Trapped quasi-inertial waves in shear oceanic currents

We studied trapped long quasi-inertial waves in horizontally inhomogeneous flows with low Rossby numbers. A simple heuristic derivation of two equations for the wave amplitude is presented. These equations are true for strong and weak density stratifications. A spectral problem is formulated to find the frequencies of trapped waves based on the amplitude equations. Exact solutions of the hyperbolic problem for a free hyperbolic shear layer are found. It is shown that the location of the trapping area principally depends on the stratification. If the buoyancy frequency is greater than the inertial frequency, trapping occurs in the region of anticyclonic velocity shear; if the buoyancy frequency is smaller than the inertial frequency, trapping occurs in the region of cyclonic velocity shear. Thus, in the first case, the frequencies of the trapped waves are smaller than the inertial frequency, while, in the second case, they are greater. The intense wave activity observed in the regions of oceanic fronts and jet currents can be related to the existence of trapped waves.     

Trapped symmetric disturbances in rotating shear flows

The structure of trapped symmetric disturbances in rotating stratified shear flows is investigated theoretically. It is shown that the arrangement of the trapping region is determined by atmospheric stratification. For example, if the characteristic Brunt-Väisälä frequency is greater (smaller) than the inertial frequency, waves are trapped in the region of anticyclonic (cyclonic) velocity shear. Accordingly, in the first (second) case, the frequencies of trapped waves are smaller (greater) than the inertial frequency. The problem of finding the frequencies of trapped waves is reduced to solving the Schrödinger equation but with a more complex dependence on a spectral parameter. Exact solutions to the problem are obtained for a triangular jet and a hyperbolic shear layer.     

Strong near-inertial oscillations in geostrophic shear in the northern South China Sea

With observational data from three Acoustic Doppler Current Profiler (ADCP) moorings, we detected strong near-inertial oscillations (NIO) in the continental shelf region of the northern South China Sea in July 2008. The amplitude of the near-inertial current velocity is much greater than that of diurnal and semi-diurnal tides. The power of the NIOs is strongest in the intermediate layer, relatively weak in the surface layer, and insignificant in the near-bottom layer. The spectral analysis indicates that the NIOs have a peak frequency of 0.0307 cph, which is 2% lower than the local inertial frequency, i.e., a red-shift. The near-inertial wave has an upward vertical phase velocity, which involves a downward group velocity and energy flux. The estimated vertical phase velocity is about 43 m day⁻¹, corresponding to a vertical wave length of about 58 m. The horizontal scale of the NIOs is at least hundreds of kilometers. This NIO event lasted for about 15 days after a typhoon’s passage. Given the northeastward background flow with significant horizontal shear, both Doppler shift and shear flow modulation mechanisms may be responsible for the red-shift of the observed NIOs. For the shear flow mechanism, the observed negative background vorticity and the corresponding effective Coriolis frequency reduce the lower limit of admissible frequency band for the NIOs, causing the red-shift. Meanwhile, the mooring area with the broadened frequency band acts as a wave-guide. The trapping and amplification effects lead to the relatively long sustaining period of the observed NIOs.     

Near inertial motion excited by wind change in a margin of the Typhoon 9019

An excitation of inertial oscillation in the upper layer east of course of Typhoon 9019 was fortuitously observed at three surface buoys deployed during the Ocean Mixed Layer Experiment (OMLET). The observed inertial oscillation was compared with wind fluctuation measured at Ocean Weather Station T (29°N, 135°E) which was placed at the center of a triangle with three vertexes occupied by the respective surface buoys. Inertial oscillation is effectively excited in the mixed layer at the eastern margin of the typhoon by a rapid decrease of wind rather than by prevailing strong wind. It is shown by means of a least square deviation that the inertial oscillation observed in the mixed layer has a period of 23.9 hours shorter than the local inertial period of 24.7 hours. This shorter period suggests that the inertial oscillation has the finite velocities of phase and group as an inertial internal wave. A theoretically obtained ratio of vertical component of group velocity to that of phase velocity, approximately agrees with observed value. The inertial internal wave is excited by fluctuation of divergence with near inertial period in the mixed layer.     

