We discuss average properties of the gluon cascade generated by an energetic parton propa- gating through a dense QCD medium. The cascade is mostly made with relatively soft gluons, whose production is not suppressed by the LPM effect. Unlike for usual QCD cascades in the vacuum, where the typical splittings are very asymmetric (soft and collinear), the medium– induced branchings are quasi–democratic and lead towaveturbulence. This results in a very efficient mechanism for the transport of energy at large angles with respect to the jet axis, which might explain the di–jet asymmetry observed in Pb–Pb collisions at the LHC.
Our measurements also show that σ I ∝ hIi = cρS P σ V 2 ,
where c has the dimension of a velocity (c ∼ 0.5 m/s and
slightly increases when the container size is increased). We also observe in Fig. 2 that the probability of neg- ative events strongly decreases when the container size is increased whereas the positive fluctuations are less af- fected. This shows that the backscattering of the energy flux from the wave field to the driving device is related to the waves reflected by the boundary that can, from time to time, drive the wave maker in phase with its motion. We note that we have less statistics for the negative tail of the PDF when the size of the container is increased.
We now proceed as in the case of the light quarks and compute, for different values of the
K-factor, the R AA of the non-photonic electrons from heavy-meson decays computed within the
FONLL approach . As expected, the suppression is reduced due to the finite mass of the heavy quarks, which is in qualitative contradiction with the experimental data as shown in Fig. 4. As noted in Ref. , the unknown relative contribution from charm and bottom decays to the final electrons introduces an additional uncertainty in this comparison. Here, an 8% theoretical uncertainty is used, as obtained by varying the heavy quark masses and the renormalization and factorization scales in the calculation . The theoretical uncertainty band is likely larger, especially for larger values of ˆ q. This uncertainty is not taken for the case in which only the charm quark contributes
Understanding the origin of intermittency is a challeng- ing problem in varied domains involving turbulent flows. Intermittency is the occurrence of bursts of intense mo- tion within more quiescent fluid flow [1, 2]. This leads to strong deviations from Gaussian statistics that become larger and larger when considering fluctuations at smaller and smaller scales. In three-dimensional hydrodynamic turbulence, the origin of these deviations has been as- cribed to the formation of coherent structures (strong vor- tices) since the 50’s . However, the physical mechanism of intermittency is still an open question . Intermit- tency has also been observed in granular systems , in magnetohydrodynamic turbulence in geophysics  or in the solar wind , and in systems involving transport by a turbulent flow . A recent observation of intermittency has been reported in waveturbulence , a system that strongly differs from high Reynolds number hydrodynamic turbulence. It could thus motivate explanations of inter- mittency different than the ones considering the dynamics of the Navier-Stokes equation.
states of equation (12) is reduced to the study of equation (13) for different choices of the constant fluxes P and Q. In the present work, we will restrict ourselves to the cases where either P = 0 or Q = 0. Moreover, having in mind physically realistic situations only, with n ≥ 0, we must take P ≥ 0 and Q ≤ 0, which a version of the Fjørtoft- Kraichnan dual-cascade statement [11, 12, 13]. ‡ The solutions with P = 0, Q ≥ 0 (or P ≤ 0, Q = 0) can be obtained from the solutions considered in the present paper using the symmetry in the equation (13) with respect to P → −P, Q → −Q, n → −n. Thus, in such solutions n ≤ 0 which makes them unphysical.
ENSTA-UME, Unit´e de Recherche en M´ecanique, Chemin de la Huni`ere, 91761 Palaiseau, Cedex, France
(Dated: October 4, 2008)
The nonlinear interaction of waves in a driven medium may lead towaveturbulence, a state such that energy is transferred from large to small lengthscales. Here, waveturbulence is observed in experiments on a vibrating plate. The frequency power spectra of the normal velocity of the plate may be rescaled on a single curve, with power-law behaviors that are incompatible with the weak turbulence theory of D¨ uring et al. [Phys. Rev. Lett. 97, 025503 (2006)]. Alternative scenarios are suggested to account for this discrepancy — in particular the occurrence of wave breaking at high frequencies. Finally, the statistics of velocity increments do not display an intermittent behavior.
