Generation of waves in a bounded basin by a traveling front of atmospheric pressure and the field of wind stresses induced by this front

A plane problem of generation of barotropic seiches in a bounded rotating basin by traveling atmospheric fronts is studied within the framework of the linear theory of long waves. The front is characterized by disturbances of the baric field and the corresponding field of tangential wind stresses. We deduce the modified Ackerblom formulas for the wind stresses according to the given anomalies of atmospheric pressure in which the uniform transport of disturbances of the baric field is taken into account. We perform the numerical analyses of the dependences of the amplitudes of oscillations of fluid in the basin on the parameters of the atmospheric front and the choice of the formulas for the tangential wind stresses. The influence of the wind stresses leads to significant quantitative and qualitative changes in the oscillations of fluid in the basin as compared with the case of pure baric action.     

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     

Generation of seiches by moving baric formations

We consider a plane problem of generation of barotropic seiches in the case of motion of a region of disturbances of atmospheric pressure over a bounded basin. The nonlinear system of equations of long waves with regard for the quadratic dependence of bottom friction is solved by the finite-difference method. The calculations are carried out for three basins of variable depth corresponding to rectangular sections of the Black Sea and Sea of Azov. It is shown that the passage of the baric anomaly over the basin is accompanied by the generation of the lowest seiches. The oscillations of fluid are especially intense in the shallow-water zones of the basins. Seiches exhibit a trend to intensification as the velocity of motion of the atmospheric disturbance increases. The dependence on the width of the baric anomaly is not monotonic. In the shelf zone, the amplitude of oscillations of the level can be several times higher that the pure hydrostatic response of the sea surface. In the analyzed basins, the influence of nonlinearity on the seiches is weak. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 6, pp. 3–15, November–December, 2007.     

Generation of spatial internal waves in a rotating ocean by moving non-stationary disturbances

In a general linear statement, the kinematic structure of spatial internal waves generated by a uniformly moving area of oscillating surface pressures in a continuously stratified ocean of constant depth is studied. The earth's rotation effects are considered. Possible types of ocean wave fields with a constant Brunt-Väisälä frequency are examined. The wave regimes for individual modes of internal and gyroscopic waves are classified on the basis of estimating the integrals asymptotically.Translated by V. Puchkin.     

Generation of internal waves by moving non-stationary disturbances in a real stratified ocean

The plane problem on the generation of linear internal waves by a moving area of time-harmonic surface pressures in a continuously-stratified ocean of constant depth is considered. An analytical relation has been derived for forced internal waves off the site of their generation in the form of an internal wave field superposition corresponding to individual vertical modes. The possible wave regimes are determined. For the Brunt-Väisälä frequency distribution in the North Atlantic, the generation conditions and amplitudes of diverse radiated waves are numerically determined.Translated by Vladimir A. Puchkin.     

Generation of long internal waves in the ocean by a moving pressure zone

The generation of plane internal waves in a continuously stratified ocean by a steadily moving anomaly of the atmospheric pressure is studied in a linear statement using a quasi-static approximation. Quantitative estimates for the parameters of internal waves in the wake are obtained for the average distribution of the Väisälä-Brunt frequency in the Caribbean Sea.Translated by Mikhail M. Trufanov.     

Thermohydrodynamics of the ocean generation of seiches by moving baric fronts in bounded basins

We consider a plane problem of barotropic seiches generated by a front of atmospheric pressure moving over a bounded basin. A system of nonlinear equations of long waves is solved by the finite-difference method with regard for the bottom friction and Earth's rotation. The numerical analyses are performed for two basins with distributions of depths typical of the Black Sea. It is shown that the passage of a baric front over the basin leads to the generation of lower seiches. The oscillations of level and the corresponding currents are especially intense in the shallow-water zones of the basins. The seiches become more intense as the velocity of transfer of the atmospheric front increases and the width of the front decreases. Earth's rotation leads to the generation of longshore currents and promotes the process of weakening of residual oscillations of the fluid following the passage of the front. The influence of nonlinearity on seiches is small for the analyzed basins. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 2, pp. 3–18, March–April, 2008.     

