Far fields of internal gravity waves in a stratified liquid of varying depth

Asymptotic representations of solutions describing the far fields of internal gravity waves in a stratified medium of varying depth are constructed. The effect of space-frequency cutoff of the wave field for a real oceanic shelf is revealed. Depending on frequency characteristics of the wave field and bottom topography, far fields of internal waves either are located in a certain confined space domain (trapped waves) or propagate in the absence of turning points over sufficiently large distances when compared with the sea depth (progressive waves). The space domain where the progressive waves penetrate is fully determined by the presence of turning points whose locations depend on the medium stratification and inhomogeneities of bottom topography.     

Internal generation of waves on an arc in a rectangular grid system

This paper presents a technique to generate waves at oblique angles in finite difference numerical models in a rectangular grid system by using internal generation technique [Lee, C., Suh, K.D., 1998. Internal generation of waves for time-dependent mild-slope equations. Coast. Eng. 34, 35–57.] along an arc-shaped line source. Tests were made for four different types of wave generation layouts. Quantitative experiments were conducted under the following conditions: the propagation of waves on a flat bottom, the refraction and shoaling of waves on a planar slope, and the diffraction of waves to a semi-infinite breakwater. Numerical experiments were conducted using the extended mild-slope equations of Suh et al. [Suh, K.D., Lee, C., Park, W.S., 1997. Time-dependent equations for wave propagation on rapidly varying topography. Coast. Eng. 32, 91–117.]. The fourth layout type consisting of two parallel lines connected to a semicircle showed the best solutions, especially for a small grid size. This technique is useful for the numerical simulation of irregular waves with broad-banded directional spectrum using conventional spectral wave models for the reasonable estimation of bottom friction and wave-breaking.     

NWF: Propagation of Tsunami and its Interaction with Continental Shelf and Vertical Wall

In this article, tsunamis represented as solitary waves was simulated using the fully nonlinear free surface waves based on Finite Element method developed by Sriram et al. (2006). The split up of solitary wave while it propagates over the uneven bottom topography is successfully established. Wave transmission and reflection over a vertical step introduced in the bottom topography is in good agreement with the experimental results from Seabra-Santos et al. (1987). The wave transformation over a continental shelf with different smooth slopes reveals that the solitary wave reflection increases while the continental slope varies from flat to steep. The interaction of the solitary wave with a vertical wall for different wave steepness has been analysed. The reflected shape of the profile is in good agreement with the observation made by Fenton and Rienecker (1982) and an increase in wave celerity is observed.     

Generation of internal waves by a barotropic tide in the coastal zone

Within the framework of the linear theory of long waves, we study internal waves generated by a barotropic tide in a two-layer ocean of variable depth taking into account the influence of the Coriolis force. Barotropic waves run over an extended unevenness of the bottom at an arbitrary angle. This unevenness is regarded as a model of the continental slope and shelf. We establish the dependences of the amplitudes of generated internal waves on the angle of incidence of the barotropic tide, topography of the bottom, and stratification. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

斜压海洋能量传递对风场的响应

风是海水运动的重要动力因素,也是海洋内部的主要能量来源.本文在应用陆架海洋模式HAMSOM对东中国海海水运动进行数值模拟的基础上,通过傅里叶变换、旋转谱分析等研究方法,对风向海洋的能量输运进行研究.研究结果显示,风场向海洋输运的最有效途径是风杨扰动量与流场扰动量的相互作用;惯性能量主要来源于海洋表层,由风场提供,向下传递;而潮频率能量大部分来自海底的内潮与底地形相互作用,向上传递.     

On nonlinear planetary waves: A class of solutions missed by the traditional quasi-geostrophic approximation

Weakly nonlinear quasi-geostrophic planetary waves on a beta-plane and topographic waves over a linearly inclined bottom are examined by use of shallow water equations for a small beta parameter. Long solitary wave solutions missed by the use of the traditional quasi-geostrophic approximation are found in a channel ocean with neither a sheared current nor a curved (non-linearly inclined) bottom topography. The solutions are missed in the traditional approach because the irrotational motion associated with the geostrophic divergence is neglected by the quasi-geostrophic approximation. Another example which calls attention to the limitation of the traditional quasi-geostrophic approximation is the nonlinear evolution of divergent planetary eddies whose scale is much larger than the Rossby's radius of deformation. Some aspects of a new evolution equation are briefly discussed.     

