Generation of internal waves by barotropic tidal flow over a steep ridge

A three-dimensional nonhydrostatic numerical model is used to study the generation of internal waves by the barotropic tidal flow over a steep two-dimensional ridge in an ocean with strong upper-ocean stratification. The process is examined by varying topographic width, amplitude of the barotropic tide, and stratification at three ridge heights. The results show that a large amount of energy is converted from the barotropic tide to the baroclinic wave when the slope parameter, defined as the ratio of the maximum ridge slope to the maximum wave slope, is greater than 1. The energy flux of internal waves can be normalized by the vertical integral of the buoyancy frequency over the ridge depths and the kinetic energy of the barotropic tides in the water column. A relationship between the normalized energy flux and the slope parameter is derived. The normalized energy flux reaches a constant value independent of the slope parameter when the slope parameter is greater than 1.5. It is inferred that internal wave generation is most efficient at the presence of strong upper-ocean stratification over a steep, tall ridge. In the Luzon Strait, the strength of the shallow thermocline and the location of the Kuroshio front could affect generation of internal solitary waves in the northern South China Sea.     

台阶型海脊俘获波的实验研究

基于物理模型实验研究瞬态冲击波在台阶地形上传播过程,揭示由于反射而在海脊上出现的波浪俘获现象。结果表明:在瞬态波产生区域附近,海脊上所测到的先导波即为最大波,其由泄漏至海脊外的深水波绕射至海脊所致。随着传播距离的增加,由于频散效应的影响,先导波逐渐减小,沿台阶近似直线传播的海脊俘获波和在台阶上曲折传播的海脊俘获波逐渐显现。在距离波浪产生较远区域所测的最大波晚于先导波出现,且这些由俘获波所叠加而成的最大波随着传播距离的增加而呈现出更加复杂的波面过程。     

双曲余弦海脊上海啸俘获波的解析与数值研究

海啸能被大洋海脊引导以俘获波的形式沿其传播上万千米,且因其特殊的运动方式,携带巨大能量影响远场地区的港口,严重威胁海岸安全。本文首先基于线性浅水方程,推导了双曲余弦平方海脊上俘获波的波面解,其为μ阶ν次的连带勒让德函数的第一类解和第二类解的组合。进一步推导出其对应的频散关系,其中对于确定的频率ω,存在无穷多个波数k_y与之对应。采用MIKE21-BW模型,模拟了产生于海脊脊顶处的海啸在理想双曲余弦平方海脊上的传播变形过程。结果表明,小部分能量以自由先驱波进行传播,海啸波的波能大部分被海脊俘获。海脊俘获波沿着海脊方向为行进波,随着海啸波传播时间的增加,波浪在沿着海脊方向的延展范围也逐渐增大,波高逐渐减小、波的个数逐渐增加。俘获波能量主要由不同频率以相同速度传播的具有孤立波特性的波浪成分和能量主要集中在特定频率范围内的波浪成分组成。     

抛物型对称海脊引导波完整解析理论

越洋海啸能够被大洋海脊引导并沿海脊传播至远场地区,虽然传播速度较慢,但携带较大的能量,会对远场地区造成灾害影响,相关研究对于提高海啸传播特性本质的认识具有重要意义。本文基于线性长波方程,推导出了抛物型对称海脊引导波完整解析理论。研究表明对称型海脊同时存在对称与反对称引导波,其自由水面波动可以表示为虚宗量Bessel函数形式。利用海脊中心对称条件给出了描述其频率与波数的频散关系。基于所提理论进一步分析讨论了引导波的运动特性,包括频散关系、波速度、能量传播速度与波面空间分布等。本研究为揭示地形坡度由脊顶至两侧逐渐增加的海脊引导波运动特征,预测实际越洋海啸中最具威胁性海啸波的到达时间提供了理论依据。     

Interaction of internal waves with a horizontally inhomogeneous density field area overlying a ridge

In the context of the general linear theory, we consider the propagation of an internal tide across a frontal zone overyling an oceanic ridge. For a uniformly stratified ocean, the solution was derived using Riemann's technique. The dependences of the generated internal wave amplitudes on the stratification parameters and bottom topography were determined. We have found that wave disturbances of high intensity inside and in the neighbourhood of the ridge may be concentrated in raytype areas. An increase of the horizontal density gradient in the frontal zone results in a perceptible deformation of these areas.Translated by Vladimir A. Puchkin.     

Disintegration of linear edge waves

It is demonstrated that offshore wavenumbers of edge waves change from imaginary wavenumbers in deep water to real wavenumbers in shallow water. This finding indicates that edge waves in the offshore direction exist as evanescent waves in deep water and as propagating waves in shallow water. Since evanescent waves can stably exist in a limited region while propagating waves cannot, energy should be released from nearshore regions. In the present study, the instability region is predicted based on both the full water wave solution and the shallow-water wave approximation.     

