The effect of a current upon the generation of internal waves by a semi-diurnal tide in the vicinity of a ridge with a continuously changing height

In the framework of the linear theory for long waves, the paper studies internal waves generated by a semi-diurnal barotropic tide impinging on a bottom ridge at an arbitrary angle. The ocean is assumed to be double-layered. In the vicinity of the ridge, whose height is continuously changing, geostrophic flows occurring due to the inclination of the free surface and interface are considered. The dependencies of the generated wave's amplitudes on the angle of incidence of the tide and on the magnitude and direction of the geostrophic current velocity are determined, allowing a conclusion that the current contributes to the generation of internal waves. Translated by Vladimir A. Puchkin.     

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     

The generation of internal waves by the diurnal barotropic tide in the area of extensive irregularity of the bottom topography

The generation of internal waves by the barotropic tide in a two-layer ocean of variable depth is studied within the framework of the linear theory of long waves in view of the Coriolis force. A barotropic wave climbs at an arbitrary angle to the axis of the extensive ridge with constantly varying profile. The relationships between the amplitudes of the generated internal waves, the location of the ridge, and the angle of climb of the barotropic tide are studied. The analogous research is given in refs 1 and 2.Translated by Mikhail M. Trufanov. UDK 532.59.     

The impact of stratification on the wave velocity field generated by a barotropic tide impinging upon an oceanic ridge

The horizontal wave velocity field generated by a barotropic tide impinging upon a subwater ridge is considered in the linear theory assumptions for long waves. The ocean is assumed to be twolayered, with the tidal wave on-running at an arbitrary angle to the ridge axis. The dependence of the horizontal velocity amplitudes on stratification, the angle of barotropic tide impinging, and the bottom feature geometry is studied.Translated by V. Puchkin.     

Investigation of internal waves generated by a diurnal barotropic tide in the vicinity of an oceanic ridge

Internal waves occurring near an oceanic ridge as a result of impingement of a barotropic tide are scrutinized in terms of the long theory for long waves. The ocean is assumed to be double-layered, the relief continuously changing, and the tidal wave on-running at an arbitrary angle. The dependences of the wave amplitudes and horizontal velocities on the ridge's latitude, the angle of tide running, and the depth of the density jump layer are obtained. Similar investigations for the model bottom relief have been conducted in refs 1 and 3.Translated by Vladimir A. Puchkin.     

The influence of stratification on the field of wave disturbances generated by a barotropic tide in the vicinity of the Mid-Atlantic ridge

In the framework of the linear theory for the long waves occurring in a fluid with a density gradient, the paper concentrates on the field of wave disturbances generated by a barotropic tide in the vicinity of the Mid-Atlantic ridge. Dependences of the wave amplitudes and velocities on the stratification parameters, the angle of onrunning and the period of the barotropic tide have been obtained. A similar study for a model ridge relief of paraboloidal shape has been conducted in ref. 1. Translated by Vladimir A. Puchkin.     

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.     

Generation of internal waves in a three-layer ocean

Within the framework of the linear theory of long waves taking into account the action of the Coriolis force, we solve the problem of generation of internal waves by a barotropic tide impinging on a bottom irregularity of the sea-ridge type. The cross section of the ridge is assumed to be rectangular and the stratification of the ocean is regarded as stepwise with two thermoclines (three-layer model). We study the dependences of the characteristics of generated waves on the parameters of stratification and the period of the impinging barotropic tide. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

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     

Transformation of a Baroclinic Tide in the Process of Motion over an Unevenness of the Sea Bottom

Within the framework of the linear theory of long waves, we study the process of incidence of a baroclinic tide on an unevenness of the sea bottom simulating an oceanic ridge. The liquid is assumed to be stratified and the action of the Coriolis force is taken into account. We determine the characteristics of wave disturbances in the region of the ridge induced by the incident baroclinic waves depending on the parameters of the bottom topography and tidal period. Thus, in particular, over the ridge, we reveal the existence of both the regions, where the amplitudes of internal waves are much higher than the amplitude of the incident baroclinic tide, and shaded regions, where the opposite phenomenon is observed.__________Translated from Morskoi Gidrofizicheskii Zhurnal, No. 6, pp. 3–9, November–December, 2004.     