A note on the effects of a thin visco-elastic mud layer on small amplitude water-wave propagation

In this note we investigated the effects of a thin visco-elastic mud layer on wave propagation. Within the framework of linear water-wave theory, analytical solutions are obtained for damping rate, dispersion relation between wave frequency and wave number, and velocity components in the water column and mud layer. The wave attenuation rate reaches a maximum value when the mud layer thickness is about the same as the mud boundary layer thickness. Heavier mud has a weaker effect on the wave damping. However, the wave attenuation rate does not always decrease as the elastic shear modulus increases. In the range of small values for elastic shear modulus, the wave attenuation can be amplified quite significantly. The current solutions are compared with experimental data with different wave conditions and mud properties. In general, good agreements are observed.     

Experimental study on internal waves in a stratified shear flow

This paper describes experiments on interfacial phenomena in a stratified shear flow having a sharp velocity shear at a density interface. The interface was visualized in vertical cross-section using dye, and the flow pattern was traced using aluminum powder. Two kinds of internal waves with different phase velocities and wave profiles were observed. They are here named p(positive)-waves and n(negative)-waves, respectively. By means of a two-dimensional visualization technique, the following facts have been confirmed regarding these waves. (1) The two kinds of waves propagate in the opposite direction relative to a system moving with the mean velocity at the interface, and their dispersion relations approximately agree with the two solutions of interfacial waves in a two-layer system of a linear basic shear flow. (2) The p-wave has sharp crests and flat troughs, and the n-wave has the reverse of this. This difference in wave profile is due to the finite amplitude effect. (3) Phase velocity of each wave lies within the range of the mean velocity profile, so that a critical layer exists and each wave has a “cat's eye” flow pattern in the vicinity of the critical layer, when observed in a system moving with the phase velocity. Consequently, these two waves are symmetrical with respect to the interface. The mechanisms of generation of these waves, and the entrainment process are discussed. It is inferred that when the “cat's eye” flow pattern is distorted and a stagnation point approaches the interface, entrainment in the form of a stretched wisp from the lower to the upper layer occurs for the p-wave, and from the upper to the lower layer for the n-wave.     

海浪外观谱及其平衡域

定义了海浪能量的广义或n阶外观分布,导出了n阶海浪外观谱的解析形式,讨论了n阶外观谱的平衡域.结果表明,n阶外观谱的平衡域指数为-(3+n);平衡域指数上界为-3.任何波动现象,只要Fourier迭加原理和射线理论对它们的描述足够准确,则本文的结论皆成立.     

Outer frequency spectrum of sea waves and its equilibrium range

Ｔｈｅｐｒｅｓｅｎｔｐａｐｅｒｄｅｆｉｎｅｓｔｈｅｇｅｎｅｒａｌｉｚｅｄａｐｐａｒｅｎｔｅｎｅｒｇｙｄｉｓｔｒｉｂｕｔｉｏｎａｎｄｄｅｒｉｖｅｓｔｈｅａｎａｌｖｔｉｃａｌｆｏｒｍｏｆｔｈｅｓｏ－ｃａｌｌｅｄｇｅｎｅｒａｌｉｚｅｄｏｕｔｅｒｆｒｅｑｕｅｎｃｙｓｐｅｃｔｒｕｍｏｒｎｔｈｏｒｄｅｒａｐｐａｒｅｎｔｆｒｅｑｕｅｎｃｙｓｐｅｃｔｒｕｍ．Ｉｔｉｓｓｈｏｗｎｔｈａｔｔｈｅｇｅｎ－ｅｒａｌｉｚｅｄｏｕｔｅｒｆｒｅｑｕｅｎｃｙｓｐｅｃｔｒｕｍｈａｓａｎｅｑｕｉｌｉｂｒｉｕｍｒａｎｇｅｗｉｔｈａｎｅｘｐｏｎｅｎｔ（ｎ＋３）ａｎｄｔｈｅｕｐｐｅｒｌｉｍｉｔｏｆｔｈｅｅｘ－ｐｏｎｅｎｔｉｓ－３．ＴｈｅｒｅｓｕｌｔｓｏｆｔｈｉｓｐａｐｅｒａｒｅｕｎｉｖｅｒｓａｌａｎｄａｒｅａｐｐｌｉｃａｂｌｅｆｏｒａｎｙｏｔｈｅｒｗａｖｅｐｈｅｎｏｍｅｎａｉｆｔｈｅｒａｙｔｈｅｏｒｙｏｆｗａｖｅｓａｎｄｔｈｅＬｏｎｇｕｅｔ－Ｈｉｇｇｉｎｓ，ｌｉｎｅａｒｒａｎｄｏｍｗａｖｅｍｏｄｅｌａｒｅｅｘａｃｔｅｎｏｕｇｈｆｏｒｔｈｅｉｒｄｅｓｃｚｉｐｔｉｏｎ．     