Coupling of linear waves and a hybrid porous TLP

An analytical solution has been developed in this paper to quantify the flow field and the surge motion of a porous tension leg platform with an impermeable top layer induced by linear waves. The porous layer of the TLP is considered to be anisotropic but homogeneous. The nonlinear form drag in the porous layer is replaced by a linear drag according to Lorentz’s hypothesis of equivalent work. The convergence of the series solution is verified. The dependence of the flow field, the surge motion of the platform, and its resonant frequency on wave and structure properties has been studied.     

Generation of internal waves by a semidiurnal barotropic tide in the Mid-Atlantic ridge area

Internal waves occurring in the specific Mid-Atlantic ridge area as a result of the impinging of a barotropic tide are studied in the terms of the linear theory for surface waves. The ocean is assumed to be double-layered, with a tidal wave running onto it at an arbitrary angle. The dependences of the wave amplitudes and horizontal velocities on the angle of run-on of a tidal wave are derived. Similar studies for the model bottom topography have been reported in refs 1–3. Translated by Vladimir A. Puchkin.     

A coupled-mode model for the refraction–diffraction of linear waves over steep three-dimensional bathymetry

A consistent coupled-mode model recently developed by Athanassoulis and Belibassakis [1], is generalized in 2+1 dimensions and applied to the diffraction of small-amplitude water waves from localized three-dimensional scatterers lying over a parallel-contour bathymetry. The wave field is decomposed into an incident field, carrying out the effects of the background bathymetry, and a diffraction field, with forcing restricted on the surface of the localized scatterer(s). The vertical distribution of the wave potential is represented by a uniformly convergent local-mode series containing, except of the ususal propagating and evanescent modes, an additional mode, accounting for the sloping bottom boundary condition. By applying a variational principle, the problem is reduced to a coupled-mode system of differential equations in the horizontal space. To treat the unbounded domain, the Berenger perfectly matched layer model is optimized and used as an absorbing boundary condition. Computed results are compared with other simpler models and verified against experimental data. The inclusion of the sloping-bottom mode in the representation substantially accelerates its convergence, and thus, a few modes are enough to obtain accurately the wave potential and velocity up to and including the boundaries, even in steep bathymetry regions. The present method provides high-quality information concerning the pressure and the tangential velocity at the bottom, useful for the study of oscillating bottom boundary layer, sea-bed movement and sediment transport studies.     

On waves propagating over a submerged poro-elastic structure

In this paper, the problem of incident waves propagating over a submerged poro-elastic structure is studied theoretically. A linear wave theory is used to describe the wave motion. The submerged poro-elastic structure is modeled based on Biot's theory, in which the fluid motion is described using the potential wave theory of Sollitt and Cross (1972). In the present approach, the problem domain is divided into four subregions. Using general solutions for each region and matching dynamic and kinematic conditions for neighboring regions, analytic solutions are derived for the wave fields and poro-elastic structure. The present analytic solutions compare very well with simplified cases of impermeable, rigid structures, and with those of porous structures. Using the present analytic solution, the effects of a poro-elastic submerged structure on waves are studied. The results show that softer poro-elastic structures can induce higher reflection and lower transmission from incident waves. For low permeability conditions, the elasticity of the structure can induce resonance, while higher permeability can depress the resonant effects.     

Generation of internal waves in the region of a bottom ridge with continuously varying height

Internal waves generated by a barotropic wave impinging on a bottom ridge with continuously varying height are studied within the framework of the linear theory of long waves. We consider the case where the diurnal tide travels at an arbitrary angle to the axis of the ridge located in the area of a geostrophic flow caused by tilting of the free sea surface and the interface of a two-layer ocean. We study the dependences of the amplitudes of internal waves on the velocity of the geostrophic flow, the direction of propagation of the barotropic tide, and the geometry of the ridge. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Propagation of solitary waves over a submerged permeable breakwater

We study the interactions between a non-breaking solitary wave and a submerged permeable breakwater experimentally and numerically. The particle image velocimetry (PIV) technique is employed to measure instantaneous free surface displacements and velocity fields in the vicinity of a porous dike. The porous medium, consisting of uniform glass spheres, is mounted on the seafloor. Due to the limited size of each field of view (FOV) for high spatial resolution purposes, four FOVs are set in order to form a continuous flow field around the structure. Quantitative mean properties are obtained by ensemble averaging 30 repeated instantaneous measurements. The Reynolds decomposition method is then adopted to separate the velocity fluctuations for each trial to estimate the turbulent kinetic energy. In addition, a highly accurate two-dimensional model with the volume of fluid interface tracking technique is used to simulate an idealized volume-averaged porous medium. The model is based on the Volume-Averaged Reynolds Averaged Navier–Stokes equations coupled with the non-linear k–ε turbulence closure solver. Comparisons are performed between measurements and numerical results for the time histories of the free surface elevation recorded by wave gauges and the spatial distributions of free surface displacement with the corresponding velocity and turbulent kinetic energy around the permeable object imaged by the PIV system. Fairly good agreements are obtained. It is found that the measured and modeled turbulent intensities on the weather side are much larger than those on the lee side of the object, and that the magnitude of the turbulent intensity increases with increasing wave height of a solitary wave at a constant water depth. The verified numerical model is then used to estimate the energy reflection, transmission and dissipation using the energy integral method by varying the aspect ratio and the grain size of the permeable obstacle.     

