A comparative analysis of unstable symmetric perturbations of the geostrophic current with a constant vertical and horizontal velocity shear in an unbounded region and a region with lateral boundaries is performed accounting for vertical diffusion of buoyancy and momentum. Calculations of the growth rate of unstable perturbations are presented as a function of the vertical wavenumber for various dimensionless parameters of the problem. It is found that in the case of the geostrophic current with lateral boundaries, the maximum-growing mode of symmetric instability arising when condition Ri · (1 + Ro) < 1 (Ri is the geostrophic Richardson number, Ro is the Rossby number) is satisfied has a finite vertical length scale, while in the case of the unbounded region, the vertical wavenumber of the maximum-growing mode is asymptotically vanishing. A combined effect of lateral boundaries and diffusion of buoyancy and momentum at Pr ≥ 1 (Pr is the Prandtl number), depending on the values of the dimensionless parameters of the problem, can significantly affect the dynamics of symmetric perturbations, namely, lead to a narrowing of the spectrum of unstable perturbations and a decrease in their growth rates, and even prevent the development of instability.

Analysis of the Rossby wave dynamics shows when waves interact with shear currents vertical focusing of the modes occurs. Due to the inhomogeneity of the background flow, Rossby waves are captured by the current, and there is a compression of the modes on vertical horizons. For the vertical mode, instead of the classical trigonometric cosine, strongly localized solutions appear in the form of exponentially modulated Hermite polynomials. Qualitatively, the situation can be described as follows: an inhomogeneous background current acts like a kind of parabolic antenna. The wave, falling into this parabolic trap, begins to reflect off the narrowing walls of the paraboloid, while the vertical transparency zone narrows and the wave’s progress towards the center of the paraboloid slows down more and more. In the linear formulation, this process lasts infinitely long, while the distance between adjacent reflection points from the paraboloid mirror gradually decreases. There is a mathematical description of this phenomenon for internal waves. Since there are no fundamental differences between internal waves and Rossby in the vicinity of the focus, the mathematical part of the work for internal waves can also be transformed for Rossby waves.
In this paper, in terms of the Fourier integral, we construct a two-dimensional analytical solution of the reference equation for the vertical focusing of a monochromatic wave in the vicinity of the focus. Using the degenerate hypergeometric function of the complex variable, we show the identity of this solution with the solution of the reference equation obtained in previous studies. We find the asymptotic behavior of the solution in the far zone by the stationary phase method. Using exponentially majored Hermite polynomials, we show the correct two-dimensional crosslinking of the obtained solution, which has in the form of a degenerate hypergeometric function of a complex variable, happens with the WKB solution in the far zone. We show the question of absorption in the focal zone is not unambiguous, and therefore both situations are possible: both the passage and the reflection from the feature.

In the early 1990s, there was a shift in the Arctic climate system towards warming. This shift was accompanied by water temperature and salinity changes in the Arctic Basin due to increased Atlantic water inflow, river runoff, precipitation, and ice melting. We estimated changes in the freshwater content (FWC) and freshwater inflows into the upper layer of the Arctic Basin decade by decade from the 1950s through the 2010s and showed the connection between changes in the Arctic Basin and the tropical North Atlantic. Our results show that the FWC in the upper layer of the Arctic Basin in the 1990–2000s decreased in the Eurasian Basin and increased in the Amerasian Basin. On average, the FWC increase prevailed for the whole basin due to the larger contribution of FWC changes in the Amerasian Basin that occupies 61 % of the Arctic Basin. The largest FWC for the entire Arctic Basin was observed in the 1960s and preceded the negative salinity anomaly that occurred in the North Atlantic in 1960–1970s. The reduction of the FWC in the Eurasian Basin happened due to the increased Atlantic water inflow since the 1990s that causes salinification of the upper 100 m layer despite the increased precipitation and river runoff into the Arctic Basin. A freshwater accumulation occurs in the Beaufort Gyre and the entire Amerasian part of the Arctic Basin. The FWC in the upper 0–100 m layer of the Beaufort Gyre increased in the 2000–2010s by 36 % compared to that in the 1970s. The largest FWC increase (46 %) occurred in the upper 50 m layer during this period.

The article considers the spatial and temporal variability of the Polar Frontal Zone (PFZ) characteristics in the Barents Sea during the warm season from 2002 to 2020. In addition, the occurrence of small eddy structures in the PFZ region in different years is investigated, and the relationship of the characteristics of the frontal zone with global atmospheric processes is described. The position and characteristics of the PFZ were derived from satellite measurements using the cluster analysis method. Eddy structures in the PFZ region were detected from images of Envisat Asar and Sentinel-1A/B synthetic aperture radars. The NAO, EA, EA/WR and SCAND indices were used to assess the influence of atmospheric processes on the PFZ properties. It was found that the intra-annual values of temperature and salinity gradients in the PFZ region remained stable during the warm season and reached 0.05 °C/km and 0.02 %/km, respectively. The variability of the interannual estimates of the PFZ properties ranged from 0.02 °C/km to 0.08 °C/km in temperature, from 0.01 to 0.03 %/km in salinity, and from 120,000 to 425,000 km² in area. The maximum monthly mean values of the PFZ area were observed in 2007, while the minimum — in 2003. The obtained results clearly showed that the intensity of the PFZ decreased after 2010, which is presumably related to the “Atlantification” of the Barents Sea. The maximum number of small eddy structures in the PFZ region was identified in 2009. It is shown that the SCAND index for the previous winter season can be used as a predictor for predicting the characteristics of the PFZ in the summer period.

