Modulation of short wind waves by a long surface wave: a mechanism for feedback with an air flow

The paper concentrates on the evolution of a spectrum of short wind waves (SW) along the profile of a long surface wave (LW). Short wave spectral variations are considered in the relaxation approximation. The SW spectrum is modulated by the orbital velocities of long waves and by the variations of wind stress along the LW profile. The latter effect occurs due to wind flux perturbations induced by both the long wave proper and variations of the sea surface roughness induced by the SW modulations. To describe this effect, a feedback mechanism is introduces—the growth of energy of short waves results in the larger roughness of the sea surface, thereby contributing to the local wind stress, which facilitates, in turn, the growth of short waves. With moderate and strong winds being involved, this effect (aerodynamic feedback) is shown to be dominant in the short wave spectrum modulation. The mechanism becomes more efficient with intensification of the wind and decreasing of the long waves' frequency. Results of model calculations are in agreement with the known experimental data. Translated by Vladimir A. Puchkin.     

Radiophysical investigations of sea roughness (radiooceanography) at the Ukrainian Academy of Sciences

Experiments on the scattering of radio waves in the range 200 m to 3 cm from a rough sea surface are described. Amplitude, frequency, and space-time characteristics of scattered radio signals at different states of the sea surface are presented. It is shown that the problem of the short and medium wave scattering from the sea can be solved by the perturbance method. In this case the mechanism of scattering is of "resonant" character. The intensity of the backscatter signals is proportional to the density of the spatial spectrum on the half-length of the radio waves. The high frequency radio wave scattering is well described by a two-scale model of the scattering surface, "ripple on the large wave." The intensity of scattered radio signals is also proportional to the spectrum density of "ripples" whose length is approximately equal to half a radio wave. The effect of the large waves is to modulate the amplitude of a scattered radio signal and to broaden its frequency spectrum. Methods of solution of the reverse problem were considered. This allowed determination of parameters of sea roughness by characteristics of scattered radio signals. The principles of design of the corresponding equipment are described.     

论风浪的局域结构──Ⅰ.风浪的局域结构与局域小波能谱

基于小波变换,引入了能刻画风浪局域结构的局域小波能谱。论述了风浪的整体结构与局域结构。指出了在不同时间尺度上,风浪具有不同的局域化特征。提出了风场演化过程中整体的共振在线性相互作用是否存在的质疑。     

论风浪的局域结构──Ⅱ.风浪局域小波能谱的性质及应用

引入了局域小波能谱的局域间歇性度量,分析了不同风速下的风浪资料,结果表明,局域小波能谱可依局域频率分为三部分。风浪的群性在三维局域小波能谱图像下显示得更为明显,与风浪有关的一切性质都是局域的,包括风浪的群性。讨论了局域小波谱峰值与谱峰频率的涨落,指出了前者在工程设计中的重要意义,并发现了后者与风浪破碎有关的两种非线性现象。     

基于微结构图像的风生微尺度波频率谱初探

利用海面微结构光学测量装置实验获取到的微尺度波图像来给出风生微尺度波的波数谱,在此基础上利用频散关系建立微尺度波波数谱和频率谱之间的关系,最终得到微尺度波频率谱.对微尺度波的频率谱随频率变化的响应进行了研究,发现频率谱与频率的a次方成正比关系,a的值随风速的增加而增加,同一风速下a几乎为定值.     

海浪外观统计与内部结构关系的数值研究

基于数值模拟的三维随机海面,从时间域和空间域两个角度对海浪的外观特征和内部结构间的关系进行了研究,得出了一些在工程应用上有参考价值的结果.文章认为,将波面看作是若干随机正弦波叠加的海浪结构模型,用于描述平稳、均匀和窄谱的海况时,其频谱分析结果与外观统计结果基本上是一致的;但是,当海面处于谱宽度较大的风浪或混合浪状态时,一些频谱分析结果必须经过修正才能应用.同一海况下,海面波动的时间过程和沿主波向的空间分布是明显不同的.当海面有突发性大浪时,外频谱能够很好地反映不平稳海况,而频谱则把这种不平稳性平滑了.文章着重讨论了波长和波陡的计算、频谱和外频谱的差异.     

