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 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.     

Warm cascade states in a forced-dissipated Boltzmann gas of hard spheres

We study the homogeneous isotropic Boltzmann equation for an open system. For the case of a hard spheres gas, we look for nonequilibrium steady solutions in the presence of forcing and dissipation. Using the language of weak turbulence theory, we analyze the possibility of observing the Kolmogorov-Zakharov steady distributions, i.e. solutions characterized by constant fluxes of conserved quantities. We derive a differential approximation model and we find that the expected nonequilibrium steady solutions have always the form of warm cascades. We propose an analytical prediction for the relation between the forcing and dissipation and the thermodynamic quantities of the system. Specifically, we find that the temperature of the system is independent of the forcing amplitude and determined only by the forcing and dissipation scales. Finally, we perform direct numerical simulations of the Boltzmann equation finding consistent results with our theoretical predictions.     

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.     

Decay of capillary turbulence on the surface of a viscous liquid

Decay of the turbulence of capillary waves on the surface of a real liquid is studied in the presence of the viscous damping of the waves at all frequencies after stepwise removal of external pumping. The investigation is performed using two different models: the weak turbulence approximation and the local turbulence model in which the energy redistribution over frequencies is described by the polynomial expression in the wave-occupation number. It is shown that the decay of turbulence in the viscous liquid proceeds self-similarly and begins at high frequencies. In the decay process, the frequency distribution of the energy of waves is close to the stationary form E _ω ～ ω^?3/2 in a wide frequency range below the boundary frequency of the inertial range during a relatively long time after removal of the external force. The calculation results agree qualitatively with the results of the experiments on capillary turbulence on the charged surface of liquid hydrogen.     

光束在强湍流区中传播的到达角起伏

 基于修正Rytov理论，导出了适用于强湍流区的无限平面波和球面波的到达角起伏方差表达式及其功率谱表达式，分析了散射盘对到达角起伏的影响。研究结果表明：导出的方差表达式在弱湍流区也适用，随着Rytov方差的增加到达角起伏趋于饱和；高频功率谱的下降速度随着散射盘尺度的增加而增加。     

光束在强湍流区中传播的到达角起伏

基于修正Rytov理论,导出了适用于强湍流区的无限平面波和球面波的到达角起伏方差表达式及其功率谱表达式,分析了散射盘对到达角起伏的影响。研究结果表明：导出的方差表达式在弱湍流区也适用,随着Rytov方差的增加到达角起伏趋于饱和;高频功率谱的下降速度随着散射盘尺度的增加而增加。     

Sustained turbulence in the three-dimensional Gross-Pitaevskii model

We study the three-dimensional forced-dissipated Gross-Pitaevskii equation. We force at relatively low wave numbers, expecting to observe a direct energy cascade and a consequent power-law spectrum of the form k^−α. Our numerical results show that the exponent α strongly depends on how the inverse particle cascade is attenuated at ks lower than the forcing wave-number. If the inverse cascade is arrested by a friction at low ks, we observe an exponent which is in good agreement with the weak wave turbulence prediction k⁻¹. For a hypo-viscosity, a k⁻² spectrum is observed which we explain using a critical balance argument. In simulations without any low k dissipation, a condensate at k=0 is growing and the system goes through a strongly turbulent transition from a 4-wave to a 3-wave weak turbulence acoustic regime with evidence of k^−3/2 Zakharov-Sagdeev spectrum. In this regime, we also observe a spectrum for the incompressible kinetic energy which formally resembles the Kolmogorov k^−5/3, but whose correct explanation should be in terms of the Kelvin wave turbulence. The probability density functions for the velocities and the densities are also discussed.     

On the stability of Kolmogorov spectra of a weak turbulence

The stability problem of Kolmogorov spectra of a weak turbulence is analytically solved for the first time in the framework of a three-wave kinetic equation. The spectrum of isotropic perturbations of a stationary not-in-equilibrium distribution is found for the capillary waves on a shallow water surface. It is shown, in the isotropic case, that the Kolmogorov solution is stable with respect to excitations local in k-space. The perturbations drift to the damping region without growth of the magnitude. The structural instability of the isotropic spectrum is found by computer simulation: a small pumping anisotropy causes the spectrum to be essentially anisotropic within the inertial range.     

