In the paper some aspects of mathematical modeling of wave and hydrodynamic regime at protected water areas are considered, examples of the dangerous hydrodynamic phenomena research (broken water, harbor seiche, resonant characteristics of harbor) are given. Recommendations of various wave and hydrodynamic models applicability for the decision of assigned tasks are given.

The run-up of irregular long sea waves on a beach of a constant slope is studied in the framework of nonlinear shallow water theory. It is shown that the problem nonlinearity does not influence on statistical moments of the velocity of the moving shoreline, but affects statistical moments of the displacement. In particular, for weak-amplitude waves it is demonstrated that the wave run-up process has a longer duration as compared to the duration of the wave run-down process, even if the incident wave field represents Gaussian stationary process with a zero mean. The probability of wave breaking during the process of wave run-up is calculated and conditions of the model validity are discussed.

Dynamics of the sea coast is characterized by both the short-term changes and the long-term trends manifested in the time scales of decades, centuries and milleniums. When modeling the short-term storm-induced deformations the process-based models turn out to be most successful as those simulate the suite of primary mechanisms responsible for sediment transport and bed deformations. Presented model CROSS-P is applicable to calculate the storm-induced deformations on sandy coasts of the seas, large lakes and water stores. To analyse the long-term coastal evolution the model SPELT is suggested determining the position and form of the profile depending on changes in sea level and imbalance of sediment budget.

We analyse the main properties of wave fields in the Gulf of Finland and their spatial and long-term variations based on visual wave observations performed since 1954 at two locations on the southern coast of the gulf and high-resolution simulations of wave fields for the entire Baltic Sea for 1970-2007. Shown is that both longterm average and maximum wave heights in the gulf are about a half for those in the Baltic Proper. The average wave heights have insignificantly changed in the gulf since the 1970s whereas the extreme wave heights have considerably increased in the northern and in the northeastern sections of the gulf. A probable reason for the changes is the enhancement of south-western winds over the last 40 years.

The experience of development and environmental expert review of the sea hydro technical projects has been generalized. Construction and operation of the sea ports, as well as continental shelf structures may cause the significant impact onto sea water environment. The modern method of coastal processes modeling and the modern construction technologies can help in assessment of the environmental effects and to minimize these effects. The separation of the global project into stages may be applied if the environmental impact assessment is possible, only.

One of the possible mechanisms of freak-waves emergence near a vertical barrier, based on the dispersive focusing of unidirectional wave packets is analyzed. This mechanism is associated with the frequency dispersion of water waves and manifested in the interference of many spectral components, moving with different group velocities. Formation of a single freak wave in a random wind wave field is considered in the frame of linear theory. The characteristic lifetime of an abnormal wave in the framework of this mechanism for typical conditions is approximately two minutes, thus such a rapid effect is difficult to predict and prepare for. A rogue wave quickly changes its shape from a high ridge to a deep depression.

The results of laboratory experiments and numerical modeling of the interaction of a solitary wave and a fixed partially submerged body of rectangular shape, located on a flat slope are presented. Carried out research allowed to determine the magnitude run-up on the body and the wave pressure on it, depending on the oncoming wave amplitude, the body length and its immersion, the angle of the slope.

The problem of impact of a water wave with flat front onto an elastic vertical plate which models the surface of a coastal structure is studied. The liquid is assumed weakly-compressible; the liquid flow is described within acoustic approximation. The deflection of the plate and its vibrations caused by impact are described by a linear theory of thin isotropic plates without accounting for shear stresses. The hydrodynamic and structural parts of the problem are coupled by both dynamic and kinematic conditions imposed on the wetted part of the structure. The problem is solved by the normal mode method. By using integral transforms the problem is reduced to a system of differential and integral equations which are numerically solved. Phenomena caused by the structural damping and liquid compressibility are investigated. It is shown that the structural damping affects the global evolution of the plate behavior; however, maximum deflection and maximum bending stress can be determined without account for structural damping. New combined model of violent wave impact is proposed. Within this model only the early stage of impact is described with taking the liquid compressibility into account, the later stage is simulated by using the model of incompressible liquid.

One of the most characteristic properties of longitudinal waves is the growth of their height near the bank line. This property is especially observed in short longitudinal, the mathematical description of which in terms of mathematical approximation was for the first time given by Stokes. In the present paper, Stokes’ solution generalized to the case of a stationary longitudinal flow is used to estimate the static stability and deformation of the sea shore slope or of the deep see and river channel slopes. The stability of shore slopes of a shallow sea or trapezoidal or triangular channels, which have cross-section dimension commensurable with the longitudinal wave length is estimated on the basis of an approximate solution of three-dimensional wave equations by the Galerkin-Kantorovich method. This solution, while preserving the three-dimensional structure of waves over the bank slope, leads to the results which can be easily used in engineering design.