For hard jets produced together with a soft background that is completely uncorrelated with the jet direction, there are a number of established techniques that allow for systematic removal of the effects of background particles fromjet observables. (See, for example, refs. [ 181 – 183 ].) These procedures, generically referred to as background subtraction, are routinely applied tojet measurements at the LHC and, at least in proton-proton collisions, they efficiently remove the effects of soft (non-perturbative) backgrounds that may be large but that are uncorrelated with the jet, allowing the measurement of theoretically controlled hard processes. However, in heavy ion collisions the fact that the medium includes a wake that carries momentum in the jet direction means, in effect, that a component of the background is correlated with the jet direction. This makes it impossible for a background subtraction procedure to separate the jet (which has been modified, via energy loss and broadening) from the medium (which has been modified, via the wake). In order to compare to experimental measurements, therefore, we have added a background and a wake and must now perform a background subtraction as if the background were uncorrelated with the jet direction, followed by jet reconstruction, just as in an experimental analysis. This procedure is not necessary for jet observables that are dominated by the harder components of a jet. This procedure is important for the softer components, since the softer components of what is reconstructed as a jet will include contributions from the jet itself and from the wake in the medium. In particular, this procedure is critical to gauging the effects of the wake on observables. We have implemented a full background subtraction procedure to analyze the events produced within our framework. In particular, we have implemented a version of the so called noise/pedestal background subtraction procedure [ 48 , 184 ] and then done a jet energy scale correction; the details of our implementation can be found in appendix B .
Fig. 1. Left: Jet R AA for K = 50 for different jet radius R. The parameter κ S C has been fitted to describe data at R = 0.3 as measured in . Right: Jet shapes ratio for R = 0.3 jets for different values of K as compared to experimental data from .
a phenomenological approach which benefits from the big separation of scales, from the virtuality to the temperature, to interleave the most relevant physical processes at each scale. Even though it is a simple prescription, the model has proven to be a powerful tool in its confrontation against available data for several jet observables [1, 2, 3], and in generating a broad range of concrete predictions for LHC run II . In these proceedings we show results for the inclusion of parton broadening due to the presence of a thermal bath, and how it is reflected in some of the jet observables measured in experiments. The e ffect of medium response to the deposition of energy by the jet will also be discussed.
c Laboratoire d’Oc´ eanographie Spatiale, Ifremer, 29280 Plouzan´ e, France
Ocean surface mixing and drift are functions of the surface Stokes drift, U ss , volume Stokes transport T S , a wave breaking height scale H swg , and the flux of energy from waves to ocean turbulent kinetic energy Φ oc . Here we describe a global database of these parameters, estimated from a well-validated numerical wave model, that covers the years 2003 to 2007. Compared to previous studies, the present work has the advantage of being consistent with the known physical processes that regulate the wave field and the air-sea fluxes, and also consistent with a very large number of observations of wave parameters using in situ measurements and satellite remote sensing. Our estimates may differ significantly from previous estimates. In partic- ular we find that the global TKE flux Φ oc is 68 TW and the mean Stokes volume transport, is typically 10 to 30% of the Ekman transport. We also have refined our previous estimates of the surface Stokes drift U ss by using a better treatment of the high frequency part of the wave spectrum. In the open ocean, U ss ≃ 0.014U 10 , where U 10 is the wind speed at 10 m height. The actual wave-induced drift is probably slightly larger due to the effect of breaking waves, which was neglected here.
