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.     

星载高级合成孔径雷达波模式算法及其反演数据精度验证

搭载在欧洲环境卫星(ENVISAT)上的高级合成孔径雷达(Advanced Synthetic Aperture Radar,ASAR)二级波模式数据提供了诸多海浪信息包括有效波高、波向、波长和二维海浪谱等,在海浪预报模式中具有重要作用。本文拟利用浮标观测数据对ASAR波模式算法及其反演数据精度进行对比验证。由于SAR卫星在海面的特殊成像机制,不同海况下会有不同的测量结果,通过与美国国家浮标中心(NDBC)的浮标数据对比,显示ASAR有效波高在高海况下低估和在低海况下高估的现象,在中等海况下的测量结果较优。通过研究ASAR数据集中对应的海浪谱,按照能量与方向分布可分为四种类型:单一方向海浪谱(Ⅰ类谱),180°方向模糊海浪谱(Ⅱ类谱),海浪两个方向且能量分布杂乱(Ⅲ类谱),多个传播方向且谱型杂乱海浪谱(Ⅳ类谱)。探究在不同类型下的海浪参数的精度,结果表明在单一波向正常海浪谱情况下,有效波高、波向与浮标数据一致性较好,存在180°方向模糊的对称海浪谱仅有效波高精度较高,谱型杂乱的海浪谱海浪有效波高和波向反演结果均较差。     

Theoretical wind wave frequency spectra in shallow water

The method developed by Wen et al. (1988 a) for deriving theoretical wind wave frequency spectrum in deep water is extended to the case of water of finite depth, in which a parameter η=H/d is introduced, where H and d represent the average wave height and water depth respectively. The derived spectra reduce to those in deep water when η=0. The case of η=1/2 corresponds to waves impending to break because of the effect of the bottom. Simplified forms of spectra are given. The theoretical results agree with the observed spectra well.     

海洋混合层深度时空分布及其与风、浪参数的相关性分析

本文应用一个经验证的全球尺度FVCOM海浪模型,模拟了2012年全球海洋海浪场的分布和演变,分析了海表面风场、海浪场与混合层深度的全球尺度分布及相关性。综合观测资料和模型结果显示,海表面10 m风速、有效波高与混合层深度的全球尺度分布随季节发生显著的变化,并且其分布态势存在明显的相似性。从相关系数的全球分布来看,海表面10 m风速在印度洋低纬度海区（纬度0°~20°）与混合层深度间有较强的相关性,相关系数大于0.5;有效波高与混合层深度间相关系数大于0.5的网格分布在北半球高纬度海区和印度洋北部。谱峰周期与混合层深度间在部分海区存在负相关关系,这些网格主要分布在低纬度海区（纬度0°~30°）。统计结果显示,有效波高、海表面10 m风速和谱峰周期与混合层深度间的平均相关系数分别为0.31、0.25和0.12。综合以上结果表明,有效波高较谱峰周期能更有效地表征波浪能对海洋上层混合的影响;相比于海表面风速,有效波高与混合层深度间存在更强的相关关系,其变化对海洋上层混合有更显著的影响。     

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.     

The limiting wave height in wind-induced wave trains

The vertical acceleration threshold concept has been applied to evaluate the limiting wave height in the train of wind-induced waves propagated over a horizontal bottom. This concept yields very simple computation of the probability of breaking for stochastic sea in deep and finite water depths. The computations confirmed the available field and laboratory observations that the limiting wave steepness in the deep water is lower than the steepness predicted by Stokes. For shallow water depth, the limiting wave height is smaller than 0.55h. This conclusion is consistent with field as well as wave tank observations.     

Phase velocities of surface waves in a sea of finite depth

Dispersion relations and phase velocities of surface gravity waves, with their non-linearity being considered, have been derived numerically from an equation for a nonvortical incompressible fluid of finite depth. For all the depths being considered, the dispersion relations are readily realized for the wavenumbers smaller than the wavenumber of the basic harmonic. Then the acquired relations tend to increasingly deviate from the linear dispersion relations. This is the case for all the depths and wave steepnesses under discussion. When the depth of the sea diminishes, the deviations dramatically increase in both cases, when waves grow steeper and when the form of the wave spectrum changes from wide to narrow. This also holds for the phase velocity of waves. Numerical results are matched up with the experimentally derived data. For calculations, JONSWAP spectra of various width have been used. Translated by Vladimir A. Puchkin.     