一个考虑潮汐、中尺度涡和地形影响的南海底部环流诊断模型

本文构造了一个考虑潮汐、中尺度涡和地形影响下的南海底部环流诊断模型。在该模型中,潮汐混合和涡致混合引起的垂直速率用一个类似的改进参数化方案来表示。该模型结果显示在南海深层吕宋海峡"深水瀑布"和斜压影响最大,潮汐作用和中尺度涡影响次之,风场的影响最小。斜压影响的整体效应与其他因素相反。潮汐混合与涡致混合具有明显的地形依赖性。潮汐混合主要集中在南海北部海盆地形较为陡峭的陆坡区和南海中部海山区,而涡致混合主要集中在海盆西边界区以及中部海山区。在不考虑吕宋海峡"深水瀑布"、潮汐和中尺度涡的情况下(对应吕宋海峡关闭),南海底部环流为反气旋式环流。考虑吕宋海峡"深水瀑布"后,南海底层环流为气旋式环流,而潮汐混合和涡致混合起到加强整个气旋式环流强度的作用。此外,该模型还给出了南海底部环流量级大小与地形坡度之间的密切关系,即地形坡度较大的地方,其流速也大。这对于现场观测有着一定的参考意义。最后,本文用尺度分析的方法从理论上分析了该模型的适用性,证实了该模型具有一定的可靠性。     

Application of desingularized approach to water wave propagation over three-dimensional topography

A numerical approach based on desingularized boundary element method and mixed Eulerian–Lagrangian formulation [Zhang et al., 2006. Wave propagation in a fully nonlinear numerical wave tank: a desingularized method. Ocean Engineering 33, 2310–2331] is extended to solve the water wave propagation over arbitrary topography in a three-dimensional wave tank. A robust damping layer applicable for regular and irregular incident waves is employed to minimize the outgoing wave reflection back into the wave tank. Numerical results on the propagation of regular and irregular incident waves over the flat bottom and linear incident waves over an elliptical shoal show good concurrence with the corresponding analytical solutions and experimental data.     

Unusual features of the distribution of Radon-222 in the bottom waters of the continental slope of the Mid-Atlantic Bight: Hydrodynamic implications

²²²Rn was measured in the near-bottom waters of the continental slope of the Mid-Atlantic Bight. Separate measurements of the ²²²Rn supported by dissolved ²²⁶Ra allowed the excess ²²²Rn that is derived from the underlying sediments to be distinguished. Measurements of production of ²²²Rn by the sediments were used to calculate fluxes of ²²²Rn from sediments that would be expected as a result of molecular diffusion. On the upper slope and on the lower slope excess ²²²Rn standing crops were, respectively, greater than and consistent with fluxes of radon from sediments by molecular diffusion as are typical of most ocean environments. On the middle slope, however, observed excess ²²²Rn concentrations and standing crops were significantly lower than what would be expected from the calculated fluxes from the underlying sediments. This unusual feature of low radon concentrations on the middle slope is referred to as the low-radon zone (LRZ). This LRZ was always present over several years and seasons, but was variable in intensity (excess-radon concentration and standing crop) and in location on the slope. Low concentrations of suspended particulate matter and low current velocities observed by others in the same region are consistent with low mixing as a possible cause of the LRZ. Radon profile shapes and recent work by others on near bottom mixing due to interactions between topography and internal waves, however, suggest that high mixing due to internal waves is a more likely cause of the LRZ.     