Spectral spreading from surface bubble motion

At low frequencies, surface bubbles contribute to acoustic backscattering in aggregate, and the motion of these bubble masses causes spectral spreading of the acoustic signals. This motion of the bubbles entrained in the surface waves is used to obtain the power spectrum of a low-frequency surface-scattered signal at a low grazing angle. A spectral distribution of the deterministic surface drift, augmented by breaking wave crests, is developed for the wave frequency components that are actively breaking. This motion is combined with the random motion in a wave cycle to predict the spectral widths of low-angle backscattered sound. To permit comparisons with measured data, convolutions of these spectra with simple square pulses of various durations are performed     

变浅作用下的长周期重力波的实验研究

利用大型水槽设计了在由深水到近岸不同坡度处海浪在变浅作用下诱导产生的长周期重力波的实验。正态随机海浪在深水生成并沿斜坡向浅水传播,记录了不同水深处波面高度随时间的变化过程并进行统计分析和谱分析。实验数据分析结果表明,长周期重力波的能量随着水深的变浅而增高,其谱锋频率位于0.2~0.3fp附近,这里fp是深水正态海浪过程的谱峰频率。长周期重力波的能量与入射波的能量比与波面高度分布的偏度密切相关。进一步分析了两种波动的能量谱峰值比和波面高度分布偏度的相关关系,获得了经验关系,为预测近岸浅水长周期重力波提供了科学依据。     

The statistics of HF sea-echo Doppler spectra

Several important statistical properties of the HF sea echo and its Doppler power spectrum, which are useful in optimizing the design of radar oceanographic experiments, are established. First- and second-order theories show that the echo signal (e.g., the voltage) should be Gaussian; this is confirmed with experimental surface-wave data i) by comparison of the normalized standard deviation of the power spectrum at a given frequency with its predicted value of unity, and ii) by cumulative distribution plots of measured spectral amplitudes on Rayleigh probability charts. The normalized standard deviation of the dominant absolute peak amplitudes of the power spectrum (which wander slightly in frequency) are shown from experimental data to besim 0.7for the first-order peaks andsim 0.5for the second-order peaks. The autocorrelation coefficient of the power spectra is derived from measured data and interpreted in terms of the spectral peak widths; from this information, the correlation time (or time between independent power spectrum samples) iS shown to besim 25-50s for radar frequencies above 7 MHz. All of these statistical quantities are observed to be independent of sea state, scattering cell size, and relatively independent of radar operating frequency. These quantities are then used to establish the statistical error (and confidence interval) for radar remote sensing of sea state, and it is shown, for example, that 14 power spectral samples result in a sample average whose rms error about the true mean is 1.0 dB.     

广东阳西近岸海域海浪谱分析

根据广东阳西近岸海域测站1a实测共4 949组的原始随机波面观测记录,用自相关函数法和快速傅里叶变换法进行谱估计,得到波谱各特征参数,并与实测波面统计的特征值进行比较,经分析,选用快速傅里叶变换法估计研究海域的实测谱,对粗谱进行平滑和分析,筛选出研究海域海浪的样本谱498个,将平滑后的谱形无维量化,得到广东阳西海域海浪无维量平均谱曲线并求出对应谱参数,计算得到谱峰频率f0为0.121,特征频率μ10、μ20分别为1.929、2.733,谱宽度ε、ν为0.83、1.39.采用5种理论频谱模式对实测无维量谱进行拟合,根据拟合结果推荐γ=1.920 5的JONSWAP谱或者b=5.7、δ=6.0、k=0.5的莆田谱作为广东阳西近岸海域的海浪谱型,对该海区的工程建设、海浪预报警报和海浪理论研究具有较好的参考作用,对我国其他类似海域也有一定的参考价值.     

Analytic solution of long wave propagation over a submerged hump

A new analytical solution of the long wave refraction by a submerged circular hump is presented. The geometry of the hump is assumed to be axisymmetric and be described by a power function in the radial direction with arbitrary values of both the exponent and the scaling factor. The submergence of the hump is also variable. The water surface elevation governed by the long wave version of the mild slope wave equation is solved by separation of variables, and a series solution of the Frobenius type is obtained. The solution is shown to be valid when the hump is sufficiently submerged or is of a relatively small height. Matching method is employed to illustrate the refraction of long waves under given conditions of incidence. Effects of the shape, the scale, and the submergence of the hump on wave refraction are discussed.     

Design of periodic signals using FM sweeps and amplitude modulationfor ocean acoustic travel-time measurements

A design procedure for an amplitude-modulated and nonlinear frequency-modulated (AM-NLFM) signal is introduced. The designed signal can drive a given transducer to its peak power to produce a sound pressure waveform into the water with a desired power spectrum and maximum possible energy. The signal can be formed either in the time domain or in the frequency domain. The frequency domain approach gives an output power spectrum precisely identical to a preferred shape. Therefore, the sidelobe levels after matched filtering are not raised by unwanted spectral magnitude ripples which exist when a time domain method is adopted. The absence of spectral ripples is desirable for applications requiring long range transmission and good multipath discrimination capability. An acceptable tradeoff between time resolution and sidelobe levels is achieved by properly choosing the desired power spectral shape. As the time resolution is usually the most critical specification for precision travel-time measurements, it is shown that by sacrificing some of the transducer's output power capability, a waveform with a considerably wider bandwidth can be transmitted, resulting in a significantly enhanced time resolution. A quasi-steady-state (QSS) approximation is used in the signal design, leading to a manageable and intuitive design procedure     

