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 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.     

The effect of the vertical density structure on internal waves in the neighbourhood of the intertial period

With the latitudinal variability of the Coriolis parameter considered, the influence of the vertical density structure on the parameters of free internal waves is stuided. Numerical calculations are performed for Brunt-Väisälä frequency profiles characteristic of the four seasons of the year in the deep section of the Black Sea. Results of the analysis of the dependences of the wavenumber and group velocity on the frequency are presented, and the domain of application of thef-plane approximation is defined.Translated by V. Puchkin.     

Internal wave dispersions in density-stratified deep oceans with a thermocline

As to two typical Väisälä frequency profiles in deep oceans, one in the Arctic Ocean and one in the Atlantic, the approximate analytical method ofHyun (1976) is used to calculate internal wave dispersion relations. The method is shown to have good agreement with the matrix numerical method. By making calculations for an exemplary Väisälä frequency profile with a thermocline, an assessment is made of the inaccuracies in the dispersion curves obtained by the ordinary WKB method which does not take into account the turning point singularities.     

A method of submersion in the problem on the determination of dispersion curves of internal waves in the presence of a current with vertical velocity shear

The previously proposed method [1] of submerging aimed at determining internal wave dispersion characteristics is generalized to consider the case of a background horizontal flow with a vertical velocity shear. The results of calculating, dispersion curves of discrete spectrum modes for the profiles of the Brunt-Väisälä frequency and the mean current velocity are given; they agree well with the results of studies carried out in ref. [5].Translated by Mikhail M. Trufanov.     

On the possible generation of low-frequency microseisms by internal waves in the ocean

The conditions under which the interaction between internal waves and the rough bottom topography may be the reason for synchronous fluctuations of pressure at the bottom have been studied. Disturbances of the depth are assumed to be small compared with the mean depth of the ocean, and the Väisälä-Brunt frequency is constant. It is shown that synchronous fluctuations of pressure exist with a frequency equal to that of internal waves. The amplitude of pulsations can be approximately an order lower than the amplitude of fluctuations generated by standing surface waves. However, local maxima can exist in the low-frequency minimum of the spectrum of microseisms (in the range of 20–1000 s).Translated by Mikhail M. Trufanov.     

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.     

Resonance excitation of internal waves by fluctuations of the atmospheric pressure and the tangential wind stress

Resonance excitation of internal waves by running waves of the atmospheric pressure and the tangential wind stress in a continuously stratified rotating ocean is studied in a linear statement. A comparative analysis of the rates of the increase in amplitude of resonance-excited waves for these external disturbances is carried out numerically for the case of the average distribution of the Väisälä-Brunt frequency in the Caribbean Sea.Translated by Mikkail M. Trufanov.     

The near field of internal waves after the moving area of atmospheric pressures

The near wave field generated by the travelling atmospheric pressure zone over a stratified fluid is studied within the framework of the linear theory of long waves allowing for the Coriolis force. The exact solution of the problem as a set of single integrals is deduced for the model distribution of pressures. The characteristics of the near wave field have been computed for the Väisälä-Brunt frequency profile takeu from observations. Their dependences on the geographical latitude and the wave generator travelling rate are analysed.Translated by Mikhail M. Trufanov.     

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.     

Transmission and reflection of the Rossby waves in a stratified ocean with bottom topography

Transmission and reflection coefficients are calculated for Rossby waves incident on a bottom topography with constant slope in a continuously stratified ocean. The characteristics of the coefficients are interpreted in terms of the quasigeostrophic waves on the slope. In the parameter range where only the barotropic Rossby waves can propagate in the region outside the slope, the bottom trapped wave plays the same role as the topographic Rossby wave in a homogeneous ocean, and hence the transmission is weak unless phase matching takes place. When both of the barotropic and baroclinic Rossby waves can propagate outside the slope, the total transmission can be strong. The bottom trapped wave affects the transmission and reflection, and it leads to the possibility that the Rossby wave is transmitted as a mode different from the incident mode. When the number of the wavy modes on the slope is smaller than that of the Rossby wave modes outside the slope, strong reflection occurs.The results for an ocean with linear distribution of the squared Brunt-Väisälä frequency are compared to those in a uniformly stratified ocean. The weakening of the stratification near the bottom is almost equivalent to reducing the effect of the slope.     

On the collapse of a vertical packet of mixed patches. Laboratory and field studies

Visualization of a collapsing vertical packet of patches in a laboratory experiment and the results of acoustical sounding under field conditions allowed us to discriminate the stage of its evolution which was previously unknown. It is defined by the variations of the horizontal dimensions of patches and their effective scattering surface with a period ofT=150–250/N, whereN is the Brunt-Väisälä frequency. The horizontal dimensions of patches can reach 40% of their final dimensions at the evolution stage discriminated.Translated by Mikhail M. Trufanov.     