Are there waves in elastic wave turbulence?

An thin elastic steel plate is excited with a vibrator and its local velocity displays a turbulentlike Fourier spectrum. This system is believed to develop elastic wave turbulence. We analyze here the motion of the plate with a two-point measurement in order to check, in our real system, a few hypotheses required for the Zakharov theory of weak turbulence to apply. We show that the motion of the plate is indeed a superposition of bending waves following the theoretical dispersion relation of the linear wave equation. The nonlinearities seem to efficiently break the coherence of the waves so that no modal structure is observed. Several hypotheses of the weak turbulence theory seem to be verified, but nevertheless the theoretical predictions for the wave spectrum are not verified experimentally.     

Analytic approximations of statistical quantities and response of noisy oscillators

Nonlinear oscillators have been utilized in many contexts because they encompass a large class of phenomena. For a reduced phase oscillator model with weak noise forcing that is necessarily multiplicative, we provide analytic formulas for the stationary statistical quantities of the random period. This is an important quantity which we term ‘response’ (i.e., the spike times, instantaneous frequency in neuroscience, the cycle time in chemical reactions, etc.) that is often analytically intractable in noisy oscillator systems. The analytic formulas are accurate in the weak noise limit so that one does not have to numerically solve a time-varying Fokker-Planck equation. The steady-state and dynamic responses are also analyzed with deterministic forcing. A second order analytic formula is derived for the steady-state response, whereas the dynamic response with time-varying forcing is more complicated. We focus on the specific case where the forcing is sinusoidal and accurately capture the frequency response with an analytic approximation that is obtained with a rescaling of the equation. By utilizing various techniques in the weak noise regime, this work leads to a better understanding of how the random period of nonlinear oscillators are affected by multiplicative noise and external forcing. Comparisons of the asymptotic formulas with a full oscillator system confirm the qualitative accurateness of the theory.     

外强迫作用下正压大气非线性特征数值模拟

在两种边界条件下用正压大气非线性位势涡度方程模拟了强迫、耗散和非线性共同作用下大气运动的若干特征.在南北两端为齐次边界条件时，单纯的热力强迫下只出现了波状定常解；在只有经向加热和波状地形共同强迫下出现了在两种基本流型之间振荡的准周期解，十分类似于旋转地球上大气运动的纬向和经向流型之间的准周期循环，前者对应于强的西风环流，后者对应于弱西风流型.在周期边界条件下，弱的下垫面加热导致定常解，较强的加热强迫可以得到周期解.尽管下垫面的波状地形也能强迫一个类似的准周期振荡，但弱西风流型是对称的，不像大气中的弱西风流型.因此，在周期边界条件下用低阶截谱模式求出的解析或数值解，不一定适合描述中高纬度大气的非线性动力特征. 关键词： 正压大气 热力强迫 地形起伏 周期解 准周期振荡     

A marine atmospheric spectrum for laser propagation

Most refractive index power spectral models currently used in atmospheric optical propagation studies were developed for terrestrial or high altitude environments. The current paper presents a new atmospheric spectral model for the marine environment. An analytical marine atmospheric spectrum is formulated to fit a numerical spectrum with the help of the downhill simplex algorithm. Theoretical irradiance fluctuation expressions are derived from the new spectrum for plane and spherical waves in weak optical turbulence. Comparisons are made between the existing scintillation theory and the new expressions developed for the marine environment, and the comparative advantage of the model is discussed. The results suggest that the current models are adequate for modeling the marine atmosphere in weak optical turbulence for small values of the inner scale of turbulence.     

A marine atmospheric spectrum for laser propagation

Most refractive index power spectral models currently used in atmospheric optical propagation studies were developed for terrestrial or high altitude environments. The current paper presents a new atmospheric spectral model for the marine environment. An analytical marine atmospheric spectrum is formulated to fit a numerical spectrum with the help of the downhill simplex algorithm. Theoretical irradiance fluctuation expressions are derived from the new spectrum for plane and spherical waves in weak optical turbulence. Comparisons are made between the existing scintillation theory and the new expressions developed for the marine environment, and the comparative advantage of the model is discussed. The results suggest that the current models are adequate for modeling the marine atmosphere in weak optical turbulence for small values of the inner scale of turbulence.     

