Non-stationary Spectra of Local Wave Turbulence

The evolution of the Kolmogorov-Zakharov (K-Z) spectrum of weak turbulence is studied in the limit of strongly local interactions where the usual kinetic equation, describing the time evolution of the spectral wave-action density, can be approximated by a PDE. If the wave action is initially compactly supported in frequency space, it is then redistributed by resonant interactions producing the usual direct and inverse cascades, leading to the formation of the K-Z spectra. The emphasis here is on the direct cascade. The evolution proceeds by the formation of a self-similar front which propagates to the right leaving a quasi-stationary state in its wake. This front is sharp in the sense that the solution remains compactly supported until it reaches infinity. If the energy spectrum has infinite capacity, the front takes infinite time to reach infinite frequency and leaves the K-Z spectrum in its wake. On the other hand, if the energy spectrum has finite capacity, the front reaches infinity within a finite time, t*, and the wake is steeper than the K-Z spectrum. For this case, the K-Z spectrum is set up from the right after the front reaches infinity. The slope of the solution in the wake can be related to the speed of propagation of the front. It is shown that the anomalous slope in the finite capacity case corresponds to the unique front speed which ensures that the front tip contains a finite amount of energy as the connection to infinity is made. We also introduce, for the first time, the notion of entropy production in wave turbulence and show how it evolves as the system approaches the stationary K-Z spectrum.Comment: revtex4, 19 pages, 10 figure

Grid-scale Fluctuations and Forecast Error in Wind Power

The fluctuations in wind power entering an electrical grid (Irish grid) were analyzed and found to exhibit correlated fluctuations with a self-similar structure, a signature of large-scale correlations in atmospheric turbulence. The statistical structure of temporal correlations for fluctuations in generated and forecast time series was used to quantify two types of forecast error: a timescale error ($e_{\tau}$) that quantifies the deviations between the high frequency components of the forecast and the generated time series, and a scaling error ($e_{\zeta}$) that quantifies the degree to which the models fail to predict temporal correlations in the fluctuations of the generated power. With no $a$ $priori$ knowledge of the forecast models, we suggest a simple memory kernel that reduces both the timescale error ($e_{\tau}$) and the scaling error ($e_{\zeta}$)

Fourier analysis of wave turbulence in a thin elastic plate

The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of the Weak Turbulence theory. A isotropic continuous spectrum of waves is excited with a non linear dispersion relation slightly shifted from the linear dispersion relation. The spectral width of the dispersion relation is also measured. The non linearity of this system is weak as expected from the theory. Finite size effects are discussed. Despite a qualitative agreement with the theory, a quantitative mismatch is observed which origin may be due to the dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov casade.Comment: accepted for publication in European Physical Journal B see http://www.epj.or

Growing condensate in two-dimensional turbulence

We report a numerical study, supplemented by phenomenological explanations, of ``energy condensation'' in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after the standard inverse cascade reaches the size of the system. It leads to emergence of a coherent vortex dipole. We show that the time growth of the dipole is self-similar, and it contains most of the injected energy, thus resulting in an energy spectrum which is markedly steeper than the standard $k^{-5/3}$ one. Once the coherent component is subtracted, however, the remaining fluctuations have a spectrum close to $k^{-1}$. The fluctuations decay slowly as the coherent part grows.Comment: 4 pages, 4 figures. This version includes some additional phenomenological explanations of the results, additional references and improved figure

Dimensional Analysis and Weak Turbulence

In the study of weakly turbulent wave systems possessing incomplete self-similarity it is possible to use dimensional arguments to derive the scaling exponents of the Kolmogorov-Zakharov spectra, provided the order of the resonant wave interactions responsible for nonlinear energy transfer is known. Furthermore one can easily derive conditions for the breakdown of the weak turbulence approximation. It is found that for incompletely self-similar systems dominated by three wave interactions, the weak turbulence approximation usually cannot break down at small scales. It follows that such systems cannot exhibit small scale intermittency. For systems dominated by four wave interactions, the incomplete self-similarity property implies that the scaling of the interaction coefficient depends only on the physical dimension of the system. These results are used to build a complete picture of the scaling properties of the surface wave problem where both gravity and surface tension play a role. We argue that, for large values of the energy flux, there should be two weakly turbulent scaling regions matched together via a region of strongly nonlinear turbulence.Comment: revtex4, 10 pages, 1 figur

FermiFermi GBM Observations of V404 Cyg During its 2015 Outburst

V404 Cygni was discovered in 1989 by the $Ginga$ X-ray satellite during its only previously observed X-ray outburst and soon after confirmed as a black hole binary. On June 15, 2015, the Gamma Ray Burst Monitor (GBM) triggered on a new outburst of V404 Cygni. We present 13 days of GBM observations of this outburst including Earth occultation flux measurements, spectral and temporal analysis. The Earth occultation fluxes reached 30 Crab with detected emission to 100 keV and determined, via hardness ratios, that the source was in a hard state. At high luminosity, spectral analysis between 8 and 300 keV showed that the electron temperature decreased with increasing luminosity. This is expected if the protons and electrons are in thermal equilibrium during an outburst with the electrons cooled by the Compton scattering of softer seed photons from the disk. However, the implied seed photon temperatures are unusually high, suggesting a contribution from another source, such as the jet. No evidence of state transitions is seen during this time period. The temporal analysis reveals power spectra that can be modeled with two or three strong, broad Lorentzians, similar to the power spectra of black hole binaries in their hard state

BATSE observations of BL Lac Objects

The Burst and Transient Source Experiment (BATSE) on the Compton Gamma-Ray Observatory has been shown to be sensitive to non-transient hard X-ray sources in our galaxy, down to flux levels of 100 mCrab for daily measurements, 3 mCrab for integrations over several years. We use the continuous BATSE database and the Earth Occultation technique to extract average flux values between 20 and 200 keV from complete radio- and X-ray- selected BL Lac samples over a 2 year period