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     

Relatioship between the intensity of tsunami and the location of the epicentre of underwater earthquakes near the continental slope of the South Coast of Crimea

Within the framework of the nonlinear theory of one-dimensional long waves, we performed the numerical analysis of the dependence of the intensity of tsunami on the shelf of the South Coast of Crimea on the location of the epicentre of underwater earthquakes near the continental slope of the basin. The calculations were carried out for the parameters of the model corresponding to the Yalta tsunami of September 12, 1927. It is shown that, for the same magnitude of the earthquake, the smaller the distance from its epicentre to the coastal line, the lower tsunami waves in the coastal zone and the smaller their vertical run-up. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Correlation between the intensity of tsunami in the Black Sea and the magnitude of underwater earthquakes

We perform the analysis of tsunami waves in the shelf zone of the Crimean peninsula generated by underwater earthquakes whose epicentres are located near the lower boundary of the continental slope. For this purpose, we use a one-dimensional nonlinear dissipative numerical model of long waves. The investigated distributions of the depth of the basin correspond to four points of the south coast of the Crimean peninsula. We use the empirical dependences of parameters of the sources of tsunami waves on the magnitude of the earthquake obtained earlier for the Pacific Ocean. It is shown that the height, vertical climb, and duration of tsunami waves increase with the magnitude of the earthquake. For equal magnitudes of the earthquake, the highest tsunamis on the south coast of the Crimea are observed between Alushta and Yalta. We also deduced a generalized regression dependence of the height of tsunami waves near the coast on the magnitude of the earthquake. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Analysis of the intensification of tsunami waves near the South Coast of Crimea

We perform the numerical analysis of the intensification of tsunami waves in the course of their propagation from the open part of the Black Sea to the shelf zone. For this purpose, we use a one-dimensional model of nonlinear long waves taking into account the effect of bottom friction. We study four profiles of the bottom corresponding to the south coast of the Crimean Peninsula and establish the predominant role of the bottom pattern and insignificant contribution of nonlinearity to the transformation of waves in the process of their propagation in the direction of the coast. Down to depths of 50 m, all changes in the height of waves are described by the Green law. For the evaluation of vertical run-up of waves, it is important to take into account nonlinear effects. The highest vertical run-ups of waves are observed in the parts of the shelf zone located near Yalta and Alushta. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Generation of internal waves in the sea by local perturbations of wind and density flows on the surface

On the basis of a nonlinear model taking into account viscosity, density diffusion, and currents, we perform the numerical analysis of propagation of perturbations formed in the abyssal part of the Black Sea as a result of the action of tangential wind stresses or density flows in the form of a strip on the sea surface. It is shown that, in the course of time, in the region of the bottom slope, these perturbations generate a train of waves in the sea, which causes oscillations of the fields of density and currents. There are some differences between the generation of internal waves by the flows of density and the wind. Unlike the wind action, in the presence of flows of density in the upper layer in the region of the strip, the initial period of generation is characterized by the formation of intense perturbations without train structure. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Internal Wave Generation by Tidal Flow over a Continental Shelf Slope

The generation process of internal waves by strong tidal flow over a continental shelf slope is reproduced using a multi-level numerical model. On the basis of the numerical results, the crucial role of the tidal advection effect in the generation process of internal waves is demonstrated. The close relation between the resulting internal waveform and the strength of the tidal advection effect is also examined. The barotropic forcing on the internal wave actually works within a relatively small horizontal scale over the top of the continental shelf slope. When the maximum internal Froude number at the shelf break (Fr_m) is less than about 0.6, the amplitude of the resulting internal wave is almost proportional to F_rm. When F_rm is more than about 0.6, however, the amplitude of the resulting internal wave becomes larger than predicted by linear theory. In particular, when F_rm is more than unity, the time period during which the shoreward propagating internal wave stays in the barotropic forcing region becomes much longer. Consequently, the internal wave is significantly amplified with the horizontal scale approaching that of the barotropic forcing, which concentrates in a relatively small region over the top of the continental shelf slope. This revised version was published online in July 2006 with corrections to the Cover Date.     