Periodic forcing of scroll rings and control of Winfree turbulence in excitable media

By simulations of the Barkley model, action of uniform periodic nonresonant forcing on scroll rings and wave turbulence in three-dimensional excitable media is investigated. Sufficiently strong rapid forcing converts expanding scroll rings into the collapsing ones and suppresses the Winfree turbulence caused by the negative tension of wave filaments. Slow strong forcing has an opposite effect, leading to expansion of scroll rings and induction of the turbulence. These effects are explained in the framework of the phenomenological kinematic theory of scroll waves.     

Theoretical study of the decaying convective turbulence in a shear-buoyancy PBL

The derivation of a theoretical model for the decaying convective turbulence in a shear-buoyancy planetary boundary layer is considered. The model is based on the dynamical equation for the energy density spectrum in which the buoyancy, mechanical and inertial transfer terms are retained. The parameterization for the buoyancy and mechanical terms is provided by the flux Richardson number. Regarding the inertial term an approach employing Heisenberg’s spectral transfer theory is used to describe the turbulence friction, caused by small eddies, responsible for the energy dissipation of the large eddies. Therefore, a novelty in this study is to utilize the Adomian decomposition method to solve directly without linearization the energy density spectrum equation, with this the nonlinear nature of the problem is preserved. Therefore, the errors found are only due to the parameterization used. Comparison of the theoretical model is performed against large-eddy simulation data for a decaying convective turbulence in a shear-buoyancy planetary boundary layer. The results show that the existence of a mechanical turbulent driving mechanism reduces in an accentuated way the energy density spectrum and turbulent kinetic energy decay generated by the decaying convective production in a shear-buoyancy planetary boundary layer.     

Decay of pure quantum turbulence in superfluid 3He-B

We describe measurements of the decay of pure superfluid turbulence in superfluid 3He-B, in the low temperature regime where the normal fluid density is negligible. We follow the decay of the turbulence generated by a vibrating grid as detected by vibrating wire resonators. Despite the absence of any classical normal fluid dissipation processes, the decay is consistent with turbulence having the classical Kolmogorov energy spectrum and is remarkably similar to that measured in superfluid 4He at relatively high temperatures. Further, our results strongly suggest that the decay is governed by the superfluid circulation quantum rather than kinematic viscosity.     

Freely decaying weak turbulence for sea surface gravity waves

We study the long-time evolution of deep-water ocean surface waves in order to better understand the behavior of the nonlinear interaction processes that need to be accurately predicted in numerical models of wind-generated ocean surface waves. Of particular interest are those nonlinear interactions which are predicted by weak turbulence theory to result in a wave energy spectrum of the form of [k](-2.5). We numerically implement the primitive Euler equations for surface waves and demonstrate agreement between weak turbulence theory and the numerical results.     

Aperture-averaged scintillation index and fade statistics in weak oceanic turbulence

With the rapid demand for underwater optical communication(UOC), studies of UOC degradation by oceanic turbulence have attached increasing attention worldwide and become a research hot-spot in recent years. Previous studies used a simplified and inaccurate oceanic turbulence spectrum, in which the eddy diffusivity ratio between temperature and salinity is assumed to be unity and the outer scale of turbulence is assumed to be infinite. However, both assumptions are not true in most of the actual marine environments. In this paper, based on the Rytov theory in weak turbulence, we derive analytical expressions of "the aperture-averaged scintillation index"(SI) for both plane and spherical waves, which can clearly demonstrate how SI is influenced by several key factors in UOC. Then, typical fade statistics of the UOC system in weak turbulence is discussed including the probability of fade, the expected number of fades per time, the mean fade time,signal-to-noise ratio and bit error rate. Our results show that spherical wave is preferable in the UOC system in weak turbulence compared to plane wave, and the aperture-averaged effect has a significant impact on UOC system's performance.Our results can be used to determine those key parameters for designing the UOC system over reasonable ranges.