Characteristics of the boundary layer at the bottom of a solitary wave

The results of direct numerical simulations of the boundary layer generated at the bottom of a solitary wave are described. The numerical results, which agree with the laboratory measurements of Sumer et al. (2010) show that the flow regime in the boundary layer can be laminar, laminar with coherent vortices and turbulent. The average velocity and bottom shear stress are computed and the results obtained show that the logarithmic law can approximate the velocity profile only in a restricted range of the parameters and at particular phases of the wave cycle. Moreover, the maximum value of the bottom shear stress is found to depend on the dimensionless wave height only, while the minimum (negative) value depends also on the dimensionless boundary layer thickness. Diagrams and simple formulae are proposed to evaluate the minimum and maximum bottom shear stresses and their phase shift with respect to the wave crest.     

Hamiltonian description of shear and gravity shear waves in an ideal incompressible fluid

Methods of studying the dynamics of wave disturbances in st;ratified shear flows of an ideal incompressible fluid are considered. The equations governing the motions of interest represent Hamilton equations and are derived by writing the velocity field in terms of Clebsch potentials. Equations written in terms of semi-Lagrangian variables are integrodifferential equations, which make it possible to consider both continuous and discontinuous solutions, as well as the cases where the parameters of the undisturbed medium are step functions. Two dynamic systems are presented. The first, canonical system of equations is most suitable for describing gravity waves in a shear flow in the case where the undisturbed medium is characterized by sharp gradients of density and flow velocity. The simplest model in which disturbances obey this system of equations is the well-known Kelvin-Helmholtz model. The second dynamic system describes, in particular, gravity-shear waves and, in the case of a homogeneous medium, shear waves in a two-dimensional flow. This system is most suitable for studying the dynamics of disturbances in models with sharp gradients of vorticity. On the basis of the approach developed in this study, the problem of the dynamics of disturbances in a flow with a continuous distribution of vorticity in a finite-thickness layer is solved. If the thickness of this layer is small compared to the characteristic wavelength and the gradient of the undisturbed vorticity in this layer is large, the solution has the form of a mode whose frequency is close to the frequency of the shear wave on a vorticity jump that would be obtained by letting the layer’s thickness approach zero. The results obtained allow, in particular, the estimation of the range of validity of finite-layer approximations for models with smooth profiles of flow and density. In addition, these results can be interpreted as the basis for the development of nonlinear aspects of the theory of hydrodynamic stability.     

Laboratory observation of boundary layer flow under spilling breakers in surf zone using particle image velocimetry

