Observation of gravity-capillary wave turbulence

We report the observation of the crossover between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non-Gaussian. The surface wave height displays power-law spectra in both regimes. In the capillary region, the exponent is in fair agreement with weak turbulence theory. In the gravity region, it depends on the forcing parameters. This can be related to the finite size of the container. In addition, the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes.     

Self-organization in nonlinear wave turbulence

We present a statistical equilibrium model of self-organization in a class of focusing, nonintegrable nonlinear Schrodinger (NLS) equations. The theory predicts that the asymptotic-time behavior of the NLS system is characterized by the formation and persistence of a large-scale coherent solitary wave, which minimizes the Hamiltonian given the conserved particle number (L2-norm squared), coupled with small-scale random fluctuations, or radiation. The fluctuations account for the difference between the conserved value of the Hamiltonian and the Hamiltonian of the coherent state. The predictions of the statistical theory are tested against the results of direct numerical simulations of NLS, and excellent qualitative and quantitative agreement is demonstrated. In addition, a careful inspection of the numerical simulations reveals interesting features of the transitory dynamics leading up to the long-time statistical equilibrium state starting from a given initial condition. As time increases, the system investigates smaller and smaller scales, and it appears that at a given intermediate time after the coalescense of the soliton structures has ended, the system is nearly in statistical equilibrium over the modes that it has investigated up to that time.     

Observation of intermittency in wave turbulence

We report the observation of intermittency in gravity-capillary wave turbulence on the surface of mercury. We measure the temporal fluctuations of surface wave amplitude at a given location. We show that the shape of the probability density function of the local slope increments of the surface waves strongly changes across the time scales. The related structure functions and the flatness are found to be power laws of the time scale on more than one decade. The exponents of these power laws increase nonlinearly with the order of the structure function. All these observations show the intermittent nature of the increments of the local slope in wave turbulence. We discuss the possible origin of this intermittency.     

Negative viscosity for Rossby wave and drift wave turbulence

The possible occurrence of a “negative viscosity effect” is studied for Rossby wave and drift wave turbulence. It is assumed that (i) the space and time scales of the wave field are much smaller than the scales of the mean field, and (ii) the small-scale field is sufficiently weak, stationary, and maintained by an external source. Such a formulation is fruitful for studying the effects (characterized by the effective viscosity) of smaller-scale motions upon larger-scale ones. The criteria of large-scale instability due to the negative effective viscosity are derived for the coherent wave motions as well as for small-scale isotropic wave turbulence. Zh. éksp. Teor. Fiz. 113, 646–663 (February 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Different regimes for water wave turbulence

We present an experimental study on gravity capillary wave turbulence in water. By using space-time resolved Fourier transform profilometry, the behavior of the wave energy density |η(k,ω)|(2) in the 3D (k,ω) space is inspected for various forcing frequency bandwidths and forcing amplitudes. Depending on the bandwidth, the gravity spectral slope is found to be either forcing dependent, as classically observed in laboratory experiments, or forcing independent. In the latter case, the wave spectrum is consistent with the Zakharov-Filonenko cascade predicted within wave turbulence theory.     

Differential approximation for Kelvin wave turbulence

I present a nonlinear differential equation model (DAM) for the spectrum of Kelvin waves on a thin vortex filament. This model preserves the original scaling of the six-wave kinetic equation, its direct and inverse cascade solutions, as well as the thermodynamic equilibrium spectra. Further, I extend DAM to include the effect of sound radiation by Kelvin waves. I show that, because of the phonon radiation, the turbulence spectrum ends at a maximum frequency of ω* ∼ (ε³ c _s ²⁰ /κ¹⁶)^1/13, where ε is the total energy injection rate, c _s is the speed of sound, and κ is the quantum of circulation. The text was submitted by the author in English.     

Non-stationary regimes of surface gravity wave turbulence

We present experimental results about rising and decaying gravity wave turbulence in a large laboratory flume. We consider the time evolution of the wave energy spectral components in ω- and k-domains and demonstrate that emerging wave turbulence can be characterized by two time scales—a short dynamical scale due to nonlinear wave interactions and a longer kinetic time scale characterizing formation of a stationary wave energy spectrum. In the decay regime we observed the maximum of the wave energy spectrum decreasing in time initially as the power law, ∝t ^?1/2, as predicted by the weak turbulence theory, and then exponentially due to viscous friction.     