Seiches in a circular basin of variable depth

Free waves (seiches) in a circular basin of variable depth are studied numerically within the framework of the linear theory of long waves taking into account the action of the Coriolis force. We determine the frequencies of axisymmetric and circular waves, study the structure of the modes of elevation of the free surface and wave velocities, and establish the dependences of the phase velocities of circular waves on the number of mode and wavelength. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

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     

地形对陆架拦截波性质及机制的影响

陆架波的性质如频散关系、形成机制等受地形影响。研究地形对陆架波的性质影响具有重要意义。基于陆架拦截波理论,数值计算了分段线性地形下不同宽度陆架上陆架拦截波的频散关系、长波假设下波动的相速度、阻尼情况下的波动耗散率以及强迫波的外力影响因子。分析了陆架宽度及坡度对自由及强迫陆架拦截波性质的影响。陆架宽度影响陆架拦截波的频散关系。陆架变宽,使得长波频散曲线的斜率增大。陆架宽度的增加使第一模态陆架拦截波有明显的性质变化:相速度增大,波动受辐散影响的程度变大,摩擦衰减距离增大,且风应力旋度在波动的生成机制中起到的作用渐强。在宽的陆架上,研究陆架拦截波的生成及强迫波的振幅时,应充分考虑风应力旋度的作用。第二、三模态波动的相速度受陆架坡度的影响较大,但摩擦衰减距离基本都在200km左右,几乎不随陆架宽度改变,属于局地波。     

North Brazil current: vertical structure

On the basis of the data ofin situ measurements of the velocities of currents and basic hydrophysical parameters (such as temperature and salinity) carried out during Cruise 41 of the R/VAkademik Vernadsky, we analyze the structure of the North Brazil Current near the continental slope and in the equatorial abyssal part of the ocean in winter, establish the regularities of changes in the current velocity with depth, and compare the structures of the North Brazil and Guiana Currents. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Generation of long barotropic waves by moving baric disturbances in a system of basins connected by a channel

We consider long barotropic waves in a system of two rectangular basins connected by a channel in the case where waves are generated by the moving region of disturbances of atmospheric pressure passing above one of the basins. By using a numerical model, we compute the characteristics of the wave process for various values of the parameters of this system. The results of numerical calculations are compared with the corresponding characteristics obtained for the case of a closed basin. We also analyze the distinctive features of long-wave processes induced in the presence of the channel. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Efficiency of dense shelf water cascading over the continental slope of Severnaya Zemlya in the Laptev Sea and its possible contribution to the ventilation of the intermediate water in the Nansen Basin

Comprehensive field observations of hydrological processes in the region of the continental slope of Severnaya Zemlya in the Laptev Sea allowed us to reveal descending dense (cold) shelf water over the slope (cascading) and to determine the spatiotemporal variability of the cascading [2]. The observations represented a series of polygon surveys in the autumn-winter-spring period. The estimates of the characteristics of the slope convection of the shelf water (cascading) were based on the results of laboratory and theoretical studies of the descending of the dense water over a sloping bottom in a rotating fluid with sources of different geometry. It was shown that the cascading of dense shelf water over the continental slope mainly corresponds to a smooth (geostrophic) regime. An analysis of some thermohaline and density sections indicates, however, the possibility of the development of a wave-eddy regime of cascading and/or generation of fast gravity waves in the upper part of the continental slope. The most representative estimation of the contribution of the cascading of dense shelf water on the northern continental slope of Severnaya Zemlya to the ventilation of the intermediate waters in the Nansen Basin for five winter months is ≈0.0614 Sv.     

Evolution of waves induced by periodic variations of pressure in a bounded basin of variable depth

Within the framework of the linear theory of long waves, we study the evolution of a wave process caused by the action of surface pressure periodically varying in time in a bounded basin of variable depth without vertical walls. We assume that the basin is filled with a homogeneous liquid nonperturbed at the initial time and take into account the action of dissipative forces. We obtain the analytic solution of the posed problem. It is used to perform the detailed analysis of the influence of the dissipative forces and the frequency of perturbing pressure on the characteristics of the process of evolution of waves. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Generation of geostrophic vortices caused by displacements of a part of the bottom of a basin

Within the framework of the general linear statement of the problem, we determine the conditions of generation of a geostrophic current in a layer of uniform rotating fluid for small displacements of the bottom of a basin. We deduce an equation relating the equilibrium shape of the surface of the fluid with residual deformations of the bottom and find its general solution. It is shown that the geostrophic current is generated only in the presence of residual deformations. We present numerical estimates of the intensity of the generated geostrophic formation for a model of motion of the bottom. The investigated mechanism of generation of geostrophic vortex fields is especially efficient in the shelf zone of the ocean. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