A boundary layer flow under spilling breakers in a laboratory surf zone with a smooth bottom is investigated using a high resolution particle image velocimetry (PIV) technique. By cross-correlating the images, oscillatory velocity profiles within a viscous boundary layer of O(1) mm in thickness are resolved over ten points. Using PIV measurements taken for an earlier study and the present study, flow properties in the wave bottom boundary layer (WBBL) over the laboratory surf zone are obtained, including the mean velocities, turbulence intensity, Reynolds stresses, and intermittency of coherent events. The data are then used to estimate the boundary layer thickness, phase variation, and bottom shear stress. It is found that while the time averaged mass transport inside the WBBL is onshore in the outer surf zone, it changes to offshore in the inner surf zone. The zero Eulerian mass transport occurs at h/h_b ≈ 0.92 in the outer surf zone. The maximum overshoot of the streamwise velocity and boundary layer thickness are not constant across the surf zone. The bottom shear stress is mainly contributed by the viscous stress through mean velocity gradient while the Reynolds stress is small and negligible. The turbulence level is higher in the inner surf zone than that in the outer surf zone, although only a slight increase of turbulent intensity is observed inside the WBBL from the outer surf zone to the inner surf zone. The variation of phase inside and outside the WBBL was examined through the spatial velocity distribution. It is found the phase lead is not constant and its value is significantly smaller than previous thought. By analyzing instantaneous velocity and vorticity fields, a remarkable number of intermittent turbulent eddies are observed to penetrate into the WBBL in the inner surf zone. The size of the observed large eddies is about 0.11 to 0.16 times the local water depth. Its energy spectra follow the − 5/3 slope in the inertial subrange and decay exponentially in the dissipation subrange.     

旋转地球上不可压缩流体惯性重力波的频率方程

用微扰动方法对旋转地球上不可压缩流体的控制方程组进行线性化,得到了扰动解和流体界面上惯性重力波的频率方程。表面惯性重力波和惯性重力内波的相速公式都是这个更普遍的频率方程的特殊情况。     

Wave-power absorption by an array of attenuators oscillating with unconstrained amplitudes

An infinite array of evenly spaced groups of oscillating bodies is considered. All groups (or ‘attenuators’) are equal and they have the same directional orientation. The angle of wave incidence is arbitrary. Regular waves diffracted and radiated from the bodies interfere constructively into rays of plane waves propagating away from the array. The number of rays depends on the ratio between the wavelength and the interspacing between adjacent groups. To each ray there corresponds one term in the ‘array radiation resistance matrix’. The maximum wave power absorbed by the array is derived under the assumption of linear theory and of unconstrained amplitudes of the oscillating bodies. It is found that, apart from exceptional cases, all of the incident wave power may be absorbed by the array provided the total number of oscillating modes in each group is at least as large as the number of rays. It is then explicitly demonstrated that the condition for maximum power absorption is that all rays have a vanishing intensity. Further, some previously known general relations between scattered waves and radiated waves have been extended.     

海底沉积物实验室剪切波速度及其与沉积物的物理性质之间的关系

采用压电陶瓷弯曲元法和共振柱试验的方法对采自我国海域的一些典型海底浅表层沉积物样品进行了剪切波速测试,获得首批可信数据.两种方法所测得的剪切波速数据具有很好的一致性,且在数赫兹至数十千赫兹频段范围内剪切波速不具明显弥散性.剪切波速与沉积物类型关系密切,不同海区和不同类型海底沉积物的剪切波速有明显差异.近海较细颗粒沉积物粉砂的剪切波速在100m/s左右,细颗粒沉积物的剪切波速在100m/s以下;陆架较粗颗粒沉积物的剪切波速最大,超过100m/s;深海、半深海细颗粒沉积物的剪切波速最低,小于50m/s.剪切波速与含水量、密度、孔隙度、塑限和液限等沉积物物理参数之间具很好的相关性,反映了剪切波速和物理性质之间的密切关系.剪切波速与压缩波速呈正相关性,但在不同的波速范围剪切波速随压缩波速的变化有很大不同.     

南海西北部半日内潮参量次谐频不稳定生成的近惯性波研究

为了研究非临界纬度上参量次谐频不稳定(parametric subharmonic instability,PSI)过程生成的近惯性波(near-inertial wave,NIW),本文基于国家重点研发项目的 准实时传输深海潜标资料,对内波速度谱、近惯性流速和动能、D2-f(半日频减惯性频)流速和动能、半日内潮流速和...     

