Generation mechanisms for capillary-gravity wind wave spectrum

We investigate the role of different physical mechanisms in the generation of the capillary-gravity wind wave spectrum. This spectrum is calculated by integrating a nonstationary kinetic equation until the solution becomes stready. The mechanisms of spectrum generation under consideration include three-wave interactions, viscous dissipation, energy influx from wind, nonlinear dissipation, and the generation of a parasitic capillary ripple. The three-wave interactions are taken into account as an integral of collisions without additional simplifications. It is shown that the three-wave interactions lead to solution instability if the kinetic equation takes into account only linear sources. To stabilize the solution, the kinetic equation should incorporate a nonlinear dissipation term, which in the range of short gravity waves corresponds to energy losses during wave breaking and microscale wave breaking. In the range of capillary waves, the account of nonlinear dissipation is also needed to ensure a realistic level of the spectrum for large wind velocities. For the steady-state spectrum, the role of three-wave interactions remains essential merely in the range of the minimum of phase velocity, where a trough on the curvature spectrum is formed. At the remaining intervals of the spectrum, the main contribution into the spectral energy balance is provided by the mechanisms of wave injection, nonlinear dissipation, and the generation of parasitic capillaries.     

Effects of three-wave interactions in the gravity-capillary range of wind waves

The formation of the spectrum of short wind waves from the gravity-capillary and capillary ranges under the effect of three-wave interactions is considered. In order to determine the spectrum, the kinetic equation for wave packets is integrated to the point where the solution is established. Three-wave interactions are described by a collision integral without introducing any additional assumptions simplifying the problem. This calculation procedure reproduces the Zakharov-Filonenko theoretical spectra, which correspond to the cases of energy equipartition and the inertial range. It is shown that the main role of three-wave interactions lies in the energy transfer from the range of short gravity waves to waves with shorter wavelengths. This transfer is accomplished both locally in the Fourier space and as a result of interactions between short and long waves. Its characteristic features are the formation of a dip on the curvature spectrum in the region of a minimum phase velocity of waves and the formation of a secondary peak in the capillary range. The dip is filled and disappears as the wind speed increases. Taking into account the interaction between short and long waves increases the spectrum in the capillary range several times, and the balance between energy input from long waves and viscous dissipation is established in the capillary range. The energy sink caused by three-wave interactions, viscous dissipation, and wind forcing cannot give the stability of the spectrum of short gravity waves.     

运动物体生成内波的一类非线性谱方程组

本文给出了由运动物体所生成内波的基本方程组和对应的谱方程组。该方程组的线性部分是一具有体积源 (其下简称为体源 )的 Sturm- Liouville本征值问题 ,而它的非线性部分是由体源与线性波场相互作用的谱表示。在这类强迫方程的源项中包含了 10类内波谱 ,这些谱最终均可利用内波的振幅谱表示。本文给出了线性波场波要素的谱表示和运动物体生成内波的非线性谱方程可解性的讨论。为了检验所得到的谱方程组 ,文中又进行了该谱方程组线性部分的数值计算。     

Calculation of the nonlinear energy transfer through the wave spectrum at the sea surface covered with broken ice

The nonlinear energy transfer through the wave spectrum is studied on the basis of the previously obtained explicit equation for matrix elements of a four-wave kinetic integral. The equation describes the evolution of a system of gravity waves at the surface of a sea of finite depth with a uniform distribution of broken ice over the sea surface. Particular attention is paid to the analytical part of the algorithm of the calculation of the kinetic integral. This part differs from the standard algorithm by a set of prominent features of the dispersion relation for wave oscillations in the ice-covered water. The kinetic integral for the system under consideration is calculated, and the results are compared with the results obtained for the ice-free water.     

