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.     

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.     

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 generation of non-linear internal waves by a barotropic tide in the area of a solitary bottom elevation

A mathematical model is suggested for calculating current, density, and pressure fields in the area of a solitary bottom rise (seamount). The model is based on a set of non-linear differential equations governing the motion of an inviscid continuously stratified fluid. The algorithm for solving the equations is based on the splitting technique. The model has been used to compute non-linear baroclinic waves generated by a barotropic tide in the seamount area. Translated by Vladimir A. 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 effect of currents on the generation of internal waves by a barotropic tide near an underwater ridge

In the frame of the linear theory for long waves, the paper studies long waves generated by a barotropic tide running at an arbitrary angle over a bottom ridge. The ocean is assumed to be two-layered. In the area of a ridge with a rectangular cross section, geostrophic flows are considered, coupled with the inclinations of the free surface and interface. Wave amplitudes are shown to depend on the angle of an onrunning tide and this allows us to reach a conclusion about the influence of a geostrophic current on the generation of internal waves. 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.     

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.     

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     

The generation of intensive short-period internal waves in the frontal zone of a coastal upwelling

The measurements data provided by an antenna of distributed temperature sensors, mounted on an oceanographic tower in the South Crimea continental shelf area, were applied to study the mechanism for the generation of short-period internal waves with anomalous amplitudes in the Black Sea. For analysis, information was incorporated concerning the background hydrological and meteorological conditions that were observed during the experiment. A mathematical model for the phenomenon under study has been constructed, and calculations of the anomalous internal wave generation have been presented. The paper contains a comparative analysis of thein situ data and simulation results, and demonstrates a good qualitative/quantitative agreement between the parameters of internal waves. Translated by Vladimir A. Puchkin.     

Nonlinear interaction of internal waves in the coastal zone of the Sea of Japan

Nonlinear interactions of the internal waves of a tidal period with low-frequency synoptic-scale internal waves are studied using instrumental measurements of the current in the coastal zone of the Sea of Japan. In the course of spectral analysis of the data of instrumental measurements, it is found that a maximum in the spectrum of the kinetic energy of coastal waters in the vicinity of the semidiurnal frequency ω₀ is surrounded by satellite maxima whose frequencies obey the relation ω _s = ω₀ ± Ω, where Ω is the characteristic frequency of synoptic-scale internal waves. The spectrum of the anticyclonic current component has a similar structure in the vicinities of the frequency ω₀ and its first and second harmonics. The general theory of nonlinear interactions of weakly dispersive waves is used to solve the problem of modulation and the parametric amplification of tidal internal waves in the coastal zone using low-frequency narrow-band internal waviness. As can be judged from the literature, the effect of parametric modulation of tidal internal waves by low-frequency synoptic-scale internal waves has been recorded in the coastal zone of a tidal sea for the first time.     

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     

Observation and analysis of solitary internal waves in the coastal zone of the Sea of Okhotsk

Experimental data on the measurement of solitary internal waves in the coastal zone of the Sea of Okhotsk are reported. The non-linear and dispersion coefficients of the Korteweg-de Vries (KdV) equation are determined for weakly non-linear disturbances of the first mode. The shapes and parameters of solitary waves are compared with the corresponding parameters of solitons. It is shown that at least ten observed solitary waves are similar to the KdV solitons. Histograms of the distribution of the amplitudes, duration, and spatial dimensions are plotted for a large number of solitary waves.Translated by Mikhail M. Trufanov.     

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 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 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 surface and internal waves in a bounded basin by a moving baric front

We consider a plane problem of generation of surface and internal waves in a bounded rotating basin of variable depth by a front of atmospheric pressure moving over the basin. The fluid is assumed to be two-layer. The system of nonlinear long-wave equations is solved numerically by the method of finite differences for the distribution of depths corresponding to a zonal section of the Black-Sea basin. It is shown that the baric front moving over the basin generates barotropic and baroclinic oscillations of the fluid. The intensity of disturbances depends on the velocity of motion and the width of the front. There exists a velocity of motion of the front for which internal waves are generated especially efficiently. When the front leaves the basin, we observe the formation of a packet of internal waves propagating from one lateral boundary of the basin to the other boundary with reflections from the boundaries.     

A barotropic model of the linear semidiurnal tide over a continental slope

Semidiurnal tides, and especially the lunar tide M₂, are dominant dynamics in the Bay of Biscay. Strong tidal currents are associated with the presence of a significant continental slope. By combining Newton's gravitation laws and Euler's equations, Laplace's equations contain the astronomical forcing responsible for the observed semidiurnal tides. In shallow waters, this direct forcing is often neglected. We study here its influence on the tidal dynamics over the continental slope through the development of a simple model describing the barotropic semidiurnal dynamics on a transect perpendicular to the slope. This new model results from the combination of two different models, i.e. the one developed by Rosenfeld and Beardsley (1987), which takes into account the tide-generating force, and that of Battisti and Clarke (1982), which neglects it. A first model is developed by neglecting the direct astronomical forcing in equations: it consists in solving a second-order homogeneous propagation equation for the barotropic semidiurnal tide and needs only coastal conditions as well as the knowledge of the along-slope wave number of the solution. For a mean slope typical of the South Brittany area, this non-forced model provides results in accordance with those of Battisti and Clarke and Le Cann (1990): in particular, in the upper part of the slope, it shows a polarization inversion of tidal ellipses characteristic of the tidal dynamics observed in this area. Then, the direct astronomical forcing is kept in equations. The simple model developed without this forcing is fitted in order to solve the resulting forced propagation equation for the barotropic tide. The solution of this second model is the sum of a forced wave responding to the direct astronomical forcing and of a free wave generated at the coastal boundary. Under the same boundary conditions, the results obtained with the influence of the tide-generating force are then compared with those obtained without it. This comparison allows one to apprehend the importance of the direct astronomical forcing on tidal dynamics across the slope: in particular, the main difference appears in deep waters where this forcing induces a phase-lag between the plain and the shelf for the sea-surface slope.