The analysis of field data at the shelf break in the Black Sea demonstrates increasing of vertical eddy diffusivity by an order of magnitude on the average with respect to the open sea conditions with the same stratification. The use of a simple model showed that increasing in the energy of quasi-inertial waves in this region can be considered as the most probable cause of the mentioned experimental fact. This phenomenon results in considerable decreasing of the Richardson number in quasi-horizontal wave currents and, as a consequence, in-creasing of the mixing intensity and vertical diffusion.

Wave motions of stratified fluid over uneven bottom are considered. The results of the laboratory experiments on the transformation of nonlinear internal waves of the first and second mode on the slope are presented. The numerical calculations of the evolution of large-amplitude internal waves using a mathematical model of the three-layer shallow water with the non-hydrostatic pressure distribution are compared with the experimental data. The exact solution, which represents an asymmetric solitary wave of the second mode, is constructed. The experimental confirmation of the existence of asymmetric solitary waves propagating along the interface between the homogeneous layers of different densities is presented.

The study of the dynamics of short-period internal waves of large amplitude in the «swash» zone located above the contact line of the bottom with the main thermocline was carried out. It is shown that the generation of packets of solitary waves is intermittent. It is observed during the months of the existence of developed sea-sonal thermocline (August-October). The spreading and breaking of internal waves contributes significantly to the mass transfer and «ventilation» in the shelf zone. The analysis of the structure of the bottom solitary waves in the «swash» zone shows that they can be detected in the form of symmetric lenses of cold water or they take the saw-shape form, depending on the breaking phase.

An asymptotic model of long internal wave transformation in horizontally inhomogeneous ocean is discussed. This model is based on the Gardner equation (extended Koreweg – de Vries equation). Verification of the model using the ocean experimental data from the SEASAM experiment on the Malin shelf is carried out. It is shown that the model is appropriate for rough estimation of amplitudes and shapes of internal waves. The ad-vantage of the model is related to the simplicity of accounting for the horizontal inhomogeneity of hydrological fields and short time needed for calculations.

The paper is devoted to the solution of the fundamental problem of mathematical modeling of ocean dynamics, related to the theoretical study of the propagation of disturbances, and evolution of far fields of internal gravity waves in inhomogeneous and non-stationary stratified media. The problem is solved using the suggested modified spatiotemporal ray-tracing method. The numerical results based on the suggested asymptotic formulas and real parameters of the ocean are presented.

A theoretical model of internal solitary waves with large amplitude in a weakly stratified fluid is considered. It is assumed that the background density profile of liquid linearly or exponentially depends on the depth. It was shown that the inverse problem of restoring the coefficient of the density fine structure based on the known amplitude dispersion curve is reduced to the solution of a linear Fredholm integral equation of first kind with the special form of the kernel. In the case of the polynomial stratification a one-to-one correspondence is established between the density coefficient and the dispersion function.

The study of the interaction of unidirectional single-mode solitary internal waves in a stratified ocean is performed. The exact two-soliton solution of the Korteweg – de Vries equation is used for the analysis. The role of this process in the dynamics of soliton turbulence is discussed. It is shown that during the interaction the third and fourth moments of the wave field, which play an important role in the theory of turbulence (skewness and kurtosis), decrease. The results are compared with the linear dynamics of soliton-like pulses, for which the third and fourth moments increase during collision.

Characteristics of tidal internal waves in the Northwest Pacific are calculated from the data of measurements of temperature and currents on a large number of moorings. Two wave systems are distinguished. One was generated to the east and southeast of the study region admittedly over the Shatsky Rise and Emperor Sea-mounts. The second system was generated in the region of the Kuril Islands. We averaged a large amount of data of measurements and calculated the ellipses of the barotropic tide currents, which appeared close to the estimates based on the satellite altimetry data. The currents of the barotropic tide were used to calculate the characteristics of tidal internal waves after subtraction of tidal currents from the data of measurements.

A new equation for the description of the transformation of two-dimensional pycnocline perturbations over fixed rigid bottom in the «solid lid» approximation is obtained. It is assumed that wave lengths are relatively large, their amplitudes are small but finite, and the bottom may be weakly sloping. The deduced equations may be applied for the simulation of the interactions between the disturbances propagating simultaneously in the opposite directions. The problem of the head-on collision of two solitary waves is solved analytically. Solutions of several characteristic problems are found numerically, and the effect of the bottom topography on the evolution of disturbances is shown.