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 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.     

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     

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 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 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.     

Long nonlinear topographic planetary waves in a rotating stratified ocean

Long nonlinear topographic waves in a continuously stratified ocean with a linear bottom slope are investigated. It is shown that odd cross-channel modes are governed by the Korteweg-de Vries (K-dV) equation. The solitary waves are those of a low pressure type. The long waves are shown to be modulationally stable because of the nonlinear effect due to irrotational motion. All these results are missed if the conventional quasi-geostrophic approximation is adopted.     

Evolution and breaking of a propagating internal wave in stratified ocean

The evolution and breaking of a propagating internal wave are directly numerically simulated using a pseudo-spectral method. The mechanism of PSI （ parametric subharmonic instability） involved in the evolution is testified clearly. It dominates gradually in nonlinear resonant interactions. As a consequence, the energy cascades to a second plant wave packet which has lower frequencies and higher wavenumbers than that of the primary wave. With the growth of this wave packet, wave breaking occurs and causes strongly nonlinear regime, i.e. stratified turbulence. The strong mixing and intermittent of the turbulence can be learned from the evolution of the total energy and kurtosis of vorticity vs. time. Some statistic properties of the stratified turbulence are also analyzed, including the spectra of KE （kinetic energy） and PE （potential energy）. The results show that the PE spectra display a wavenumber range scaling as 0. 2 N^4ky^-3 （N is the Brunt - Vaisala frequency, k, is the vertical wavenumber）, which is called buoyancy sub-range. However, the KE spectra cannot satisfy the negative cubic law of vertical wavenumber, which have a much larger downtrend than that of the PE spectra, for the potential energy is transferred more efficiently toward small scales than the kinetic energy. The Cox number of diapycnal diffusivity is also calculated, and it shows a good consistency with the observations and deductions in the ocean interior, during the stage of the stratified turbulence maintaining a fairly active level.     

Study of the generation of non-stationary non-linear long waves by atmospheric pressure disturbances

In a non-linear statement, this paper considers the generation of long waves by periodic atmospheric pressure disturbances in a confined basin of variable depth filled with homogeneous fluids. The study is conducted using a non-stationary finite-difference model. The contribution of dissipative forces to the development and stabilization of fluid oscillations is analysed. The paper also considers how the growth of the amplitude of atmospheric pressure disturbances may enhance the non-linearity of the wave process. It is shown that as the pressure amplitude becomes larger, the number of significant harmonics with multiple frequencies in the spectrum of sea level elevations increases. For the weakly non-linear case, wave velocities and free surface elevations, with oscillations stabilized, are compared with their counterparts derived through the perturbation technique.Translated by Vladimir A. Puchkin.     

Experimental study on internal waves in a stratified shear flow

This paper describes experiments on interfacial phenomena in a stratified shear flow having a sharp velocity shear at a density interface. The interface was visualized in vertical cross-section using dye, and the flow pattern was traced using aluminum powder. Two kinds of internal waves with different phase velocities and wave profiles were observed. They are here named p(positive)-waves and n(negative)-waves, respectively. By means of a two-dimensional visualization technique, the following facts have been confirmed regarding these waves. (1) The two kinds of waves propagate in the opposite direction relative to a system moving with the mean velocity at the interface, and their dispersion relations approximately agree with the two solutions of interfacial waves in a two-layer system of a linear basic shear flow. (2) The p-wave has sharp crests and flat troughs, and the n-wave has the reverse of this. This difference in wave profile is due to the finite amplitude effect. (3) Phase velocity of each wave lies within the range of the mean velocity profile, so that a critical layer exists and each wave has a “cat's eye” flow pattern in the vicinity of the critical layer, when observed in a system moving with the phase velocity. Consequently, these two waves are symmetrical with respect to the interface. The mechanisms of generation of these waves, and the entrainment process are discussed. It is inferred that when the “cat's eye” flow pattern is distorted and a stagnation point approaches the interface, entrainment in the form of a stretched wisp from the lower to the upper layer occurs for the p-wave, and from the upper to the lower layer for the n-wave.     

海洋内波对水声场的扰动

针对海洋内波对水声传播影响的问题，在简要引出内波方程，水声方程和内波解，射线理论之后，以水深2100m等Vaisala频率的全板造波内波解对双线性水声剖面情况计算了内波和内波对声场及声线传播的影响，结果表明，内波对声线传播的路径和时间的影响是不可忽略的。     

Generation of quasiinertial internal waves in the process of evolution of local perturbations in the ocean

Within the framework of a linear model of long waves in a two-layer ocean, we obtain the analytic solution of the problem of evolution of an axially symmetric initial displacement of the jump of density. In the process of adaptation of the fields, internal waves in the form of a decaying (in time) wave packet are emitted from the zone of initial perturbation. These waves are quasiinertial and their dispersion is conditioned by Earth’s rotation. We study the time evolution of the wave packet and the dependence of its characteristics on the width of the zone of initial perturbation and the depth of the jump of density. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 2, pp. 12–23, March–April, 2006.     

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     

Edge waves generated by atmospheric pressure disturbances moving along a shoreline on a sloping beach

Edge waves generated by moving atmospheric disturbances parallel to the shoreline are investigated. Following a standard transformation method, an analytical expression of the surface elevation is derived, which consists of an infinite number of modes. Each mode is expressed as the sum of three singular integrals. Using the contour integration method, these singular integrals are converted to regular integrals, which are evaluated by numerical integration methods. The numerical results of two atmospheric pressure distributions studied by Greenspan (1956) are presented, and the resonance conditions are discussed.     

Nonlinear ocean internal waves observed by multifrequency synthetic aperture radar

A numerical model which consists of the Korteweg-de Vries (KdV) equation, the action balance equation and the radar backscat- tering model is developed to simulate the frequency dependence of synthetic aperture radar (SAR) remote sensing of nonlinear o- cean internal waves. Muhifrequency data collected by NASA SIR - C SAR and NASA JPL AIRSAR are used as comparison. Case studies show that the results of simulation agree well with the results of SAR data.     

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.     

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.     

Fine structure of a conical beam of periodical internal waves in a stratified fluid

Stratified fluid flows caused by torsional or linear harmonic oscillations of a ring along the surface of an infinite vertical cylinder have been calculated by methods of the perturbation theory. The complete solutions of the linearized system of equations with sticking boundary conditions for velocity and impermeable boundary conditions for substance have been obtained taking into account viscosity and diffusion. Disturbances forming a conical beam of three-dimensional internal waves and families of small-scale components are identified. Formulas for calculating waves in media with different Schmidt numbers are described.     

Far fields of internal gravity waves in a stratified liquid of varying depth

Asymptotic representations of solutions describing the far fields of internal gravity waves in a stratified medium of varying depth are constructed. The effect of space-frequency cutoff of the wave field for a real oceanic shelf is revealed. Depending on frequency characteristics of the wave field and bottom topography, far fields of internal waves either are located in a certain confined space domain (trapped waves) or propagate in the absence of turning points over sufficiently large distances when compared with the sea depth (progressive waves). The space domain where the progressive waves penetrate is fully determined by the presence of turning points whose locations depend on the medium stratification and inhomogeneities of bottom topography.     

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.