Downward flow of dense water leaning on a submarine ridge

Large-scale dense bottom currents are geostrophic to leading order, with the main flow direction along the continental slope. Bottom friction makes the water descend to greater depths, but only at a small angle to the horizontal. Here the effect of a submarine ridge that intersects the slope is considered. It is shown that the presence of a submarine ridge greatly enhances the downward transport. By leaning against the ridge it is possible for the dense water to flow downhill, perpendicular to the depth contours, even though the first-order dynamics are geostrophic. The requirement for downward flow next to the ridge is that the frictional transport that it induces is sufficiently large to counteract geostrophic advection along the isobaths and out of the ridge region. The dynamics are similar to those of downward flow in submarine canyons, but ridges appear to be more effective in channeling the dense water downhill, in particular for narrow ridges/canyons with small seaward slope of the ridge/canyon axis. The downward flow is analyzed using a simplified analytical model and the results are compared to data from the Filchner Overflow, which agree qualitatively with the model.     

The generation of internal waves by the barotropic tide at an oceanic ridge

The generation of internal waves by the barotropic tide in a two-layer ocean of variable depth is studied within the framework of the linear theory of long waves in view of the Coriolis force. The relationships between the internal wave amplitude, the angle of climb of the barotropic tide, and the bottom elevation geometry are studied.Translated by Mikhail M. Trufanov.     

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.     

Assessing the west ridge of Luzon Strait as an internal wave mediator

The Luzon Strait is blocked by two meridional ridges at depths, with the east ridge somewhat higher than the west ridge in the middle reaches of the Strait. Previous numerical models identified the Luzon Strait as the primary generation site of internal M₂ tides entering the northern South China Sea (Niwa and Hibiya, 2004), but the role of the west-versus-east ridge was uncertain. We used a hydrostatic model for the northern South China Sea and a nonhydrostatic, process-oriented model to evaluate how the west ridge of Luzon Strait modifies westward propagation of internal tides, internal bores and internal solitary waves. The dynamic role of the west ridge depends strongly on the characteristics of internal waves and is spatially inhomogeneous. For M₂ tides, both models identify the west ridge in the middle reaches of Luzon Strait as a dampener of incoming internal waves from the east ridge. In the northern Luzon Strait, the west ridge is quite imposing in height and becomes a secondary generation site for M₂ internal tides. If the incoming wave is an internal tide, previous models suggested that wave attenuation depends crucially on how supercritical the west ridge slope is. If the incoming wave is an internal bore or internal solitary wave, our investigation suggests a loss of sensitivity to the supercritical slope for internal tides, leaving ridge height as the dominant factor regulating the wave attenuation. Mechanisms responsible for the ridge-induced attenuation are discussed.     

Internal tide in the Kara Gates Strait

We observed strong internal tidal waves in the Kara Gates Strait. Internal tides are superimposed over a system of mean currents from the Barents to the Kara Sea. Field studies of internal tides in the Kara Gates were performed in 1997, 2007, and 2015. In 2015, we analyzed data from towed CTD measurements, numerical model calculations, and satellite images in the region. An internal tidal wave with a period of 12.4 h is generated due to the interaction between the currents of the barotropic tide and the bottom relief on the slopes of a ridge that crosses the strait from Novaya Zemlya to the continent. The depths of the ridge crest are 30–40 m. A constant current of relatively warm water flows from the Barents to the Kara Sea. An internal wave propagates in both directions from the ridge. In the Barents Sea, internal waves are intensified by the current from the Barents to the Kara Sea. Internal bores followed by a packet of short-period internal waves are found in both directions from the strait. Satellite images show that short-period internal waves are generated after the internal bore. A hydraulic jump was found on the eastern side of the strait. Numerical modeling agrees with the experimental results.     