Generation of quasiinertial internal waves in the process of evolution of local perturbations in the ocean

Within the framework of a linear model of long waves in a two-layer ocean, we obtain the analytic solution of the problem of evolution of an axially symmetric initial displacement of the jump of density. In the process of adaptation of the fields, internal waves in the form of a decaying (in time) wave packet are emitted from the zone of initial perturbation. These waves are quasiinertial and their dispersion is conditioned by Earth’s rotation. We study the time evolution of the wave packet and the dependence of its characteristics on the width of the zone of initial perturbation and the depth of the jump of density. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 2, pp. 12–23, March–April, 2006.     

西太平洋暖池时空分布特征及其与ENSO的关系

应用NCEP/NCAR SST资料和SODA海温资料,分析研究了热带太平洋海温场的变化特征,讨论了气候突变前后热带西太平洋暖池(以下简称WPWP)形态的显著变化及其差异,由此重新界定了WPWP的范围,并进一步分析了WPWP的时空变化特征。结果表明,新界定的WPWP气候平均场与前人定义的气候平均场分布特征基本相同,但也存在一定的差异。新界定的WPWP的优点在于它不仅能够客观反映出气候(海洋)突变前后西太平洋暖池的时空变化特征,而且重要的是可以避免由前人定义的WPWP与东太平洋暖池合为一体的现象发生,从而避免人为地计算WPWP面积变化带来的结果差异。新界定的WPWP平均深度可达130 m左右,呈现出西浅东深的"耳状"分布特征,在冬春季节,南北(经向)窄东西(纬向)宽,呈纬向带状分布;在夏秋季节,WP-WP明显向北扩展。平均深度最大中心位于(5°S,180°)附近。由WPWP区域不同深度的异常海温变化与Niño3指数的相关分析可知,WPWP次表层异常海温变化与Niño3指数呈显著的负相关关系,而与表层的异常海温的关系并不密切,这一结果进一步证明了西太平洋暖池对ENSO的贡献是来自次表层异常海温的东传。     

基于遥感与现场观测数据的南海北部内波传播速度

南海北部是全球海洋中内波最为活跃、生成和演变机制较为复杂的海域,本文利用多源卫星遥感数据(MODIS、GF-1、ENVISAT ASAR、RADARSAT-2)和现场观测数据开展了南海北部内波传播速度的研究。通过匹配捕获同一条内波的相邻两幅遥感图像,由内波的空间位移和时间间隔反演传播速度,并以0.5°×0.5°网格给出了南海北部内波传播速度的分布图。研究结果表明,内波传播速度受背景流场、水体层结和底地形变化等多因素影响,特别是水深。在南海北部由东至西、由南至北方向,内波传播速度逐渐递减。深海区内波传播速度最大,可达3m/s以上;内波在向西大陆架传播过程中,随着水深变浅速度逐渐减慢,传播速度为1—2m/s;大陆架浅海的内波传播速度较小,仅为零点几米每秒。同时,利用Kd V方程反演了内波传播速度理论值,对遥感数据提取的内波传播速度进行了精度验证,结果较为一致。     

Shipboard measurements of the modulation characteristics of 3.2 cm radar signals scattered by the sea surface

The results of shipboard measurements of the modulation characteristics of 3.2 cm radar signals scattered by a rough sea surface at low grazing angles are reported. The experiments were carried out from on-board a drifting research vessel in the Atlantic trade wind zone at wind speeds of 7–10 m s⁻¹ and coinciding directions of the wind and waves. Azimuthal isotropy of the modulation spectra was observed. It is emphasized that the ‘sea surface-scattered signal’ modified modulation transfer function is somewhat larger for horizontal polarization than for vertical polarization. Translated by V. Puchkin.     

