Purpose . The work is purposed at summarizing the results of studies both of the spatio-temporal variability of water density stratification and the internal wave characteristics in the Barents, Kara, Laptev, East Siberian, Chukchi and Beaufort seas. Methods and Results. Based on the World Ocean Atlas data, the average monthly profiles of buoyancy frequency were calculated at the 0.25 degrees x 0.25 degrees grid points for 1959-2020. To study the vertical structure and dispersion characteristics of internal waves, the eigenvalues and eigenfunctions of the main boundary value problem of the Sturm - Liouville type were found at the fixed values of a wave number. The regional features of vertical structure and intra-annual variability of the V & auml;is & auml;l & auml; - Brunt frequency were revealed. The relationship between the water density vertical structure and the free internal wave characteristics in the seas under consideration was analyzed. Conclusions. It is shown that maximum water stability in the Barents Sea takes place in July - August, in the Kara Sea - in September and November, in the Laptev Sea - from June to November, in the East Siberian and Chukchi seas - in July, and in the Beaufort Sea - in June. In the same months, the smallest values of the amplitude of vertical velocity component as well as the smallest own periods of internal waves are noted. The depth of maximum values of the vertical component amplitude of internal wave velocities exceeds that of the density gradient maximum values by about 10-20 m.

The trend assessment of the dynamic state of the Powell Basin waters in the Weddell Sea was made on the basis of the hydrological data of the 79th cruise of the R/V AkademikMstislavKeldysh (January 16–February 6, 2020) and the World Ocean Database-2018 data for January-February from 1975 to 2020. At each node of the quarter-degree grid, a linear trend was constructed for the calculated values of the maximum buoyancy frequency and the maximum amplitude of the vertical component of the internal wave velocity. It is shown that the southwestern and northwestern parts of the Powell Basin differ significantly in their hydrophysical characteristics. In the northwest of the basin, the linear trend of the maximum buoyancy frequency is negative, the trends of the depths of the maximum values of the Väisälä-Brent frequency and the amplitude of the vertical velocity component are positive. In the southwestern part of the basin, the opposite is true: the trend of the maximum buoyancy frequency is positive, the trends in the depths of the maximum values of the Väisälä-Brunt frequency and the amplitude of the vertical velocity component are negative.

Purpose. The aim of the study is to analyze the river runoff impact on density stratification in the Chukchi and Beaufort seas, and to identify the areas where the response to seasonal fluctuations in the river runoff volumes is the most pronounced. Methods and Results. Based on the ECMWF ORAP5 reanalysis data on the monthly mean values of temperature and salinity for May - September of each year, the water density in the Chukchi and Beaufort seas was calculated. To study the river runoff impact on the density stratification of sea water, applied were the calculated maximum monthly average values of the Vaisala - Brunt frequency over depth at each grid node, and the monthly average water discharges in the closing gates of the Kolyma, Yukon and Mackenzie rivers for the period 1979-2013. The results of statistical analysis showed that density stratification of the Chukchi and Beaufort seas was most strongly affected by the Mackenzie and Yukon river runoffs for a previous month and also by the Kolyma river runoff for 3 and 6 previous months. Conclusions. The impact of the Mackenzie runoff is found to be most pronounced from July to September. The areas of statistically significant correlation coefficients between the buoyancy frequency and the runoff volumes for the previous month are in the southeastern and central parts of the Beaufort Sea. The areas where the impact of the Yukon runoff is pronounced are in the Bering Strait area, in the northern region of the Chukchi Sea, and on the western periphery of the Beaufort gyre. The Kolyma runoff impact on the water density stratification is manifested near the western coast of the Chukchi Sea, in the Bering Strait area, the Kotzebue Bay, and on the southwestern periphery of the Beaufort gyre.