Laboratory modeling of the propagation of periodic internal waves over bottom slopes

The experimental investigation of the run-up of periodic internal waves in a two-layer fluid on the coastal slope is performed in an open hydrochannel at the Physical Department of the Lomonosov Moscow State University. The waves are produced by a wave generator. We study the transformation of waves, the vertical structure of the field of velocities of mass transfer, and the behavior of the parameters of internal waves propagating over the sloping bottom. It is shown that the run-up and breaking of internal waves are accompanied by periodic emissions of portions of the heavier fluid from the bottom layer upward along the slope. The Stokes drift velocity changes its sign as a function of depth. Moreover, both the wave length (the horizontal distance between the neighboring crests) and the height of waves over the sloping bottom (the elevation of the crest over the slope along the vertical) decrease as the wave approaches the coast.     

An alternating direction implicit (ADI) numerical model for two-dimensional hydrodynamic equations

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An extended time-dependent numerical model of the mild-slope equation with weakly nonlinear amplitude dispersion

In the present paper, by introducing the effective wave elevation, we transform the extended ellip- tic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. (2003), the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. (2007)’s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly vary- ing topography and wave breaking, the present model is applied to study: (1) wave refraction and diffraction over a submerged elliptic shoal on a slope (Berkhoff et al., 1982); (2) Bragg reflection of monochromatic waves from the sinusoidal ripples (Davies and Heathershaw, 1985); (3) wave transformation near a shore attached breakwater (Watanabe and Maruyama, 1986). Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models (REF/DIF model and FUNWAVE model) show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone.     

Control of pelagic sediment distribution by internal waves of tidal period: Possible interpretation of data from the southern East Pacific Rise

Sediment depositional patterns were observed on acoustic-reflection profiles at 36 and 42°S across the East Pacific Rise, near 100°W longitude. The sediment thickness as a function of distance from the crest shows a remarkable linearity on the east side of the rise, where the bottom topography is unusually subdued. The rate of sedimentation is 3.8 m/m.y at 42°S and 7.2 m/m.y. at 36°S. Disturbance to the even sedimentation appears to be correlated with topographic features more than 300 m high, and may therefore be associated with the interference between the barotropic tides and the topography. The group velocity of internal waves of semi-daily period is 15 cm sec⁻¹ in this area for a vertical wave number of 300 m⁻¹, and the characteristic slopes at 9° to the horizontal. The waves travel faster than the flow velocity of the tides and at an angle less than the slopes associated with the larger topographic features. Therefore a typical tidal velocity of 3 cm sec⁻¹ can be magnified substantially before the particle velocity approaches the group velocity and breaking occurs. Less magnification is possible near smaller topography because the group velocity is proportional to wavelength for internal waves of constant period. The tidal flow is magnified most near the boundary where the internal waves are reflected, and the higher velocities should cause settling sediment particles to remain in suspension locally. Thick boundary layers caused by breaking and mixing can shield the smaller-scale topography from the tidal motion.     

A note on the accuracy of the mild-slope equation

The mild-slope equation is a vertically integrated refraction-diffraction equation, used to predict wave propagation in a region with uneven bottom. As its name indicates, it is based on the assumption of a mild bottom slope. The purpose of this paper is to examine the accuracy of this equation as a function of the bottom slope. To this end a number of numerical experiments is carried out comparing solutions of the three-dimensional wave equation with solutions of the mild-slope equation.For waves propagating parallel to the depth contours it turns out that the mild-slope equation produces accurate results even if the bottom slope is of order 1. For waves propagating normal to the depth contours the mild-slope equation is less accurate. The equation can be used for a bottom inclination up to 1:3.     

Run-up of tsunamis and long waves in terms of surf-similarity

In this paper we review and re-examine the classical analytical solutions for run-up of periodic long waves on an infinitely long slope as well as on a finite slope attached to a flat bottom. Both cases provide simple expressions for the maximum run-up and the associated flow velocity in terms of the surf-similarity parameter and the amplitude to depth ratio determined at some offshore location. We use the analytical expressions to analyze the impact of tsunamis on beaches and relate the discussion to the recent Indian Ocean tsunami from December 26, 2004. An important conclusion is that extreme run-up combined with extreme flow velocities occurs for surf-similarity parameters of the order 3–6, and for typical tsunami wave periods this requires relatively mild beach slopes. Next, we compare the theoretical solutions to measured run-up of breaking and non-breaking irregular waves on steep impermeable slopes. For the non-breaking waves, the theoretical curves turn out to be superior to state-of-the-art empirical estimates. Finally, we compare the theoretical solutions with numerical results obtained with a high-order Boussinesq-type method, and generally obtain an excellent agreement.     