Dissipation observations of drag coefficients over the open ocean

Forty-three open-ocean observations of drag coefficients observed at Argus Island Tower near Bermuda by the dissipation technique resulted in constant drag coefficients for mean horizontal wind velocities between 7.8 and10.4 m .s^{1}in good agreement with the larger near-neutral data set of DeLeonibus and Simpson [1] and the neutral data of Large and Pond [2], both of whom observed10^{3}C_{10} = 1.2whereC_{10}is the drag coefficient at l0 m. Ratios of vertical-to-horizontal wind velocity spectral densities averaged over an inertial subrange of 0.8 to 1.6 Hz ranged from 0.7 to 1.07 in agreement with the Busch and Panofsky [3] result that isotropy is approached only when the observation height is much greater than the Nyquist wavelength.     

Analytical solutions for long waves over a circular island

In this study, we derive an analytical solution for long waves over a circular island which is mounted on a flat bottom. The water depth on the island varies in proportion to an arbitrary power, γ, of the radial distance. Separation of variables, Taylor series expansion, and Frobenius series are used to find the solutions, which are then validated by comparing them with previously developed analytical solutions. We also investigate how different wave periods, radii of the island toe, and γ values affect the solutions. For a circular island with a small value of γ (e.g. γ = 2/3, as in the equilibrium beach (Bruun, 1954)), the wave rays approaching near the island center reach the coastline, whereas the rays approaching away from the center bend away from the coastline, leading to smaller wave amplitudes along the coast. However, for a circular island with a large value of γ, e.g. γ = 2, all the rays on the island reach the coast, giving large coastline wave amplitudes. If the island domain is small compared to the wavelength, the wave amplitudes on the coastline do not increase significantly; however, when the island domain is not small, the wave amplitudes increase significantly. If γ is also large, the amplitudes can be so large as to cause a disaster on the island.     

Harmonic generation by waves propagating over a submerged step

Harmonic generation by waves propagating over a two-dimensional submerged step is investigated. A nonlinear theory correct to second order is presented for steps of infinite and finite lengths subjected to single harmonic waves.The boundary value problem for the second-order scattered velocity potential is linearly decomposed into two separate boundary value problems, each having only one inhomogeneous boundary condition.Theoretical results indicate that the higher harmonics are generated in the shallow-water region over a step and then are transmitted to the deeper water as free waves.Numerical calculations compare favourably with existing experimental data.     

Ocean waves propagating over a porous seabed of finite thickness

In the past few decades, considerable efforts have been devoted to the phenomenon of wave-seabed interaction. However, conventional investigations for determining wave characteristics have been focused on the wave nonlinearity. On the other hand, most previous works have been only concerned with the seabed response under the wave pressure, which was obtained from the assumption of a rigid seabed. In this paper, the inertia forces and employing a complex wave number are considered in the whole problem. Based on Biot’s poro-elastic theory, the problem of wave-seabed interaction is first treated analytically for a homogeneous bed of finite thickness and a new wave dispersion relationship is also obtained, in which the soil characteristics are included. The numerical results indicate that the effects of soil parameters significantly affect the wave characteristics (such as the damping of water wave, wave length and wave pressure). Furthermore, the effects of inertia forces on the wave-induced seabed response cannot always be ignored under certain combination of wave and soil conditions.     

Evolution of waves and currents over a submerged laboratory shoal

The vertically-integrated effect of interaction between waves and wave-induced currents on wave transformation over a submerged elliptic shoal was investigated based on numerical simulations of the Vincent and Briggs experiment [Vincent, C.L., Briggs, M.J., 1989. Refraction- diffraction of irregular waves over a mound. Journal of Waterway, Port, Coastal and Ocean Engineering, 115(2), pp. 269–284.]. The numerical simulations were performed using two numerical wave-current model systems: one, a combination of the wave model SWAN and the current model SHORECIRC, and the other, a combination of the wave model REF/DIF and the same current model. A time-dependent, phase-resolving wave and current model, FUNWAVE, was also utilized to simulate the experiment. In the simulations, the developed wave-induced currents defocused waves behind the shoal and brought on a wave shadow zone that showed relatively low wave height distributions. For the breaking case of monochromatic waves, the wave heights computed using FUNWAVE showed good agreement with the measurements and the resulting wave-induced currents showed a jet-like velocity distribution in transverse direction. And the computed results of the two model combinations agreed better with the measurements than the computed results obtained by neglecting wave-current interaction. However, it was found that for the case in which transverse interference pattern caused by refracted waves was strong, REF/DIF-SHORECIRC did not correctly evaluate radiation stresses, the gradients of which generate wave-induced currents. SWAN-SHORECIRC, which cannot deal with the interference patterns, predicted a jet-like wave-induced current. For breaking random wave cases, the computed results of the two model combinations and FUNWAVE agreed well with the measurements. The agreements indicate that it is necessary to take into account the effect of wave-induced current on wave refraction when wave breaking occurs over a submerged shoal.