Spectral evolution of surface waves in a deep sea due to the effect of wave-wave interactions

The wave-wave kinetic equation for surface gravity waves in a deep sea is solved numerically, using the Runge-Kutta technique. Spectral evolution of waves resulted only from their being non-linear, with no wave generation and decaying taking place. To perform computations the JONSWAP-type frequency spectra and a variety of angular wave spectra were used. The angular spectrum of waves turned out to be stable. The frequency spectrum differed from the JONSWAP spectrum in that it had a high-frequency part, which was not similar to the Phillips spectrum. The form of the high-frequency spectral slope was determined as a result of spectral evolution and proved to have the form of the ‘−6’ law. Translated by Vladimir A. Puchkin.     

The Role of Evolution Mechanisms in the Formation of a Wind-Wave Equilibrium Spectrum

The formation of a stationary (equilibrium) range in a wind-wave spectrum is investigated by numerical simulation. The equation of evolution of the wind-wave spectrum is solved using the exact calculation of the Hasselmann kinetic integral and involving various modifications of known parameterizations of the mechanisms of wave pumping by wind (In) and of wave dissipation (Dis). It is shown that it is these two mechanisms that are responsible for the shape of the stationary range of the wind-wave spectrum, whereas the nonlinear mechanism plays a stabilizing but subsidiary role. With an appropriate choice of mathematical representations for In and Dis, any known empirical shape of the stationary range of the spectrum can be obtained. During the calculations it is found that, for real wind waves, the known representations of In and Dis do not ensure the existence of the inertial interval required for Kolmogorov-type spectra formation due to the nonlinear interactions between waves.     

深水波中进动共振的数值模拟研究

进动(precession)共振是一种非线性共振相互作用,2016年才有学者对这一现象进行研究。采用非静压二维自由表面流模型模拟了深水条件下重力波的进动共振现象。通过边界造波的方法产生双色波,分析了触发进动共振的初始条件;探讨了进动共振在小振幅前提条件下发生的简化初始条件。数值模拟分析两组对称测点,对不同测点的波面、能量谱进行对比分析。数值结果表明:非静压二维自由表面流模型可以模拟进动共振现象,并且可以采用双色波作为条件来研究深水五波进动共振现象,进动共振需要一定的能量转化时间,进动共振发生的条件是三波组合的进动频率等于一个系统存在的非线性频率。     

北太平洋副热带逆流区涡旋动能谱的季节性变化及其机制

本文利用了23年的卫星高度计数据和WOA13气候态月平均温盐资料,考察了北太平洋副热带逆流(STCC)区涡旋动能谱及其涡旋尺度季节变化的动力过程。为了揭示其动力机制,本文采用了斜压2.5层模式并结合动能串级的理论进行分析。结果表明,在STCC区由于海洋层结及地转流的垂向剪切发生了季节性变化,从而产生的斜压不稳定是导致涡旋动能谱季节变化的原因。涡旋动能最大的时间发生在5—6月份,滞后于斜压最不稳定发生的时间(3月份)约2—3个月左右,这是由于斜压不稳定产生的扰动需要一定时间才能发展成振幅足够大的涡旋。斜压不稳定提供的能量使得涡旋相互作用加强,产生了动能逆向串级,动能谱向更大尺度转移。涡旋能量尺度在3月份仅为280km,而在9月份达到最高值335km左右。另一方面,我们发现STCC区动能谱斜率及动能谱通量也有季节变化,在涡旋动能最大的5—6月份,当尺度小于罗斯贝变形尺度时,谱斜率达到1k–3,而动能谱通量达到最大值。对STCC区涡动能谱及涡旋尺度季节变化的研究,对深入认识中尺度涡旋的产生及其演变机制有着重要的意义。     

Instability of Two Interacting Quasi-Monochromatic Waves in Shallow Water

The nonlinear interactions of waves with a double-peaked power spectrum have been studied in shallow water.The starting point is the prototypical equation for nonlinear unidirectional waves in shallow water,i.e.the Korteweg de Vries equation.By means of a multiple-scale technique two defocusing coupled Nonlinear Schrdinger equations are derived.It is found analytically that plane wave solutions of such a system are unstable for small perturbations,showing that the existence of a new energy exchange mechanism which can influence the behavior of ocean waves in shallow water.     

