海洋表面波的3-4-5波共振守恒理论

面对海洋表面完整的两大波要素–-张力波和重力波, 构建出一个确定、丰富、基本的有限水深海洋表面波的“3-4-5波共振守恒理论”. 与以往经典、现代的多种结果相比, 充分保证了该理论的“精确性、对称性、完备性”, 为后继、普适的海洋波湍流统计理论提供了一个必备基础. 关键词： 海洋表面波 Hamilton描述 3-4-5波共振 波湍流     

Weak turbulence for a vibrating plate: can one hear a Kolmogorov spectrum?

We study the long-time evolution of waves of a thin elastic plate in the limit of small deformation so that modes of oscillations interact weakly. According to the theory of weak turbulence (successfully applied in the past to plasma, optics, and hydrodynamic waves), this nonlinear wave system evolves at long times with a slow transfer of energy from one mode to another. We derive a kinetic equation for the spectral transfer in terms of the second order moment. We show that such a theory describes the approach to an equilibrium wave spectrum and represents also an energy cascade, often called the Kolmogorov-Zakharov spectrum. We perform numerical simulations that confirm this scenario.     

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.     

Observation of an inverse energy cascade in developed acoustic turbulence in superfluid helium

We report observation of an inverse energy cascade in second sound acoustic turbulence in He II. Its onset occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is developed and shown to be in good agreement with the experiments.     

Anomalous wave as a result of the collision of two wave groups on the sea surface

The numerical simulation of the nonlinear dynamics of the sea surface has shown that the collision of two groups of relatively low waves with close but noncollinear wave vectors (two or three waves in each group with a steepness of about 0.2) can result in the appearance of an individual anomalous wave whose height is noticeably larger than that in the linear theory. Since such collisions quite often occur on the ocean surface, this scenario of the formation of rogue waves is apparently most typical under natural conditions.     

Energy spectra stemming from interactions of Alfvén waves and turbulent eddies

We present a numerical analysis of an incompressible decaying magnetohydrodynamic turbulence run on a grid of 1536{3} points. The Taylor Reynolds number at the maximum of dissipation is approximately 1100, and the initial condition is a superposition of large-scale Arn'old-Beltrami-Childress flows and random noise at small scales, with no uniform magnetic field. The initial kinetic and magnetic energies are equal, with negligible correlation. The resulting energy spectrum is a combination of two components, each moderately resolved. Isotropy obtains in the large scales, with a spectral law compatible with the Iroshnikov-Kraichnan theory stemming from the weakening of nonlinear interactions due to Alfvén waves; scaling of structure functions confirms the non-Kolmogorovian nature of the flow in this range. At small scales, weak turbulence emerges with a k{perpendicular}{-2} spectrum, the perpendicular direction referring to the local quasiuniform magnetic field.     

Weak turbulence of gravity waves

For the first time weak turbulent theory was demonstrated for surface gravity waves. Direct numerical simulation of the dynamical equations shows Kolmogorov turbulent spectra as predicted by analytical analysis [1] from kinetic equation.     

Generation and amplification of magnetic islands by drift interchange turbulence

We investigate the multiscale nonlinear dynamics of a linearly stable or unstable tearing mode with small-scale interchange turbulence using 2D MHD numerical simulations. For a stable tearing mode, the nonlinear beating of the fastest growing small-scale interchange modes drives a magnetic island with an enhanced growth rate to a saturated size that is proportional to the turbulence generated anomalous diffusion. For a linearly unstable tearing mode the island saturation size scales inversely as one-fourth power of the linear tearing growth rate in accordance with weak turbulence theory predictions. Turbulence is also seen to introduce significant modifications in the flow patterns surrounding the magnetic island.     

On the generation and maintenance of waves and turbulence in simulations of free-surface turbulence

