The main properties of the Stokes waves are considered. Several methods of numerical investigation of wave dynamics are discussed. A conformal surface-following coordinate system is defined. Stationary potential waves equation in this coordinate system are represented. Algorithm of very fast numerical solving of stationary one-dimensional potential equations for the case of optional depth is described. The characteristics of numerical runs for the deep depth case are investigated: time of experiments, iteration number, potential, kinetic and total energy, asymmetry, excess. Area in coordinates of depth and steepness where solution exists is specificated. The geometrical characteristics of the Stokes waves as function of steepness and depth are investigated: asymmetry, maximum of the local steepness, maximum of the local second derivate and also phase velocity. The forms of waves for steepness 0.01 are shown. Possible application of obtained results is considered.

The derivation of the fifth-order Korteweg—de Vries equation is presented for internal waves in two-layer fluid with surface tension on the interface between the layers. The fluid motion is not supposed to be potential, therefore similar derivation can be used for consideration of wave motion in viscous fluid, in rotated fluid or for the shear flows with nonzero vorticity. Explicit expressions are obtained for the coefficients of the equation depending on the parameters of the background medium: widths of the layers, densities of the fluids, coefficient of surface tension. It is shown that for some combinations of the parameters of background medium the coefficients of the quadratic nonlinear and lowest order dispersive terms in the derived generalized equation can vanish and change their signs. Especially interesting is the situation when these terms become small simultaneously, and the coefficients at the nonlinear dispersive terms are also small. This is possible when the widths of the layers are almost equal. In the vicinity of such a double critical point the derived equation reduces to Gardner-Kawahara equation, which possesses solitary wave solutions with oscillating tails. Such a property makes this equation attractive theoretically and from the point of view of practical applications in the problems of flows in thin surface films of immiscible fluids. The characteristics of the flow in the presence of solitons significantly differ from those in the laminar flows, and this can lead to either negative or positive effects. On the base of the derived generalized equation and its solutions one can propose a method of control over a flow.

A method of modelling of signals of components of the velocity vector sensor that is placed in the stream consisting of whirls with different sizes is suggested. The description of the power spectra of the components is obtained. It is shown that the power spectra of model signals corresponds to the spectra of power components of the velocity vector of isotropic turbulence.

On the basis of review of ice; snow and oil optical properties the analysis of the possibility of detecting oil pollution on the lower ice/water boundary is presented. The cases of observation from above by standard TV-system at daylight and from below by underwater laser-pulsed imaging system and the moving narrow-angle receiver are considered. It was shown that if the rare case of the pure crystal ice is excluded; observation from above under natural illumination is possible when the maximum ice thickness (without snow) is less than one meter. Observation from below by use of laser system is possible independently of snow presence and ice thickness from depth up to 30 m in the coastal waters and more than 40 m in ocean waters. If the moving narrow-angle receiver with an axis directed to zenith is used at daylight; the contrast oil-ice equals almost unity.

The results of level rise simulation in the Gulf of Finland during the passage of the extreme and really observed cyclones over the Baltic Sea are presented. The analytical expression of atmospheric pressure field when passing intense cyclones was developed in the model of the Baltic Sea, which reproduces storm surges. This allows to simulate a wide range of trajectories and parameters of dangerous cyclones and resulting dangerous fluctuations in water level in the Gulf of Finland. Operation of St.-Petersburg Flood Protection Barrier was considered in the numerical experiments. It is shown that local level slope occurs in the Neva Bay under the closed Flood Protection Barrier and this slope can reach dangerous values. The simulation results are confirmed by level observations in the Gulf of Finland and in the Neva Bay during floods 2011 and 2013. These floods in St.-Petersburg were actually prevented. However, a more thorough analysis of the model calculations and the characteristics of specific cyclones will allow to carry out Protection Barrier gates maneuvers with most optimal way in the future.

Amplitude modulation of the sea vessel noise is widely used for automatic target recognition. Using the amplitude modulation parameters one can determine the vessel type; her displacement; the number of shafts and propeller blades; the velocity; the moment of course or velocity changing. There are two types of amplitude modulation: shaft and blade modulation due to the cavitations on the blade at large speed of rotation and roll and pitch modulation due to periodical changing of submerged part of the vessel. The paper contains the syntheses of optimal maximum likelihood automatic target recognition algorithm on base of amplitude modulation of their signals. It is shown that the same algorithm can be used both individually and as a part of the complex algorithm using several signal parameters. The effectiveness of automatic target recognition algorithm is investigated.

The relationship between the characteristics (sizes and numbers) of the Sun glints (or other light source of small angular size) on the rough sea surface and a wave spectrum is investigated. It is assumed that for each individual glint, formed on a real wave there is the «effective wave», which is the sum of two harmonic waves propagating in different directions and forming the glint with the same size. Based on this assumption and using the density distribution of the size of the glints, the expression for the wave spectrum, which agrees well with the known spectra, is derived. On the basis of theoretical calculations and numerical experiments the dependences of the characteristics of Sun glints on the wind speed, the width of the angular distribution of the energy of harmonics, as well as different parts of the wave spectrum are studied. Thus, a new method for determining the wave spectrum on the distribution of the Sun glints sizes is proposed.

Modification of the analytical model of lidar images of the nonlinear internal wave which was developed earlier in our works is performed. The influence of background horizontal current on the lidar signal is studied. The two-layer ocean with background flow in the upper layer is considered. For a theoretical description of moderate amplitude solitary waves in shallow water, the Korteweg— de Vries equation is used. Characteristic features of lidar images of nonlinear internal waves are calculated and analyzed using actual profiles of hydrooptical and hydrologic data obtained in the Barents Sea. It is shown that background horizontal flow can significantly affect the structure of lidar image of internal wave. The character of these variations depends on the profile of the attenuation coefficient. In particular, if a turbid layer is situated near the pycnocline, then with a current in an upper layer the reflective image of soliton is formed with higher level of returned signal than in the absence of current. It occurs due to the shift of the turbid layer upwards. The shadow image results not in attenuation but in amplification of the signals coming from the bottom water layer with homogeneous optical properties. It occurs due to thickening of the lower less turbid water layer affected by an internal wave. These results can be used for solution the problems of lidar remote sensing of internal waves and shear flows.