Acoustic plane-wave scattering from a rough interface over an inhomogeneous transition fluid layer

Acoustic scattering of a plane wave incident upon a rough surface over a transition fluid layer within which both the density and sound speed vary with depth is considered. A theory based upon a boundary perturbation method has been applied to a typical seabed environment to study the power spectral density representing the energy distribution of the scattered field over the space. The effects of frequency and roughness properties, including the roughness height, spatial correlation, and power spectrum, on the power spectral density have been investigated. The results demonstrate that the power spectral density of the scattered field depends upon all the aforementioned parameters, particularly the correlation length and the power spectrum of the rough surface, a conclusion in distinct contrast to the results for the coherent field obtained in an earlier study. It was found that the constituents of the rough surface such as the correlation length and wavenumber spectrum dominate the angular distribution of the scattered energy. These results indicate that it is crucial to employ a suitable topological model in the study of rough seabed scattering.     

Water waves induced by a fluctuating tangential stress

In the framework of linear wave theory both the effects of tangential and normal stresses on the water waves are discussed without the assumption of irrotational water motion. A formal solution initially at rest with level surface and developed under the actions of the surface stresses depending arbitrarily on time and sinusoidally on space is obtained.A progressive wave type tangential stress whose wave number and frequency are satisfying the dispersion relation of the water waves is shown to be equivalent to the normal stress of the same type on the growth of the waves except the phase relations between the stresses and the water motion. The growth rate of the waves induced by the tangential stress is also shown to be quite insensitive to the actual value of the viscosity.The rotational part of the water motion can dominate only in the early stage of wave generation and becomes negligible with the growth of the waves relative to the irrotational part of the motion even in the case where the motion is induced by the tangential stress alone. Therefore it is not reasonable to neglect effect of the tangential stress on wind waves even if the developed wind waves seem to be irrotational.     

由波浪压力记录计算表面波谱

对目前仍广为使用的压力测波仪来说,如何通过波浪在某深度处的压力信息来推算海面的波浪状况呢?根据深水小振幅简单波动的经典理论,关系式H_o=H_z exp[kz]成立,式中H_o、H_z分别表示海面和水深z处的波高。将这一关系式应用于实际资料,则由波浪压力记录可以求出H_z、T_z(或λ_z),再由记录的深度z就可以求出H_o。     

A derivation of the scaling law, the power law and the scaling relation for fetch-limited wind waves using the renormalization group theory

A state of wind waves at a fetch is assumed to be transformed into another state of wind waves at a different fetch by the renormalization group transformation. The scaling laws for the covariance of water surface displacement and for the one-dimensional and two-dimensional spectrum and the power law for the growth relation are derived from the fact that the renormalization group transformation constitutes a semigroup. The scaling relation or the relation among the exponents of the power law is also derived, using the two assumptions that the renormalization group transformation is applicable to fetch-limited wind waves and that the saturated range exists, which implies that the directional distribution function of energy in the wave number region much larger than the peak wave number does not depend on wave number.     

Possibilities of using optical spectral analysis to estimate characteristics of roughness in the presence of films on the sea surface

The possibility of using an optical spectrum analyzer (OSA) to determine the degree of short gravity-capillary wave damping by films of surface-active substances (SAS) is studied. Nonlinear mechanisms of optical surface imaging associated with a complex profile of sky brightness and long waves are analyzed. Using the model of free short gravity waves damping by the films, it is shown that the difference between the contrast of roughness and imaging in film-covered surface regions can be substantial and attributed to a variability of the damping degree within a specified wavelength range rather than to the wave-damping value. In addition, it is illustrated that Doppler shifts of the OSA space-time spectrum in regions covered with films can substantially increase due to nonlinear distortions of the surface images. This fact should be taken into account when obtaining additional information on the state of the surface and roughness based on the Doppler shift values.     

Local and far-field surface elevation around a vertical cylinder in unidirectional steep wave groups

The problem of diffraction of a unidirectional incident wave group by a bottom-seated cylinder is considered. We assume the amplitude of the incoming wave to be small in comparison with other linear scales of the problem, and develop the corresponding second-order perturbation theory. We use the Fourier transform to treat time variation and separate spatial variables when solving the non-homogeneous second-order problem. The resulting set of non-homogeneous Bessel equations is solved numerically.Solutions for various types of incoming wave spectrum are obtained including the Gaussian spectrum and the Pierson–Moskowitz spectrum. To validate the method, problems with gradually decreasing bandwidth of Gaussian spectrum are solved and it is shown that the corresponding solution approaches that for the monochromatic case. The Pierson–Moskowitz spectrum with a set of realistic physical parameters is used as an example of extreme wave interaction with an offshore structure. The corresponding first- and second-order solutions are obtained and the effect of non-linearity on the solution is discussed with the emphasis on the growth of maximum free-surface elevation on the cylinder’s surface and generation of high frequency free radiated waves.     

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.