Evolution of surge in the sea of finite depth under the effect of wave-wave interactions

The wave-wave kinetic equation for surface gravity waves occurring in a deep sea and a sea of finite depth is solved numerically, using the Runge-Kutta technique. Spectral evolution was the result only of the waves’ being non-linear, without any contribution from wave generation and dissipation. The JONSWAP frequency spectra and the angular spectra of various widths were used to perform calculations. The existence of a steady angular wave spectrum, following its long evolution in a deep sea, has been confirmed here. For the sea of finite depth, a new result has been obtained. It exhibits the ‘focusing’ of the frequential and the angular spectra when the wavelength of a harmonic from the spectral maximum equals 2π, of the depth of the sea. With the depth further decreasing, the wave spectrum swiftly expands. The three-dimensional wave field in a deep sea becomes two-dimensional in the shallows. Translated by Vladimir A. Puchkin.     

A coupled discrete wave model MRI-II

An ocean wind-wave prediction model MRI-II is developed on the basis of the energy balance equation which contains five energy transfer processes, namely, the input by the wind, the nonlinear transfer among the components of windsea by resonant wave-wave interactions, wave breaking, frictional dissipation and the effect of opposing winds. The nonlinear energy transfer is expressed implicitly together with the wind effect by Toba's one-parameter representation of windsea, but neither swell-swell nor swell-windsea resonant interactions are considered. Hypothetical assumptions are introduced to describe wave breaking effects. The numerical constant required in the assumptions of wave breaking is determined through trial test runs for a hindcast performed on the North-western Pacific Ocean. The significant wave height, one-dimensional wave spectrum and two-dimensional wave spectrum hindcasted by this new model are in more reasonable agreement with observations than those obtained with our old model MRI.     

On the calculation of the depth of the upper mixed layer in the equatorial ocean

The equation for the turbulence kinetic energy balance as applied to the horizontally-inhomogeneous upper ocean layer encompassing the equatorial zone is analysed. A partial solution of the equation has been derived for the equilibrium conditions. Using the equatorial Atlantic as an example, the prime importance of considering the effect of horizontal heterogeneity in calculating the upper mixed layer thickness is shown.Translated by Vladimir A. Puchkin.     

Numerical modelling of flux spectra for the case of angular anisotropy

On the basis of numerical solution of a kinetic equation governing non-linear wave energy redistribution over the spectrum from sourceG to sinkD, it has been found that spectra of constant flux occur in the case of anisotropic distribution of the source (or sink) with respect to angle. It has been shown that with sourceG(ω) localized in the upper part of the frequency band, as compared with the sink localization area,D(ω), a flux spectrum that is anisotropic with respect to angle is realized. WithG(ω) andD(ω) being inversely located, the stabilized flux spectrum is essentially anisotropic with respect to angle. Unidimensional stabilized spectraS(ω), averaged by angle, then have power functions similar to those of the isotropic case of source/sink distribution studied by Zakharov in 1996. Spectral characteristics have been obtained and the calculated results interpreted. Translated by Vladimir A. Puchkin.     

Physical model of the spectrum of capillary-gravity waves

A model for the spectrum of capillary waves has been constructed. These waves are generated at the crests of short gravity waves and decay due to viscosity. Capillary wave generation leads to short gravity wave dissipation. Using empirical data on the short gravity wave dissipation spectrum, a relation for the capillary wave spectrum is derived from the equation of energy balance of capillary waves. The capillary wave spectrum is matched with the known Donelan-Pierson spectrum for short gravity waves. The obtained relation for the spectrum of wind-generated ripple is compared with the data of laboratory experiments. Translated by Vladimir A. Puchkin.     