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     

海啸波传播的线性和非线性特征及近海陆架效应影响的数值研究

浅水方程被广泛应用于海啸预警报业务及研究,而针对线性浅水方程与非线性浅水方程在不同海区水深地形条件下的适用范围、计算效率问题是海啸研究人员急需了解的。本文应用基于浅水方程的海啸数值预报模型就海啸波在南海、东海传播的线性、非线性特征以及陆架对其传播之影响进行了数值分析研究。海啸波在深水的传播表征为强线性特征,此时线性系统对海啸波幅的模拟计算具有较高的精度和效率,而弱的非线性特征及弱的色散特征对海啸波幅的预报影响甚微,可以忽略不计。海啸波传播至浅水大陆架后受海底坡度变化、海底粗糙度等因素影响,波动的非线性效应迅速传播、积累,与线性浅水方程计算的海啸波相比表现出较大差异,主要表现为:在南海区,水深小于100m时,海啸波首波以后的系列波动非线性特征比较明显,两者波幅差别较大,但首波波幅的区别不大,因此对于该区域在不考虑海啸爬高的情况下,应用线性系统计算得到的海啸波幅也可满足海啸预警报的要求;在东海区由于陆架影响,海啸波非线性特征明显增强,水深小于100m区域,首波及其后系列波波幅均差异较大,故在该区域必须考虑海啸波非线性作用。本文就底摩擦项对海啸波首波波幅的影响进行了数值对比分析,结果表明:底摩擦作用对海啸波首波波幅影响仅作用于小于100m水深。最后,该文通过敏感性试验,初步分析了陆架宽度及陆架边缘深度对海啸波波幅的影响,得出海啸波经陆架传播共振、变形后,海啸波幅的放大或减小与陆架的宽度及陆架边缘水深有关。     

Rotation of orbital currents in the trains of internal solitons in the ocean

We analyze the results of measurements of currents in the trains of internal solitons on the New-York shelf of the Atlantic Ocean performed in the course of the Joint US/Russia Internal Wave Remote Sensing Experiment (JUSREX). It was discovered that the thermocline is characterized by an almost monotonic anticyclonic variation of the direction of orbital currents in the trains of solitons but the direction of waves in each train is practically constant. As a rule, the current significantly deviates to the left from the direction of waves in the leading soliton and approaches the indicated direction in the rear solitons of the train. The angular rotation current velocity corresponded to periods varying within the range 12–24h and, on the average, was close to the local inertial period. It is shown that this rotation cannot be caused by the distorting influence of advection of background shear currents but, most likely, is connected with the unknown properties of internal solitons in the rotating ocean. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Trapped bottom topographic waves over the inclined bottom

In the Boussinesq approximation, we study baroclinic topographic waves trapped by the flat meridional slope. The existence of these waves is explained by stratification, inclined bottom, and Earth's rotation. We deduce the evolutionary equation for the square of the envelope of a narrow-band wave packet of trapped waves. In the second order of smallness relative to the wave amplitude, we find the mean fields of velocity and density induced by the packet. It is shown that, in the limiting case of weakly nonlinear plane waves, the induced current is zonal. In the Northern hemisphere, depending on the slope of the bottom γ₁, the sign of the phase velocity σ/k (k is the zonal wave number) is either always positive (for γ₁>γ_1cr) or always negative (for γ₁<γ_1cr). If we neglect the vertical component of the Coriolis acceleration, then γ_1cr=0. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Structure and kinematics of waters in the region of the Argentine Islands in the autumn of 1998

On the basis of the data of the complex oceanographic experiment carried out in the course of the second Ukrainian Antarctic expedition in March 1998, we study the structure and kinematics of waters in the region of the archipelago of Argentine Islands. The regularities of thermohaline stratification of waters are discovered. We determine the most important environmental parameters premoting the variability of hydrophysical fields on time scales varying from several days up to a week, analyse the data of actual observations over the currents, and estimate the relative contribtions of diurnal and semidiurnal tidal waves to the total dispersion of hydrophysical parameters of the environment. The residual currents are filtered out. We propose a hypothesis about the mechanism of their formation. Various types of tidal currents are revealed and the directions of propagation of diurnal and semidiurnal tidal waves are determined. 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.