L. Deike, C. Laroche E. Falcon
Experimental set-up. – The experimental setup is similar to the one used in . It consists in a square plas- tic vessel, L = 20 cm side, filled with mercury up to a height h = 18 mm. The properties of mercury are: den- sity, ρ = 13.5 × 10 3 kg/m 3 , kinematic viscosity, ν = 10 − 7 m 2 /s and surface tension γ = 0.4 N/m. Mercury is used because of its low kinematic viscosity. Surface waves are generated by a rectangular plunging wave maker (13 cm in length and 3.5 cm in height) driven by an electromag- netic vibration exciter. The crossover frequency between gravity and capillary linear waves is fgc = 2π 1 p2g/lc ≃ 17 Hz with g = 9.81 m/s 2 the acceleration of the gravity, and lc = pγ/(ρg) is the capillary length . Gravity waves thus occurs for frequency f < fgc whereas capillary waves occurs for f > fgc. The wave maker is driven around fgc in order to generate small scale gravity waves to be able to observe an upscale transfer regime from this small scale to larger ones. The wave maker is either driven si- nusoidally at a frequency fp = 19 Hz close to fgc or with a random noise (in amplitude and frequency) band-pass filtered around fp ± 3 Hz unless otherwise stated. The depth H of the wave maker immersion is varied in a range 9 ≤ H ≤ 17 mm. The amplitude of the surface waves η(t) at a given location is measured by a capacitive wire gauge plunging perpendicularly to the fluid at rest . The fre- quency cut-off of this probe is near 400 Hz. The signal η(t) is recorded during 500 s using an acquisition card with a 2 kHz sampling rate. The instantaneous injected power into the fluid I(t) is given by the product of the wave maker velocity V (t) and the force F (t) applied by the vibration exciter to the wave maker . The mean injected power is thus hIi ≡ hF (t)V (t)i where h·i denotes a time average. σF and σV will denote the rms value of F (t) and V (t).
(2) Acoustics and Audio Group, University of Edinburgh, James Clerk Maxwell Building, Edinburgh,
Summary. Nonlinear (large amplitude) vibrations of thin elastic plates can exhibit strongly nonlinear regimes characterized by a broadband Fourier spectrum and a cascade of energy from the large to the small wavelengths. This particular regime can be properly described within the framework of waveturbulence theory. The dynamics of the local kinetic energy spectrum is here investigated numerically with a finite difference, energy-conserving scheme, for a simply-supported rectangular plate excited pointwise and har- monically. Damping is not considered so that energy is left free to cascade until the highest simulated frequency is reached. The framework of non-stationary waveturbulence is thus appropriate to study quantitatively the numerical results. In particular, numerical simulations show the presence of a front propagating to high frequencies, leaving a steady spectrum in its wake, which has the property of being self-similar. When a finite amount of energy is given at initial state to the plate which is then left free to vibrate, the spectra are found to be in perfect accordance with the log-correction theoretically predicted. When forced vibrations are considered so that energy is continuously fed into the plate, a slightly steeper slope is observed in the low-frequency range of the spectrum. It is concluded that the pointwise forcing introduces an anisotropy that have an influence on the slope of the power spectrum, hence explaining one of the discrepancies reported in experimental studies.
the wave steepness. It is thus due to a nonlinear effect, probably related to the sharp-crested waves, occurring homogeneously in the wave field, and visible directly from the shore once a steady state is reached (see movies in ). Dissipation by nonlinear localized structures in the energy balance equation is indeed often referred in fore- casting models of wind-driven ocean waves [32, 42] and remains very challenging to estimate. Numerical sim- ulations of fully nonlinear equations demonstrate that such structures are enhanced in the presence of an inverse cascade , and induce an effective large-scale dissipa- tion not taken into account in WWT [39, 40]. However, we have currently no way to quantify it since the wave probes are distributed discreetly over the basin surface, and localized structures are most of the time not cap- tured. Indeed, the probability distributions of η(t) and of ∂η(t)/∂t are found similar before and after the satura- tion, and close to a Tayfun distribution. Spatio-temporal measurements seem necessary to ascertain the role of lo- calized structures, for instance by measuring the nonlin- ear corrections to the dispersion relation (see  for a numerical study), but are difficult to implement in such a large wave basin .