The northern rivers runoff is an important factor in the hydrological regime formation of the Arctic Seas. Under the influence of winds and currents, river waters spread over and interacting with sea water. As a result of their mixing, the areas of slightly salty water are formed on vast regions of the Arctic shelf and continental slope. In this work the effect of the rivers runoff on the density stratification of the Barents, Kara, Laptev and East Siberian Seas has been studied. It was done using reanalysis data (ECMWF ORAP5) on the average monthly values of temperature and salinity, and data on the average monthly water discharge at hydrological stations from 1979 to 2013. It is found that the influence of the Pechora runoff is most pronounced in the southeastern part of the Barents Sea and the southwestern part of the Kara Sea. The Ob runoff is shown itself in the southwestern, northwestern and central regions of the Kara Sea. The Yenisei affects the eastern part of the Kara Sea and in the northwestern region of the Laptev Sea. The influence of the Khatanga River is manifested in the western and northwestern regions, the Lena runoff influence—in the shelf coastal zone of the Laptev Sea. The Kolyma runoff is noticeably reflected in the density stratification of the East Siberian Sea.

Purpose. The work is aimed at studying the ice compression influence on the components of fluid motion velocity under a floating ice cover in propagation of the wave formed by the nonlinear interaction of wave harmonics. Methods and Results. Based on the obtained solution of the problem on nonlinear interaction of the progressive surface waves in a finite depth basin with floating and longitudinally compressed elastic ice, analyzed were the distributions of the components of fluid particles motion velocity along the generated wave length depending on the ice characteristics. The impact of thickness, elasticity modulus and compressive force of the ice cover, nonlinearity of the ice vertical acceleration and the amplitude of the second interacting harmonic upon the vertical and horizontal components of the fluid particles motion velocity was studied. Conclusions. It is established that the compressive force conditions reduction of the phase and the maximum values of the fluid motion velocity components. Change in the sign of the second interacting harmonic amplitude is manifested in a significant profile transformation, and affects the generated perturbation phase at the regard for the nonlinearity of ice vertical acceleration. When the compression force value is fixed, a decrease in the ice cover rigidity results in a noticeable delay of the oscillation phase.

Purpose. The aim of the paper is to study dependence of the homogeneous fluid movement velocity (moving in the direction of wave propagation and formed by nonlinear interaction of the wave harmonics) upon the characteristics of the ice cover. Methods and Results. Based on the movement velocity potential of the fluid of finite depth obtained in a form of an asymptotic expansion up to the values of the third order of smallness, analyzed was the velocity of fluid particles movement under the floating elastic ice at nonlinear interaction of the wave harmonics. Influence of the ice cover thickness and elasticity module, nonlinearity of the ice vertical acceleration, and the amplitude of the second interacting harmonic upon the components of the orbital velocity of the fluid particles movement under the floating ice was studied. Conclusions. It is shown that the influence of nonlinearity of the vertical displacements' acceleration of floating ice upon the components of the fluid movement velocity is manifested in an increase of the phase shift. A change of a sign of the second interacting harmonic results in transformation of the profiles and decrease of the phase. Growth of the Young's modulus value is manifested in a noticeable increase of the phase shift and in a weak increase of the maximum values of the fluid movement velocity components as compared to the case when there is no ice.

Purpose.The aim of the paper is to study dependence of the homogeneous fluid movement velocity (moving in the direction of wave propagation and formed by nonlinear interaction of the wave harmonics) upon the characteristics of the ice cover.Methods and Results.Based on the movement velocity potential of the fluid of finite depth obtained in a form of an asymptotic expansion up to the values of the third order of smallness, analyzed was the velocity of fluid particles movement under the floating elastic ice at nonlinear interaction of the wave harmonics.Influence of the ice cover thickness and elasticity module, nonlinearity of the ice vertical acceleration, and the amplitude of the second interacting harmonic upon the components of the orbital velocity of the fluid particles movement under the floating ice was studied.Conclusions.It is shown that the influence of nonlinearity of the vertical displacements' acceleration of floating ice upon the components of the fluid movement velocity is manifested in an increase of the phase shift.A change of a sign of the second interacting harmonic results in transformation of the profiles and decrease of the phase.Growth of the Young's modulus value is manifested in a noticeable increase of the phase shift and in a weak increase of the maximum values of the fluid movement velocity components as compared to the case when there is no ice.