Observation of wave turbulence in vibrating plates

The nonlinear interaction of waves in a driven medium may lead to wave turbulence, a state such that energy is transferred from large to small length scales. Here, wave turbulence 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 Düring et al. [Phys. Rev. Lett. 97, 025503 (2006)10.1103/PhysRevLett.97.025503]. 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.     

Fluctuations of energy flux in wave turbulence

We report that the power driving gravity and capillary wave turbulence in a statistically stationary regime displays fluctuations much stronger than its mean value. We show that its probability density function (PDF) has a most probable value close to zero and involves two asymmetric roughly exponential tails. We understand the qualitative features of the PDF using a simple Langevin-type model.     

Wave turbulent statistics in non-weak wave turbulence

In wave turbulence, which is made by nonlinear interactions among waves, it has been believed that statistical properties are well described by the weak turbulence theory, where separation of linear and nonlinear time scales derived from weak nonlinearity is assumed. However, the separation of the time scales is often violated. To get rid of this inconsistency, closed equations are derived in wave turbulence without assuming the weak nonlinearity according to Direct-Interaction Approximation (DIA), which has been successful in Navier-Stokes turbulence. The DIA equations is a natural extension of the conventional kinetic equation to not-necessarily-weak wave turbulence.     

Gravity wave turbulence in a laboratory flume

We present an experimental study of the statistics of surface gravity wave turbulence in a flume of a horizontal size 12 x 6 m. For a wide range of amplitudes the wave energy spectrum was found to scale as Eomega approximately omega(-nu) in a frequency range of up to one decade. However, nu appears to be nonuniversal: it depends on the wave intensity and ranges from about 6 to 4. We discuss our results in the context of existing theories and argue that at low wave amplitudes the wave statistics is affected by the flume finite size, and at high amplitudes the wave breaking effect dominates.     

Nonstationary wave turbulence in an elastic plate

We report experimental results on the decay of wave turbulence in an elastic plate obtained by stopping the forcing from a stationary turbulent state. In the stationary case, the forcing is seen to induce some anisotropy and a spectrum in disagreement with the weak turbulence theory. After stopping the forcing, almost perfect isotropy is restored. The decay of energy is self-similar and the observed decaying spectrum is in better agreement with the prediction of the weak turbulence theory. The dissipative part of the spectrum is partially consistent with the theoretical prediction based on previous work by Kolmakov. This suggests that the nonagreement with the weak turbulence theory is mostly due to a spurious effect of the forcing related to the finite size of the system.     

Magnetic shear damping of dissipative drift wave turbulence

The influence of local and global magnetic field line shear on structure formation and transport in dissipative drift-Alfvén turbulence is explored. It is found that the generation of zonal flow shear is connected to magnetic shear in ways not accounted previously. The concept of a locally sheared slab flux tube model (including toroidicity) is introduced in order to extend previous analyses to general local variations of magnetic field line shear. It is shown that local shear damping is efficient even when flux surface averaged shear is low.     

Mode selective control of drift wave turbulence.

Experiments on spatiotemporal open-loop synchronization of drift wave turbulence in a magnetized cylindrical plasma are reported. The synchronization effect is modeled by a rotating current profile with prescribed mode structure. Numerical simulations of an extended Hasegawa-Wakatani model show good agreement with experimental results.     

薄板状周期栅格结构中弹性波传播特性研究

相位常数面可以描述特定频率、特定结构中波的传播方向及传播区域.将相位常数面这一分析方法应用于薄板状周期栅格结构中弹性波传播特性的研究，采用集中质量法计算了周期栅格结构的相位常数面，得到了直观的三维能带结构图.相位常数面可以用二维等高线图描述，通过计算等高线上每一点的法线方向，得到了在特定通带频率下弹性波的传播方向及传播区域.这些研究对于通带频率范围内的弹性波传播特性具有重要意义. 关键词： 声子晶体 弹性波带隙 集中质量法 相位常数面     

Plasma-maser interaction of langmuir wave with kinetic Alfvén wave turbulence

A theoretical study is made on the generation mechanism of Langmuir mode wave in the presence of kinetic Alfvén wave turbulence in a magnetized plasma on the basis of plasma-maser interaction. It is shown that a test high frequency Langmuir mode wave is unstable in the presence of low frequency kinetic Alfvén wave turbulence. The growth of the Langmuir wave occurs due to direct and polarization coupling terms. Because of the universal existence of the kinetic Alfvén waves in large scale plasmas, the results have potential importance in space and astrophysical radiation processes.