Trapping mechanism of submerged ridge on trans-oceanic tsunami propagation

Based on the linear shallow water equations,an analytic solution of trapped waves over a symmetric parabolicprofile submerged ridge is derived.The trapped waves act as propagating waves along the ridge and as standing waves across the ridge.The amplitude gets the maximum at the ridge top and decays gradually towards both sides.The decaying rate gets more gently with higher modes.Besides,an explicit first-order approximate dispersion relation is derived to simplify transcendental functions in the exact solution,which is useful to describe trapped waves over shallowly submerged ridges in reality.Furthermore,the trapping mechanism of the submerged ridge waveguides on the trans-oceanic tsunami propagation can be explained by the ray theory.A critical incident angle exists as a criterion to determine whether the wave is trapped.Besides,a trapped parameter γ is proposed to estimate the ratio of the energy trapped by the oceanic ridge if a tsunami is generated at its top.     

海啸俘获波在弯曲海脊上的传播规律

越洋海啸会受大洋海脊的引导以俘获波的形式沿其传播上万千米,其携带的巨大能量会严重影响远场地区、威胁海岸地区的安全。本文基于MIKE21-BW模型,分别模拟0°(直海脊)至90°(直角弯曲海脊)不同弯曲角度海脊上俘获波的传播变形过程,并定量比较其能量分配。结果表明,海脊俘获波传至海脊转弯处,少部分能量会泄露出海脊重新以自由波的形式扩散至整个海域;部分能量会被反射回来形成与初始海啸波相反方向的俘获波沿海脊传播,反射的能量会随着海脊弯曲角度的增加而增加;还有一部分能量继续沿着弯曲的海脊向前传播,其随着海脊弯曲的角度增加而减小。     

Modeling the Tide System of the East China Sea with GIS

This article describes systematic research on the tide dynamic system under the support of the Geographic Information System and ocean fluid dynamics model. Through the high-resolution numerical simulation, we found some previously unreported phenomena, such as a low tide amplitude zone of the M2 constituent near Zhoushan isles, a low tide amplitude zone of the K1 constituent near Taiwan island, and a circular flow point band. The results of this research also show that the formation of the tide system is affected by sea-bottom friction coefficient, topography under water, and shoreline morphology. The change of shoreline morphology and significant change of topography under water play important roles in the tide system. Under specified conditions on input tide waves, shoreline morphology has a dominant impact on the formation of the tide system. With the systematically reconstructed sea level and the coastal change of 30 periods since the Pleni Glacier, the evolution process of the tide system of the East China Sea was simulated. Based on the simulation analysis of relationships among topography, shoreline and tide flow, this study concludes that the characteristic of the tide dynamic system is a dominant influencing factor on the formation of large-scale sand ridge clusters. In this article, the integration of the Geographic Information System, tide numerical simulation system, and tide movement visualization system are discussed as an example for related studies.     

Investigation of transformations of barotropic tides in the coastal zone

Within the framework of the linear theory of long waves, we perform the numerical investigation of transformations of a barotropic diurnal tide in the process of its motion from the deepwater region of the sea into the region of continental slope and shelf zone at any angle to the coast line. For a linear profile of the bottom of the continental slope and shelf, we establish dependences of the amplitudes and velocities of waves on the direction of propagation of the tidal wave and the latitude of the place. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Response of a two-layer ocean to typhoon passage in the western boundary region

Effect of the typhoon passage on the western boundary region of a two-layer ocean with bottom topography is studied. The ocean is initially at rest and is set in motion by a typhoon passing parallel to the west coast. Equations that represent barotropic and baroclinic modes of motions are solved numerically by means of the method of finite differences. Motions of the barotropic mode are assumed to be horizontally non-divergent. In this mode, an elongated vortex is produced by the typhoon and propagates toward the south after passage of the typhoon. Behavior of the vortex may be interpreted as continental shelf waves. It is found that the formation and propagation of continental shelf waves are hardly affected by the density stratification. As for the baroclinic response, the typhoon causes considerable interface displacements along its track. The interface displacements are associated with geostrophic motions and remain for long time, though they are formed on the continental slope. Besides the large scale baroclinic response, internal Kelvin waves are induced along the artificial east wall.