of CPSO, PSO and GA-based models are obtained for all ranges of prediction. Comparison of these results demonstrates that the proposed CPSO and PSO-based models yield superior performance compared to the GA one. However the CPSO model provides the best performance compared to other two.artificial immune system; clonal selection principle; CSP; particle swarm optimisation; PSO; genetic algorithms; GAs; stock market prediction; adaptive forecasting models; stock markets; simulation.