The main approaches in direct modeling of surface waves based on complete equations of dynamics of the inviscid liquid with a free surface are briefly considered. Most of the models are intended for study of the applied and engineering problems. It is assumed that the main model is written in the curvilinear coordinate system where the height is counted off from wave surface. In the two-dimensional periodic formulation, when using a conformal system, the problem is reduced to the system of one-dimensional equations that can be easily solved using Fourier-transform method. For three-dimensional waves such simplifications do not exist, thus, the vertical velocity on the surface is calculated by solving a three-dimensional Poisson equation or using a surface integral method. An approximate scheme based on the two-dimensional equations is considered. The scheme allows reproducing the statistical mode of waves with high accuracy consistent with the similar results obtained from the accurate three-dimensional model.

The paper presents the results of a study of the lifetime of wind-wave breaking (“whitecaps”) and the spatial distribution of the moments of wave-breaking initiation along the profile of a long surface wave. The results obtained during the specialized experiments from an oceanographic platform in the Black Sea are given. The registration of the whitecaps was carried out based on the video recordings of the sea surface. The surface waves’ characteristics were measured and the meteorological information was recorded simultaneously with the video recordings. It is shown that the distribution of the whitecaps’ lifetime is well described by an exponential law. It was found that the ratio of the lifetime of an individual whitecap to the period of the breaking wave is 0.3. The distributions of the above-mentioned ratio are similar for different wind and wave conditions. It is indicated that the generation of whitecaps occurs mainly in the region of the crest of a long wave with a shift to its front slope on average by 9.6 of the phase of the long wave. The whitecap having arisen at the leading edge shifts to the trailing edge of the long wave during its lifetime, so that the phase difference between the breaking initiation and the maximum of the surface fraction covered by the whitecaps equals 21.6.

The coupled wind-wave model is considered. The model includes two components: the 1-D wave boundary layer model and the 2-D wave model. The coupled model is used in two versions: in the presence and the absence of the wave produced momentum flux. A series of experiments was performed for different external parameters: wind speed at the upper boundary of the wave boundary layer and the inverse wave age. The vertical profiles of wind velocity, turbulent and wave produced momentum fluxes were studied and compared to the results obtained from the wave boundary layer model. The comparison showed that the results of coupled modeling coincide exactly with the results from the wave boundary layer model in the case of fully developed waves and differ significantly if developing waves are considered. It is demonstrated that wave produced momentum flux produces considerable deviations of the wind velocity profile in the lower part of the wave boundary layer from the logarithmic profile.

The Barents Sea is one of the key areas in the Arctic for monitoring of climate change. Although the Barents Sea is one of the Arctic seas, it is never completely covered with ice. One of the parameters characterizing the change in the ice regime is the date of ice retreat (DOR). The study is based on ice concentration data from the NOAA / NSIDC Climate Data Record (CDR) from 1979 to 2019 and the GLORYS12V1 ocean reanalysis data from 1993 to 2019. The analysis of the spatial and temporal variability of DOR for the Barents Sea using the HDBSCAN cluster analysis method made it possible to identify areas (clusters) with the synchronous dynamics of DOR. A number of the identified areas are located on the path of the Atlantic waters (AW) in the Barents Sea, which made it possible to relate the revealed temporal variability of the DOR to the variability of the AW transport across the western boundary of the sea. Over the entire Barents Sea, after 2003, there has been a steady trend in the timing of seasonal ice removal to earlier ones. At the same time, each of the six regions identified has its own dynamics and rate of changes in DOR. A noticeable effect of the advective heat flux across the western boundary of the Barents Sea on the DOR was revealed for areas in the central and eastern parts of the sea. At the same time, for different regions, the maximum correlation coefficient is observed at different time lags (from 0 to 6 months). The value of the time lag indirectly indicates the time the thermal signal travels the distance from the western boundary of the sea to the corresponding region. The continuing trend towards an increase in the duration of the ice–free season in the Barents Sea is one of the manifestations of the growing “Atlantification” of the East Atlantic sector of the Arctic Ocean which opens up new prospects for socio–economic activity in this Arctic region.

Changes in near surface air temperature (SAT) and vorticity of the wind speed field of the White Sea and the territory of the Murmansk and Arkhangelsk regions and the Republic of Karelia are investigated. We analyzed the monthly average NCEP/ NCAR reanalysis data for the period 1950–2020. The average surface air temperature growth estimated using a linear trend was +0.24⁰C/10 years. Against the background of this linear growth, significant interdecadal changes in surface air temperature are observed. The following periods are highlighted: the strengthening of the continentality of the climate (1950–1976), a more maritime climate (1977–1998), and the rapid growth of surface air temperature (1999–2020). The transition from a period of increasing continentality of the climate to a period of a more maritime climate is associated with an increase in the influence of the North Atlantic on the region under study. A hypothesis has been put forward that the period of rapid growth of surface air temperature is caused by the transition of the climatic system of the western part of the Russian Arctic into a new phase state. The observed warming in the Arctic has caused a reduction in sea ice, which has led to an increase in solar energy absorption by the surface of the Barents and White Seas.

This research article is continuation case study based on a model of radar monitoring of vibration waves occurring on the sea surface near the source of a bottom earthquake. The vibration wave is generated parametrically, has near (hydrodynamic) and far (sound) components. The amplitude of the near (generating) wave depends on the bottom vibrator parameters and the depth of the bottom, the far wave propagates in the waveguide formed by the surface and the flat bottom. The vibrator will be installed at a shallow depth (30 m) and the modern aircraft radar will be used to create amplitude and velocity radar images during the experiment. The length of the generated vibration wave will be ~1.5 cm, which corresponds to the frequency of the generating wave ~30 Hz and the “resonant” wave of the radar with a length of ~3 cm (radar X-band). The possibility of monitoring vibration waves in the amplitude and velocity channels of the SAR (synthetic aperture radar) in L, P and UHF-bands is estimated. Also, the expected view of the SAR images is shown. Calculations of the necessary parameters of the aircraft radar are provided, including algorithms for processing the initial signal when creating amplitude and velocity radar images of vibration waves.

On a qualitative level, the possibilities of using optical stereo images of the sea surface, registered from under the water, are considered in relation to the problem of remote diagnostics of waves. The task is implemented in a numerical experiment using a stereo image model of the Snell’s window (underwater image of the sky) for a given relief of the sea surface. The influence of the camera parameters, observation geometry, illumination and excitement on the quality of constructing disparity maps, necessary to restore the distances to the sighted elements of the sea surface, is analyzed. Recommendations on the methodology of a full-scale experiment in order to test the proposed method are formulated.

The problem of systematizing information about the historical floods of the Neva seems to be extremely urgent today. The construction of predictive models, the feasibility of building new hydraulic structures, planning of engineering, economic, environmental, social and cultural activities are impossible without a comprehensive analysis of information about floods. The official catalogs available to researchers, unfortunately, are not informative enough and are full of distortions. Working with a large array of numerical values characterizing the flood heights of the Neva of different eras, the inconsistency of these values, even within the framework of individual events, the importance of clarifying them in order to preserve all information aspects — all this led to the need to form the Database of floods. The main task of its creation is information support of research related to the restoration of distorted rows (or individual historical floods of the Neva).