The form of the asymptotic depth-limited wind-wave spectrum: Part II — The wavenumber spectrum

Data from a spatial array of wave gauges is analysed using the Wavelet Directional Method (WDM) to directly determine the wavenumber spectrum. The data shows that the asymptotic depth-limited wavenumber spectrum can be represented as a two-parameter form, which is far simpler than the corresponding frequency spectrum. The WDM analysis shows that there are significant nonlinear processes active in the finite depth water, which results in energy being “smeared” across a range of wavenumbers and frequencies around the standard dispersion shell. As a result, the wavenumber spectrum has much less peak enhancement than seen in the frequency spectrum obtained with standard Fourier analysis. In addition, the wavenumber spectrum does not have the clear harmonic previously observed in the finite depth frequency spectrum. This result demonstrates that the harmonic is nonlinearly phase-locked to the spectral peak.     

Statistical Distribution of Depth-Integrated Local Horizontal Momentum for Second-Order Random Ocean Waves in Finite Water Depth

Based on the second-order random wave solutions of water wave equations in tinite water depth, statistical distributions of the depth-integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all detemained by the water depth and the wavenumber spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.     

Three-dimensional nonlinear random wave groups in intermediate water depth

High waves at ocean occur during a complex space–time evolution of wave groups. In this paper the nonlinear structure of three-dimensional sea wave groups at intermediate water depth is investigated. To this purpose, the Boccotti's Quasi-Determinism theory is firstly applied to describe the linear wave groups when a given exceptionally high crest occurs. Then, the second-order correction to the linear solution is derived for the general condition of three-dimensional wave groups, at a finite water depth. Several numerical applications, finally, have been carried out in order to show how both the spectral bandwidth and the directional spreading modify the nonlinear high waves at different water depth.     

Representation of double-peaked sea wave spectra in Jiaozhou Bay

The spectrum shape characteristics of double-peaked sea wave spectia actually measured in the Jiaozhou Bay were analysed and one representation of double-peaked sea wave spectra with six-parameters which can be determined from a given sea wave spectrum is proposed in this paper. After verifying by fitting process with the data sets of double-peaked sea wave spectra measured in the Jiaozhou Bay, it can be seen from the results that the representation mentioned above may be used to express the double-peaked sea wave spectra generated in the Jiaozhou Bay under various sea states, and that the absolute values of maximum deviation index (D.I.) do not exceed 30. 0.     

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.     

一种计算有限水深波能功率的新方法

海洋波浪能平均功率的准确计算是波浪能开发和利用的基础。实践中,波浪能转换装置一般安装在有限水深区域。对于随机波,只有当详尽的波浪谱已知的时候,有限水深区的波能功率才能被准确计算出来。由于种种原因,实践中波浪的实测数据大多以散点图或有义波高和统计波周期的形式给出,而波浪谱信息有时则很难获得。基于这种情况,传统上人们利用无限水深条件下的相关公式来估算有限水深区域的波能功率,但这种做法会造成较大的误差。本研究显示,对于50 m水深的理论波谱JONSWAP谱来说该误差高达14.6%。为了提高波能功率计算的准确性,本文提出了一种基于能量频率的一阶和二阶近似算法,可以在未知波浪谱的情况下较为准确地计算不同水深时的波能功率。针对两种理论波浪谱的计算结果表明,本方法在计算有限带宽内的波能功率时计算误差低于2.8%。     

South China Sea wave characteristics during typhoon Muifa passage in winter 2004

The responses to tropical cyclones of ocean wave characteristics in deep water of the western Atlantic Ocean have been investigated extensively, but not the regional seas in the western Pacific such as the South China Sea (SCS), due to a lack of observational and modeling studies there. Since monsoon winds prevail in the SCS but not in the western Atlantic Ocean, the SCS is unique for investigating wave characteristics during a typhoon’s passage in conjunction with steady monsoon wind forcing. To do so, the Wavewatch-III (WW3) is used to study the response of the SCS to Typhoon Muifa (2004), which passed over not only deep water but also the shallow shelf of the SCS. The WW3 model is forced by the NASA QuikSCAT winds and tropical cyclone wind profile model during Typhoon Muifa’s passage from 0000UTC 16 on November to 1200UTC on 25 November 2004. The results reveal the unique features of the SCS wave characteristics in response to Muifa, such as non-decaying, monsoon-generated swell throughout the typhoon period and strong topographic effects on the directional wave spectrum.