Numerical Wave Channel with Absorbing Wave-Maker

The numerical wave channel has been developed based on the volume of fluid method (VOF) in conjunction with the Navier-Stokes equations. The absorbing wave-maker boundary on the left side of the channel is presented by prescribing velocity reference to linear wave-maker theory. The principle of which is that the numerical wave-maker is designed to move in a way that generates the required incident wave and cancels out any reflected wave that reach it at the same time. On the right side of the channel, the open boundary is set to permit incident waves to be transmitted freely. The parametric studies have been carried out at a range of ratios of water depth to wave length d/ L from 0.124 to 0.219, with wave height in the front of paddle/water depth ratio (H0 / d) from 0.1 to 0.3. Wave height, wave pressure distribution along the channel and velocity field are obtained for both open boundary condition and reflective boundary condition at the other end of the channel. For a reflective case, it is shown that     

石岛地震台远震记录反演研究

利用石岛地震台的远震体波记录,采用旋转相关函数法和接收函数法分别反演了台站下方介质的各向异性特征和速度结构.(1)对震中距25°~35°且记录良好的5次地震的ScS震相,采用旋转相关函数法反演了岩石圈的剪切波分裂参数.对深源地震的反演结果表明,石岛地震台快波偏振方向为N94°E,这意味着西沙附近处于近东西向微偏南的拉张或地壳下方的地幔流方向为近东西微偏南,西沙地区地壳是过渡性的,其底部的驱动力主要来自与欧亚板块运动一致的物质流.快慢波时间延迟为1.3 s,估算各向异性层厚度为100 km左右.(2)对震中距20°~60°的9次远震P波波形三分向记录,采用接收函数法反演了地壳和上地幔的S波速度结构.反演结果表明,石岛地震台下方地壳分为3层:约5 km以上有一速度梯度带,S波速度从1.5 km/s逐渐增加到3.5 km/s,其间有若干小的分层;在5~16 km的平均速度为3.8 km/s左右,其间有若干小的分层;在16.0~26.5 km的速度为3.6 km/s左右,这是一个明显的低速层;莫霍面埋深为26.5 km,莫霍面以下平均速度为4.7 km/s,也有若干小的分层,尤其是在莫霍面之下有一个明显的低速层.根据转换波到时分析和速度剖面左右摆动现象,认为反演结果中的小分层可能是不真实的,但在16.0~26.5 km的低速层的真实程度还是较高的,表明下地壳具有一定的塑性.     

Transformation of a strongly nonlinear wave in a shallow-water basin

The transformation of a nonlinear wave in shallow water is investigated analytically and numerically within the framework of long-wave theory. It is shown that the nonlinearity parameter (the Mach number), which is defined as the ratio of the particle velocity in the wave to the propagation velocity, can be well above unity in a deep trough and that a jump appears initially in the trough. It is demonstrated that shockwave amplitudes at large times change in accordance with the prediction of weakly nonlinear theory. The shock front generates a reflected wave, which, in turn, transforms into a shock wave if the initial amplitude is large enough. The amplitude of the reflected wave is proportional to the cube of the initial amplitude (as predicted by weakly nonlinear theory) over a wide range of amplitudes except for the case of anomalously strong nonlinearity. When there is a sign-variable sufficiently intense initial perturbation, the basic wave transforms into a positive shock pulse (crest) and the reflected wave turns into a negative pulse (trough).     

Inertial oscillations as deep ocean response to hurricanes

We discuss the deep ocean response to passing hurricanes (aka typhoons), which are considered as generators of near-inertial, internal waves. The analysis of data collected in the northwestern parts of the Pacific and Atlantic oceans in the hurricane season permit us to assess the deep ocean response to such a strong atmospheric forcing. A large number of moorings (more than 100) in the northwestern Pacific have allowed us to characterize the spatial features of the oceanic response to typhoons and the variable downward velocity of near-inertial wave propagation. The velocity of their downward propagation varies in the range 1–10 m/hour. It is higher in the regions of low stratification and high anticyclonic vorticity. The inertial oscillations generated by a hurricane last for 10–12 days. The mean anticyclonic vorticity in the region increases the effective frequency of inertial oscillations by 0.001–0.004 cyc/hour.