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     

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 long waves in a basin by short-term displacements of the lateral boundary

A simplified model of generation of tsunamis by earthquakes occurring on the dry land is proposed. The transfer of horizontal momenta to the liquid medium is realized via the horizontal displacements of the vertical lateral boundary according to a given time law. The problem is solved by the method of finite differences for elastic and inelastic displacements of the lateral boundary of the basin. The efficiency of the process of generation of tsunami-type waves by similar external disturbances is analyzed. It is shown that the efficiency of generation of the surface waves by the elastic displacements of the lateral boundaries of the basin is much higher than that in the case of displacements of the boundary with residual deformations     

Generation of internal waves of the near-inertial period by a periodic wind

Internal waves at the inertial periods and outside them generated by the tangential stress of a periodic wind are studied in a linear statement. At a constant Väisälä-Brunt frequency and the ocean's depth, formulae have been derived which permit the computation of parameters of forced internal waves close to and at the inertial periods. It is shown that when approaching the inertial period, one can observe not only a general increase of the amplitudes of waves and velocities, but also the emergence of separate spikes at the resonance periods. When the periods exceed the inertial one, the wave disturbances attenuate rapidly in the ocean's depths.Translated by Mikhail M. Trufanov.     

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     

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.     

The generation of plane internal and gyroscopic waves by moving unsteady disturbances

The plane linear problem on the generation of the internal and gyroscopic waves in continuously stratified ocean by a moving area of surface pressures which are harmonic over time is considered. The possible types of the forced waves, the amplitudes and the resonance conditions of generation of the wave fields are determined based on the analytical solution derived for the case of a uniformly stratified ocean.Translated by Mikhail M. Trufanov. UDK 551.466.81.     

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.     

Scattering of surface waves in a basin with a statistically uneven bottom

The propagation of surface waves over a statistically uneven bottom is considered on the basis of equations of the linear potential theory. The expression which emphasizes the dispersion influence is obtained for the spatial decrement of the average field. The north-east Pacific is considered as an example.Translated by Mikhail M. Trufanov.     

Generation of vertical fine structure in inhomogeneous flow by inertial-gravity internal waves

Corrections to the vertical distribution of mean density and current velocity non-oscillating on the wave's time scale have been derived in the approximation, quadratic by the wave's steepness. It has been shown that the horizontal volume transport of both the induced current and the Stokesian drift, integrated over depth, equates zero in the Boussinesq approximation.Translated by V. Puchkin.     

On the generation of lateral internal waves by a surface seiche in a partially mixed estuary

Dyer (1982) observed internal oscillations in Southampton Water of predominantly 8 and 4 min periods. These were thought to be lateral standing waves generated by the interaction of the first- and second-order surface seiches, respectively, with estuarine topography. The present paper extends the work of Rattray (1960) to model the cross-sectional topography of Southampton Water, and shows that internal waves of the observed periods, wavelengths and amplitudes could indeed have been generated in the manner envisaged, but only near the times of certain internal resonant conditions. In general, about two or three such resonances occur per half tidal cycle, and this is in qualitative agreement with Dyer's observations.     

Propagation and interaction of non-linear surface and internal waves in a two-layer fluid

This paper focuses on the study of linear and non-linear surface and internal waves, in a complete setting, using a two-layer model of a stratified fluid. The respective Korteweg-de Vries evolutionary equations have been obtained, analysed, and compared with the rigid lid model data. Boussinesq-type equations have been derived for the interacting modes pertaining to one type and to different types. It is shown that in addition to the known mechanisms of interaction between internal and surface waves, interaction between long non-linear baroclinic modes and barotropic modes, propagating in the same direction, is likely in such a system.Translated by Vladimir A. Puchkin.