Generation of internal waves resulting from the interaction of a barotropic tide with a horizontallyinhomogeneous density field and bottom topography

This paper addresses the problem of the generation of internal waves by a barotropic tide propagating in a uniformly stratified sea across the frontal zone overlying a submerged ridge or a continental slope. Using Riemann's technique, we have performed computations and analysed the wave fields' spatial characteristics and have defined the dependences of the generated wave amplitudes, bottom topography parameters, and density field. It is shown that the presence of a horizontally-inhomogeneous density region over a subwater feature may lead to substantial alteration of the maximum amplitudinal values of internal waves, both inside and around the frontal zone.Translated by Vladimir A. Puchkin.     

The variation of turbulent diapycnal mixing at 18°N in the South China Sea stirred by wind stress

The spatial and temporal variations of turbulent diapycnal mixing along 18°N in the South China Sea(SCS) are estimated by a fine-scale parameterization method based on strain, which is obtained from CTD measurements in yearly September from 2004 to 2010. The section mean diffusivity can reach ~10~(–4)m~2/s, which is an order of magnitude larger than the value in the open ocean. Both internal tides and wind-generated near-inertial internal waves play an important role in furnishing the diapycnal mixing here. The former dominates the diapycnal mixing in the deep ocean and makes nonnegligible contribution in the upper ocean, leading to enhanced diapycnal mixing throughout the water column over rough topography. In contrast, the influence of the wind-induced nearinertial internal wave is mainly confined to the upper ocean. Over both flat and rough bathymetries, the diapycnal diffusivity has a growth trend from 2005 to 2010 in the upper 700 m, which results from the increase of wind work on the near-inertial motions.     

Effects of nonlinear inertial forces on nearshore currents

A perturbation method is developed to investigate the effects of nonlinear inertial forces on breaking-wave-induced nearshore currents. Obliquely incident waves are considered and the bottom topography varies periodically in the shoreline direction. For simplicity, lateral turbulent mixing is ignored. Numerical examples are given for a specified bottom topography with various angles of incidence and surf zone width. The nearshore currents of interest mainly belong to the meandering type. When the nonlinear terms are included, there appears an advective shift as well as an amplitude reduction in the current pattern.     

孤立内波对过渡海域声场干涉结构的影响分析

南海北部陆坡海域是孤立内波的活跃区,孤立内波在该海域能够引起水体环境较强烈的水平不均匀性,从而影响声场干涉结构。将描述宽带声信号强度干涉条纹斜率的波导不变量视为一种分布,能更准确地分析声场的距离*频率干涉结构。本文研究了孤立内波环境下过渡海域声场的距离*频率干涉结构,依据实测孤立内波海洋环境,得到孤立内波环境下随距离变化的声速剖面,利用抛物方程方法仿真过渡海域声场干涉结构。在此基础上,利用拉东变换和傅里叶变换结合的谱值分离方法在低信噪比环境下提取波导不变量分布。分析表明孤立内波环境下过渡海域的声场类影区、类会聚区的波导不变量取值更丰富。     

Reflection of a long wave from an underwater slope

Reflection of long sea waves from an underwater slope described by a power law is studied within the shallow water theory. The slope is connected with the flat bottom. This model allows us to estimate the roles of a pointwise reflection from the inflection point of the bottom profile and distributed reflection at the underwater slope. The case of the underwater slope described by the so-called nonreflecting beach (h(x) ∼ x ^4/3, where h is the depth of the basin and x is the coordinate) when the wave is reflected only from the inflection point (pointwise reflection) is specially considered. The reflection and transmission coefficients over the bottom topography were calculated, and it was shown that the sum of the squared absolute values of these values differs from unity for all profiles except the nonreflecting one. This difference is related to the distributed re-reflections (resonances) over the underwater slope that lead to the deviations in the wave height from the known Green’s law.