Kazantsev model in nonhelical 2.5D flows

We study the dynamo instability for a Kazantsev-Kraichnan flow with three velocity components that depends only on two-dimensions u = (u(x, y, t), v(x, y, t), w(x, y, t)) often referred to as 2.5 dimensional (2.5D) flow. Within the Kazantsev-Kraichnan frame- work we derive the governing equations for the second order magnetic field correlation function and examine the growth rate of the dynamo instability as a function of the control parameters of the system. In particular we investigate the dynamo behaviour for large magnetic Reynolds numbers Rm and flows close to being two-dimensional and show that these two limiting procedures do not commute. The energy spectra of the unstable modes are derived analytically and lead to power-law behaviour that differs from the three dimensional and two dimensional case. The results of our analytical calculation are compared with the results of numerical simulations of dynamos driven by prescribed fluctuating flows as well as freely evolving turbulent flows, showing good agreement

Cascades and transitions in turbulent flows

Turbulence is characterized by the non-linear cascades of energy and other inviscid invariants across a huge range of scales, from where they are injected to where they are dissipated. Recently, new experimental, numerical and theoretical works have revealed that many turbulent configurations deviate from the ideal 3D/2D isotropic cases characterized by the presence of a strictly direct/inverse energy cascade, respectively. We review recent works from a unified point of view and we present a classification of all known transfer mechanisms. Beside the classical cases of direct and inverse cascades, the different scenarios include: split cascades to small and large scales simultaneously, multiple/dual cascades of different quantities, bi-directional cascades where direct and inverse transfers of the same invariant coexist in the same scale-range and finally equilibrium states where no cascades are present, including the case when a condensate is formed. We classify all transitions as the control parameters are changed and we analyse when and why different configurations are observed. Our discussion is based on a set of paradigmatic applications: helical turbulence, rotating and/or stratified flows, MHD and passive/active scalars where the transfer properties are altered as one changes the embedding dimensions, the thickness of the domain or other relevant control parameters, as the Reynolds, Rossby, Froude, Peclet, or Alfven numbers. We discuss the presence of anomalous scaling laws in connection with the intermittent nature of the energy dissipation in configuration space. An overview is also provided concerning cascades in other applications such as bounded flows, quantum, relativistic and compressible turbulence, and active matter, together with implications for turbulent modelling. Finally, we present a series of open problems and challenges that future work needs to address.Comment: accepted for publication on Physics Reports 201

Shell to shell energy transfer in MHD, Part II: Kinematic dynamo

We study the transfer of energy between different scales for forced three-dimensional MHD turbulent flows in the kinematic dynamo regime. Two different forces are examined: a non-helical Taylor Green flow with magnetic Prandtl number P_M=0.4, and a helical ABC flow with P_M=1. This analysis allows us to examine which scales of the velocity flow are responsible for dynamo action, and identify which scales of the magnetic field receive energy directly from the velocity field and which scales receive magnetic energy through the cascade of the magnetic field from large to small scales. Our results show that the turbulent velocity fluctuations are responsible for the magnetic field amplification in the small scales (small scale dynamo) while the large scale field is amplified mostly due to the large scale flow. A direct cascade of the magnetic field energy from large to small scales is also present and is a complementary mechanism for the increase of the magnetic field in the small scales. Input of energy from the velocity field in the small magnetic scales dominates over the energy that is cascaded down from the large scales until the large-scale peak of the magnetic energy spectrum is reached. At even smaller scales, most of the magnetic energy input is from the cascading process.Comment: Submitted to PR

An investigation of price - volume intraday patterns under "Bull" and "Bear" market conditions

There has been a common belief among stock market practitioners that stock prices move along with trading volume creating certain patterns in price and volume formation. Nevertheless, the above argument was hardly recognised by the academic community since for a number of years statistical results indicated that the stock market is an efficient market i.e. a market where past available information is of no use in predicting future returns profitably, and/or non rational factors do not influence stock prices; The last decade the research for market efficiency was expanded and the use of new large data sets and advanced techniques indicated deviations from the predictions of the Efficient Market Hypothesis (E.M.H.). This study investigates whether there exists a relationship between stock returns and trading volume in the Athens Stock Exchange (A.S.E.) and if such a relationship forms evidence against the E.M.H. We believe that we add to the research in this area since we use intraday data and investigate for a possible relationship under different market states and for different categories of shares.peer-reviewe

Anisotropic fluxes and nonlocal interactions in MHD turbulence

We investigate the locality or nonlocality of the energy transfer and of the spectral interactions involved in the cascade for decaying magnetohydrodynamic (MHD) flows in the presence of a uniform magnetic field $\bf B$ at various intensities. The results are based on a detailed analysis of three-dimensional numerical flows at moderate Reynold numbers. The energy transfer functions, as well as the global and partial fluxes, are examined by means of different geometrical wavenumber shells. On the one hand, the transfer functions of the two conserved Els\"asser energies $E^+$ and $E^-$ are found local in both the directions parallel ($k_\|$-direction) and perpendicular ($k_\perp$-direction) to the magnetic guide-field, whatever the ${\bf B}$-strength. On the other hand, from the flux analysis, the interactions between the two counterpropagating Els\"asser waves become nonlocal. Indeed, as the ${\bf B}$-intensity is increased, local interactions are strongly decreased and the interactions with small $k_\|$ modes dominate the cascade. Most of the energy flux in the $k_\perp$-direction is due to modes in the plane at $k_\|=0$, while the weaker cascade in the $k_\|$-direction is due to the modes with $k_\|=1$. The stronger magnetized flows tends thus to get closer to the weak turbulence limit where the three-wave resonant interactions are dominating. Hence, the transition from the strong to the weak turbulence regime occurs by reducing the number of effective modes in the energy cascade.Comment: Submitted to PR

Anomalous exponents at the onset of an instability

Critical exponents are calculated exactly at the onset of an instability, using asymptotic expansiontechniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical behavior can be anomalous, i.e. the mode amplitude X scales with departure from onset \mu as $~ \mu^\beta$ with an exponent $\beta$ different from its deterministic value. This behavior is observed in a direct numerical simulation of the dynamo instability and our results provide a possible explanation to recent experimental observations