is enhanced by coherent structures such as breaking waves (Falcon et al. 2010b). Third, strongly nonlinear waves involved in laboratory experiments may lead to non-local interactions in k-space, dissipation at all scales of the cascade (energy flux not conserved), and no scale separation between linear, nonlinear, and dissipating time scales, unlike weak turbulence hypotheses. Finally, it has been recently reported in different experimental systems of waveturbulence that increasing dissipation leads to a spectrum that departs from weak turbulence prediction (Humbert et al. 2013; Miquel et al. 2014; Deike et al. 2014a). Note that several numerical simulations of gravity waveturbulence validated the weak turbulence derivation (Ono- rato et al. 2002; Pushkarev et al. 2003; Dyachenko et al. 2004; Yokoyama 2004; Lvov et al. 2006; Korotkevitch 2008). Limited inertial range (no larger than one decade), nonlinear- ity truncation, and artificial numerical dissipation at large scales are the main obstacles to further comparisons of simulation and observations of gravity waveturbulence.
0 ¼ 0.84. This is the signature
of the TRI of the base waves, which induces a regime of discrete wave interactions, as described above. Further, from the threshold of the first triadic instability, for Re ¼ 350, one notices the nonlinear broadening of the resonance peaks in the bicoherence map. At large distance from the TRI threshold, for Re ¼ 3080, the bicoherence has become a smooth function that takes low values ranging from 5 × 10 −2 to 10 −1 , comparable to the Rossby number based on the rms velocity ( 1.7 cm=s) and the injection wavelength (14 cm inside the PIV plane), Ro ≃3 × 10 −2 . Thus, the experimental bicoherence confirms the gradual transition from a discrete-wave-interaction regime to a proper weak turbulence regime as Re increases. In the latter regime, the discreteness of the modes is smoothed out by the nonlinear broadening of the resonances, and both the temporal spectrum and the bicoherence become smooth functions. The bicoherence settles at a low value, of order Ro, compatible with a weakly nonlinear wave field that satisfies the random phase approximation.
Therefore, we used this basic contrast optimization strategy for all the free-surface contour mappings.
4.2.2. Calibration procedure
Using IRIS, it is possible to obtain the pixel coordinates of each point of the picture just by clicking with the mouse on the desired point of the computer screen. Then, an output window allows export of a set of pixel coordinates (X, Y) as a text file which can be used in a spreadsheet program. Due to the change of the refraction index between air, water and glass, refraction effects prevent the direct determination of the real geometrical dimensions and these appear larger than they are in reality. So, it was important to calibrate the acquisition method to transform a pixel map given by IRIS into a real geometric map useful for the studies carried out. For the calibration experiments, the stirred vessel was filled with 109 litres of water at ambient temperature and the square jacket around the cylindrical part of the reactor was also filled with water at the same temperature to the maximum level. The volume of liquid in the stirred vessel corresponded to the initial water level of 700 mm used in all of the following experiments. A rectangular grid (360 mm×600 mm) with regular cells (15 mm×30 mm) was plunged vertically into the reactor in the vortex measurement area, just behind the baffles to determine whether the curvature of the shell led to a non-uniform deformation of lengths in the tank. It was demonstrated that the modification of the grid size was regular on the entire grid and the curvature of the shell had no visible effect. Thus, only one standard for X and one for Y were sufficient for the calibration. The horizontal standard was the distance between the two baffles (281 mm) and the vertical standard was a metallic ruler with two phosphorescent marks spaced 200 mm apart, suspended from the reactor lid into the liquid in a central position. The calibration procedure has been tested for the determination of the real contour and position of the baffles, the initial liquid level and the position of the vertical standard marks.
Currently there is no theoretical framework which
can describe strong and weak coupling processes at dif- ferent scales in a consistent manner. For this reason our model should be regarded as a phenomenological ap- proach which exploits the big separation of scales from the virtuality to the temperature to combine the most rel- evant physical processes at each scale. Despite its sim- plicity, the model has proven to be a powerful tool in its confrontation with available measurements for various jet observables [1, 2], and in producing a broad range of definite predictions for LHC run II . In these pro- ceedings we extend the comparison carried out in [1, 2] by both confronting the model with ATLAS jet data and exploring new sets of observables.