论运动坐标系中的海浪谱

基于Galieo变换，导出了运动坐标系与静止坐标系中海浪谱间的关系。由于海浪是频散的，两者间的关系是频率相关的。运动坐标系中的海浪频谱是与静止坐标系中的海浪方向谱相联系的。以文氏谱作为静止坐标系中的海浪频谱，给出了不同速度下运动坐标系中的海浪频谱。     

Modeling nonlinear wave–wave interactions with the elliptic mild slope equation

An approach is developed to simulate wave–wave interactions using nonlinear elliptic mild-slope equation in domains where wave reflection, refraction, diffraction and breaking effects must also be considered. This involves the construction of an efficient solution procedure including effective boundary treatment, modification of the nonlinear equation to resolve convergence issues, and validation of the overall approach. For solving the second-order boundary-value problem, the Alternating Direction Implicit (ADI) scheme is employed, and the use of approximate boundary conditions is supplemented, for improved accuracy, with internal wave generation method and dissipative sponge layers. The performance of the nonlinear model is investigated for a range of practical wave conditions involving reflection, diffraction and shoaling in the presence of nonlinear wave–wave interactions. In addition, the transformation of a wave spectrum due to nonlinear shoaling and breaking, and nonlinear resonance inside a rectangular harbor are simulated. Numerical calculations are compared with the results from other relevant nonlinear models and experimental data available in literature. Results show that the approach developed here performs reasonably well, and has thus improved the applicability of this class of wave transformation models.     

A Eulerian–Lagrangian method for the simulation of wave propagation

A Eulerian–Lagrangian method (ELM) is employed for the simulation of wave propagation in the present research. The wave action conservation equation, instead of the wave energy balance equation, is used. The wave action is conservative and the action flux remains constant along the wave rays. The ELM correctly accounts for this physical characteristic of wave propagation and integrates the wave action spectrum along the wave rays. Thus, the total derivative for wave action spectrum may be introduced into the numerical scheme and the complicated partial differential wave action balance equation is simplified into an ordinary differential equation. A number of test cases on wave propagation are carried out and show that the present method is stable, accurate and efficient. The results are compared with analytical solutions and/or other computed results. It is shown that the ELM is superior to the first-order upwind method in accuracy, stability and efficiency and may better reflect the complicated dynamics due to the complicated bathymetry features in shallow water areas.     

A Eulerian–Lagrangian method for the simulation of wave propagation

A Eulerian–Lagrangian method (ELM) is employed for the simulation of wave propagation in the present research. The wave action conservation equation, instead of the wave energy balance equation, is used. The wave action is conservative and the action flux remains constant along the wave rays. The ELM correctly accounts for this physical characteristic of wave propagation and integrates the wave action spectrum along the wave rays. Thus, the total derivative for wave action spectrum may be introduced into the numerical scheme and the complicated partial differential wave action balance equation is simplified into an ordinary differential equation. A number of test cases on wave propagation are carried out and show that the present method is stable, accurate and efficient. The results are compared with analytical solutions and/or other computed results. It is shown that the ELM is superior to the first-order upwind method in accuracy, stability and efficiency and may better reflect the complicated dynamics due to the complicated bathymetry features in shallow water areas.     

Analysis of medaka cytochrome P450 3A homotropic and heterotropic cooperativity

We have previously demonstrated that medaka CYP3A is associated with metabolism of several endobiotics including steroids and bile acids. In this study, we demonstrate that medaka CYP3A catalysis exhibits unusual kinetic behaviors consistent with allosteric interaction which cannot be described by hyperbolic kinetic models. Using 7-benzyloxy-4-(trifluoromethyl)-coumarin (BFC) and nonylphenol as CYP3A substrates, we describe both homotropic and heterotropic cooperative interactions. Given the role of CYP3A in maintaining the homeostatic balance for numerous endobiotics, enzymatic activation/inhibition by endocrine disruptors (EDCs) represents a putative (non-genomic) mechanism for endocrine disruption.     

海浪同化预报模型理论基础

将共轭变分同化方法应用于 LAGFD- WAM海浪数值模式 ,导出了海浪谱能量平衡方程的共轭方程以及风输入、破碎、底摩擦、波波非线性相互作用和波流相互作用的相应共轭源函数 ,建立了海浪同化模型 ,数值计算仍采用特征线嵌入计算格式 ,为合成孔径雷达波谱反演资料和卫星高度计有效波高资料同化奠定理论基础