The effect of tidal currents on internal waves

Internal waves were observed by measuring temperature variations of several subsurface layers at the innermost part of Suruga Bay from December 1968 to October 1971. Spectral energy densities of temperature fluctuations were computed from the records of the measurements. In the shorter period range from one minute to one hour, peaks of energy density were found occasionally in the range shorter than the minimum of VÄisÄlÄ periods computed from the vertical distribution of water density. It has been generally understood, however, that the periods of internal waves in a stable stratum should be within the range between the inertial and VÄisÄlÄ periods.The measurements of tidal currents in the surface and lower layers, which were undertaken simultaneously with the temperature measurements, revealed that the short-period oscillations were associated with the increase of current velocity and of vertical shear of current at the pycnocline.It is considered that observed periods shorter than the minimum of VÄisÄlÄ period are not real but apparent periods due to the Doppler effect, because the waves are generated in the velocity shear of tidal current and the source is moving towards the station with the tidal current.     

Generation of small-scale turbulence in the Antarctic circumpolar current

A functional connection between probability of turbulence generation by shear instability in current velocity and Väisälä-Brunt frequency is obtained. Examples are cited of sections with isoclines of probable turbulence generation in the 30–500-m layer in the Antarctic circumpolar current north of Kergelen island.UDK [551.465.15+551.46.08] (269)     

The generation of baroclinic tides over steep non-uniform bottom topography

The internal waves generated by semi-diurnal barotropic tides over steep non-uniform bottom topography are considered within the framework of the general linear theory. For the distribution of a fairly general form of the Bruth-Väsälä frequency, a method is suggested for computing the wave fields over critical and post-critical topographic non-uniformities which takes into account wave motion in shadow areas. A specific analysis has been carried out for the fluid stratification, modelling pycnocline, and the bottom profile given by a simple trigonometric relation.Translated by V. Puchkin.     

Current Dynamics of Estuarine Circulation in the Lateral Boundary Layer

High spatial resolution measurements of current velocity performed by the shipboard mounted Acoustic Doppler Current Profiler (ADCP) in the lateral boundary layer of the southern Gulf of Finland during two 5-day periods are described and analysed with a focus on the dominant dynamics. The measurement site represents a small (15×20 km), relatively deep (up to 100 m) bay opened to large-scale estuarine circulation. The measurement period was characterized by calm winds and a strong seasonal pycnocline (Brunt-Väisälä frequencyN=6–9*10⁻² s⁻¹). The quasi-steady velocity field revealed polarization of currents along the shore whereas an intensive baroclinic coastal jet was observed over a cross-shore scale of 1–2 km. The level of vertical separation of the alongshore flow coincided with the pycnocline at the coast, but was shifted below it in the offshore region. The cross-shore flow was considerably weaker and showed a three-layer structure with an opposite phase between the first and second surveys. It is suggested that the observed jet resembles a non-locally forced eastward propagating coastally trapped wave. In the offshore area the alongshore flow field satisfies local geostrophic balance quite well, except in the pycnocline where strong vertical stratification exerts considerable vertical stress. As vertical velocity shear is well correlated with vertical stratification, the horizontal advection prevails over vertical mixing. Horizontal inhomogeneities of density distribution are partly explained by vertical velocities with an estimated magnitude of less than 0·6 mm/s and the spatial pattern following bottom topography.     

Contribution of breaking internal waves to structure formation,energy dissipation,and vertical diffusion in the ocean

The relationship between the scale of the spectral minimum of the first differences in temperature fluctuationsL and the local value of the Väisälä-Brunt frequencyN has been analysed using the results of more than 600 soundings made in various regions of the world's oceans. Allowing for the series of theoretical and experimental indications of the fact that the vertical scaleL at the boundary between the fine structure and microstructure in the ocean exists under the effect of processes of breaking of internal waves and hydrodynamic instability with the formation of turbulent patches, and using the energy relationships, the relationship for a solitary patch has been derived through the determining parameters. Based on two expressions forL, derived experimentally and using the energy estimations, the relationships for the averaged rate of absorption of the wave field energy by patches and the coefficient of the density vertical diffusion are derived, which do not contradict a series of independent estimations fromin situ measurements.Translated by Mikhail M. Trufanov.     

Mean Vertical Distribution of the Dissipation Rate of Turbulent Energy in the Black Sea. Comparison with the Existing Models

We compare the results obtained by using theoretical and semiempirical models developed for the evaluation of the dissipation rate of turbulent energy in a stratified ocean with independent distribution of this quantity established by the authors for the active layer of the Black Sea (50–300 m) by using a one-dimensional model taking into account the balance of heat, salt, and fluid inside the layer. It is shown that, in a layer with gradual variation of the Väisälä–Brunt frequency N as a function of depth, the predominant sink of the energy of motion into dissipation N ² is ensured by the flow of energy through the spectrum of internal waves toward low frequencies and small vertical scales. On the contrary, in layers with abrupt drops of density as a function of depth (layers with jumps of density), an important role is played by the interface-type waves and the dependence of on N transforms into N .     

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.     

Investigating internal waves east of the Hainan Island using optical satellite remote sensing data

Marginal water of east Hainan Island was an area that internal waves occurred frequently, however, few studies was found and mechanism for internal waves formation was unclear. In the paper, China Brazil earth Resources Satellite data (CBERS) was used to detect and calculate distribution, direction, wavelength and amplitude of internal waves in marginal water of east Hainan Island and the mechanism of internal waves formation was also analyzed, results showed that direction of internal wave was off shoreward and wavelength was about 150-200m . The mechanism for internal wave’s formation can be postulated as by upwelling or tide tracing back.