One of the challenges in numerical simulation of wave–turbulence interaction is the precise setup and maintenance of wave and turbulence fields. In this paper, we investigate techniques for the generation and suppression of specific surface wave modes, the generation of turbulence in an inhomogeneous physical domain with a wavy boundary-fitted grid, and the generation and maintenance of waves and turbulence during the complex wave–turbulence interaction process. We apply surface pressure to generate and suppress waves. Based on the solution of linearized Cauchy–Poisson problem, we derive three pressure expressions, which lead to a δ-function method, a time-segment method, and a gradual method. Numerical experiments show that these methods generate waves as specified and eliminate spurious waves effectively. The nonlinear wave effect is accounted for with a time-relaxation method. For turbulence generation, we extend the linear forcing method to an inhomogeneous physical domain with a curvilinear computational grid. Effects of force distribution and computational grid distortion are examined. For wave–turbulence interaction, we develop an algorithm to instantaneously identify specific progressive and standing waves. To precisely control the wave amplitude in a complex turbulent flow field, we further develop an energy controlling method. Finally, a simulation example of wave–turbulence interaction is presented. Results show that turbulence has unique features in the presence of waves. Velocity fluctuations are found to be strongly dependent on the wave phase; variations of these fluctuations are explained by the pressure–strain correlation associated with the wave-induced strain field.     

具有基本流动的两层流体界面和表面孤波

本文研究了具有基本流动的两层流体浅水孤波,利用多重尺度摄动方法求得了两流体界面和表面波所满足的KdV方程和相应单孤波解;对所得结果进行了讨论,并将其应用到海洋温跃层和有剪切流动的均匀密度流体两种常见情形。 关键词：     

Weak turbulence of short equatorial waves

We derive a normal form of nonlinear equations for short equatorial waves considered in the framework of the rotating shallow water model. We show dynamical splitting of equatorial Rossby and inertia-gravity waves. We derive an effective Hamiltonian for the short inertia-gravity waves and consider their kinetics using the weak turbulence approach. Stationary power-law energy spectra are obtained. They have different slopes for eastward and westward propagating waves due to the fact that resonant triads of inertia-gravity waves exist only in specific regions of the phase-space.     

Stochastic simulation of unidirectional intense waves in deep water applied to rogue waves

The results of numerical and laboratory simulation of ensembles of quasi-random unidirectional intense surface gravity waves in deep water have been summarized. The role of nonlinear self-modulation of the waves applied to the problem of ocean rogue waves, as well as the appearance, dynamics, and manifestation of non-linear wave packets in stochastic wave fields, is discussed.     

Complex Ginzburg-Landau equation for nonlinear travelling waves in extrinsic semiconductors

We study the nonlinear state of a travelling-wave instability occurring close to the onset of impact ionization in extrinsic semiconductors. Our investigations are based on a complex Ginzburg-Landau equation (CGLE). For a simple generation-recombination function including impact ionization and thermal recombination of the charge carriers, we find a supercritical bifurcation of stable travelling waves for most parameter values. The results are compared with a numerical solution of the basic equations of motion. Furthermore, we expect that weak turbulence phenomena should be observed in semiconductors if their specific generation-recombination kinetics leads to a CGLE with appropriate coefficients.     

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.     

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.     

Induced scattering and two-photon absorption of Alfvén waves with arbitrary propagation angles

An equation for the spectral energy density of collisionless Alfvén waves, propagating at arbitrary angles to the average magnetic field, is derived on the basis of the theory of weak turbulence. The main nonlinear processes for the case studied are induced scattering and two-photon absorption of Alfvén waves by thermal ions. An equation is derived for thermal particles which describes particle diffusion, accompanying these processes, in momentum space. The results are qualitatively different from previous results obtained by other authors for Alfvén waves propagating along the average magnetic field.     

Weakly nonlinear non-Boussinesq internal gravity wavepackets

Internal gravity wavepackets induce a horizontal mean flow that interacts nonlinearly with the waves if they are of moderately large amplitude. In this work, a new theoretical derivation for the wave-induced mean flow of internal gravity waves is presented. Using this we examine the weakly nonlinear evolution of internal wavepackets in two dimensions. By restricting the two-dimensional waves to be horizontally periodic and vertically localized, we derive the nonlinear Schrödinger equation describing the vertical and temporal evolution of the amplitude envelope of non-Boussinesq waves. The results are compared with fully nonlinear numerical simulations restricted to two dimensions. The initially small-amplitude wavepacket grows to become weakly nonlinear as it propagates upward due to non-Boussinesq effects. In comparison with the results of fully nonlinear numerical simulations, the nonlinear Schrödinger equation is found to capture the dominant initial behaviour of the waves, indicating that the interaction of the waves with the induced horizontal mean flow is the dominant mechanism for weakly nonlinear evolution. In particular, due to modulational stability, hydrostatic waves propagate well above the level at which linear theory predicts they should overturn, whereas strongly non-hydrostatic waves, which are modulationally unstable, break below the overturning level predicted by linear theory.