The article presents the results of verification and application of the proposed automatic algorithm of upwelling detection and presents the results of its work based on the CMEMS Baltic Sea Physical Reanalysis product in the southeastern part of the Baltic Sea for 2010–2019. The algorithm was verified by using the data of observations on the offshore ice-resistant stationary platform D-6, ship data obtained in the 127th cruise of the research vessel “Professor Shtokman”, and the results of upwelling detection based on the sea surface temperature derived from measurements of the MODIS Terra/Aqua spectroradiometer. It is shown that the lowest frequency of upwellings is observed in August-September (5–6 days per year), the highest — in May — June and October (11–15 days per year). In the period 2010–2013 in the study area, on average, up to 10 % of negative thermal anomalies were observed during the warm period of the year. Since 2014 (with the exception of 2017), an increase in the frequency of upwellings has been noted — on average, about 20 % of days were days with upwelling. It is shown that the winter East Atlantic/ West Russia and East Atlantic indices and the spring Scandinavia pattern index can be used to assess the characteristics of the future summer upwelling.

Two experiments with a regional Earth System Model (ESM) are performed. We discovered that in a simulation where light attenuation is calculated taking into account the water temperature–phytoplankton feedback the average sea surface temperature (SST) is lower over most of the tropical Indian ocean in comparison with the reference experiment in which a constant light attenuation coefficient equal to 0.06 m^-1, typical in global ESM runs, is used. We also find that the strongest differences (more than 1 °C) in SST occur in the summer period and a cooling of subsurface layers and a rise of the thermocline are noted in the experiment with the above feedback. Thus, including the full water temperature–phytoplankton feedback with corresponding light attenuation coefficient generally lowers the SST and water temperature in subsurface layers of the Indian ocean, with strong implications for the ocean-atmosphere coupling and, therefore for the simulated regional climate.

The article presents the results of the assessment of the phosphorus load on the largest European transboundary water body — Lake Chudsko-Pskovskoye under the conditions of the minimum flow rate typical for the dry period of 2010–2015. The external phosphorus load was calculated using the nutrient load model ILLM (Institute of Limnology Load Model) developed at the Institute of Limnology of the Russian Academy of Sciences and taking into account the contribution of point and non-point sources. Phosphorous losses from agricultural fields were determined based on the P_tot content in the arable soil layer, application rates of mineral and organic fertilisers, and nutrient uptake by crops. Free-access satellite imagery data was used to estimate the current areas of various types of land cover, which were the input data for modeling. The internal phosphorus load on the lake ecosystem due to the secondary phosphorus release from bottom sediments was calculated by the data from field observations in the water area. The study applied the methodology developed at the Institute of Limnology RAS and based on balance estimates of the main fluxes of phosphorus, such as sedimentation, burial, and release into the water from bottom sediments, in the “water–bottom” boundary zone. The study demonstrated that under the conditions of the considered low-water period, the internal phosphorus load exceeded the external one, having an adverse effect on the lake eutrophication.

The subject of our interest is the sound of the middle-frequency range from 1 to 5 kHz. Its scattering significantly depends on the state of the sea surface: the Rayleigh parameter can range from small numbers for a calm sea to values of the order of one for developed waves. The purpose of this study is to reproduce some of the effects that are observed in experiments on sound scattering on the sea surface using modern numerical methods. To simulate the sea surface we use the direct method for numerical simulation of potential flows with a free surface of a two-dimensional fluid, known as the Zakharov and Dyachenko method. The system of transformed Euler equations is numerically integrated to get how the surface evolves from the initial state. So nonlinear interaction of surface harmonics is taken into the account. We have proposed the original modification of the boundary element method (in 2D), which is suited for studying sound scattering separately on the surface, and it does not impose significant restrictions on the shape of the surface. We calculated the pressure field of the scattered sound wave, the backscattered force, and the Doppler spectrum of the signal depending on the angles of incidence and scattering at different wind speeds. The calculation results are compared with the predictions of classical models.

Stereo imagery of the roughness sea surface is one of the most effective tools for remote sensing wave characteristics. Typically, this method is implemented from the decks of fixed oceanographic platforms or onshore structures using two or more calibrated cameras. The topography accuracy from stereopairs directly depends on the quality of camera calibration. With a well-functioning procedure for reconstructing the sea surface from the data of a calibrated stereo system, considerable interest is associated with data obtaining with close accuracy using uncalibrated systems. This work is devoted to the study of this issue using the example of ship stereo survey in the Atlantic. The paper considers the process of image processing from uncalibrated cameras, presents the results of reconstructing the sea surface reliefs at several wind speeds and spatial spectra of long surface waves, and analyzes the practical applicability of uncalibrated systems.

The few preserved information about the flood of the Neva on November 5 (16), 1721 testifies to its catastrophic character. The flood was reported by F. Kh. Weber, F.V. Berchgoltz, Anri de Lavi, N.N. Golovin et al. The height of the flood was estimated by I.G. Leutman and published in article with L. Euler in 1729. However, it is known that a number of techniques for handling samples from level-gauge observations do not stand up to criticism from modern observatory and metrological positions. Thus, the negative attitude of A.I. Mordukhai-Boltovsky to a series of floods of the Neva of I.G. Leutman, supplemented by W.L. Kraft with events of 1723 and 1725 defies reasonable explanation. This accusation formally «justified» the dismemberment of a number of various leveling amendments determined in the XX century in the process of reducing to the zero of Kronstadt footstock.