The turbulent inflation introduced here is mainly a phenomenological theory, inspired by the analytical re- sults obtained in weak GW turbulence. At present, an essential part of it remains in conjecture, specifically the view that the inverse cascade will continue through the strongly turbulent stage. Indeed, strictly speaking the dual cascade behavior relies on the conservation of the wave action, which is a property of the four-wave kinetic equation and therefore breaks down when this equation is no longer applicable. The situation here is similar to the behavior described by the Gross-Pitaevskii model: when the inverse cascade becomes strong, the energy invari- ant ceases to be quadratic, and the dual cascade argu- ment becomes, technically, invalid. However, it is known from numerical simulations of the Gross-Pitaevskii model [45, 46] that the condensation process started at the weakly turbulent regime as an inverse cascade, contin- ues at the strongly turbulent stage with the appearance of strongly nonlinear defects which move like hydrody- namic vortices. These tend to continuously annihilate, so that no defects remain after a finite time, with the correlation length becoming infinite. By this analogy, we conjecture that in the vacuum Einstein model, the con- densation process will also continue through the strongly turbulent stage, possibly with some singular coherent ob- jects, such as wormholes, PBH or solitons, appearing in the system at a transient stage (similar to the appearance of the vortices in the Gross-Pitaevskii model). Obviously some work remains to be performed for such a conjecture to be confirmed by direct numerical simulations (this is- sue is left for future work) and if possible by analytical calculations.
Waveturbulence is thus an interdisciplinary subject that involves different com- munity: astrophysics, geophysics, mathematics, fluid mechanics and different fields of physics. Since the early developments of theoretical tools by applied mathe- maticians and physicists, the first ones to be interested on waveturbulence were oceanographers and meteorologists. Their motivations are numerous such as to de- velop climatic models, predict the sea state with more precision, or extract some energy from ocean waves as a source of alternative energy... At a more fundamental level, the goal is to understand the energy transfers between nonlinear interacting 2000 Mathematics Subject Classification. Primary: 7605, 76B15; Secondary: 76F99, 76D33. Key words and phrases. Waveturbulence, N-wave interaction process, weak turbulence, surface waves, experiments, intermittency, power spectrum, energy flux, gravity waves, capillary waves.
Here, we propose a plausible alternative based on the nonlinearities of the (non-modified) general relativity equations which have been neglected so far when considering the primordial universe. Our approach is, therefore, different from the Starobinsky’s model where an extra R 2 term was introduced in the Hilbert–Einstein action [ 13 ]. As the fundamental hypothesis of our study we will neglect the role of inflaton in the mechanism of inflation and we will focus our attention only on gravitational wave (GW) turbulence. Since the problem is highly non-trivial, we will examine a simplified theoretical framework from which analytical results were recently derived for the regime of weak GW turbulence [ 14 ]. We will use these results to develop a theory of strong GW turbulence which is phenomenological by nature because, unlike for weak turbulence, the problem of strong turbulence is unsolvable perturbatively. In this way we will follow a very classical approach of turbulence based on the idea of critical balance (see, e.g., [ 15 – 20 ]).
Turbulence is a general term used for describing the erratic motions displayed by nonlinear systems that are driven far from their equilibrium position and thus display complicated motions involving different time and length scales. Without other precision, the term gen- erally refers to hydrodynamic turbulence, as the main field of research has been directed towards irregular motions of fluids and the solutions of Navier-Stokes equations. During the XXth century, the theory has shown important breakthrough thanks to the qualitative ideas of Richardson and the quantitative arguments of Kolmogorov that culminated in the so-called K41 theory [Kol41a, Kol41b, Fri95]. This statistical approach, although giving successful predictions, still faces an irreducible obstacle due to the lack of closure in the infinite hierarchy of moment equations.