The investigation of the correlation between the sea ice concentration and the downward solar radiation flux was made on the base of NCEP data from 1982 to 2016. The regional distribution of the correlation coefficients is analyzed and areas with high correlation are identified. The calculation and analysis of the temporal trends of downward solar radiation flux and sea ice concentration has been carried out. The relationship between annual total values of downward solar radiation flux and the annual catch capacity of Antarctic krill in subareas 48.1–48.3 of the Convention of the Conservation of Antarctic Marine Living resources was estimated for period from 1993 till 2016.

Investigation of the features of spatial-temporary distribution of the Brunt-Väisäla frequency maximum and its occurrence depth in the Barents and Kara Seas is considered on the basis of the World Ocean Atlas 2013 reanalysis for the period 1955–2012 with 0.25° × 0.25° grid. The regional features of the vertical structure of the buoyancy frequency are revealed. Correlations between intra-annual variability of the Brunt-Väisäla maximum frequency and climatic indexes are investigated.

Purpose. The aim of the work is to investigate vertical structure and phase characteristics of free shortperiod internal waves (IW), and to assess their dependence on density stratification in the Barents, Kara, Laptev and East Siberian seas. © Букатов А. А., Соловей Н. М., Павленко Е. А., 2021 МОРCКОЙ ГИДРОФИЗИЧЕСКИЙ ЖУРНАЛ том 37 № 6 2021 645 Methods and Results. Solving the main boundary problem of the Sturm-Liouville theory has resulted in calculating the amplitudes of velocity vertical component, own frequencies and periods of the first mode of internal waves. The density field was calculated using the reanalysis data (World Ocean Atlas 2018) on temperature and salinity for 1955–2017 with a resolution 0.25°× 0.25°. The relation between the internal waves’ vertical structure and dispersion features, and the density depth distribution was analyzed. It is shown that the averaged over the sea area depth of the maximum amplitude of the IW velocity vertical component in the Barents and Kara seas is ∼ 90 m in the mid winter and ∼ 75–80 m in summer, and in the Laptev and East Siberian seas – ∼ 60 m throughout the whole year. Conclusions. In the months when the density gradients are maximal, the internal waves of the highest frequency and the shortest period are observed. The maximum water stability in the Barents Sea takes place in July – August, in the Kara Sea – in July – September and November, in the Laptev Sea – in June, November, and in the East Siberian Sea – in July. Just in the same months, the maximum values of the averaged own frequencies, and the minimum values of the averaged own periods and amplitudes of the vertical component of the internal waves’ velocity are observed.

Purpose. The aim of the paper is to investigate spatial-temporal dependences of the dispersion features of short-period free internal waves on the density field vertical structure in the Barents and Kara seas. Methods and Results. Based on the linearized equations of motion of the ideal incompressible and continuously stratified fluid, the dispersion features of free internal waves in the Barents and Kara seas were studied. Solution of the main boundary problem of the Sturm-Liouville type made it possible to obtain the own frequencies of five lowest modes and the own period of the internal waves’ first mode. To calculate the density field, the World Ocean Atlas 2013 reanalysis data on temperature and salinity for 1955–2012 with resolution 0.25° × 0.25° were applied. The relation between the dispersion features of free internal waves and the density field vertical structure was analyzed, and dispersion characteristics of theinternal waves in the Barents and Kara seas were compared. Conclusions. During the months when the density gradients are maximal, the internal waves of the highest frequency and the shortest period are observed. Among the intra-year maximums of the buoyancy depth-averaged frequency, the highest values (≈ 0.02 s) are observed in the Barents Sea in July and August, and those of the Kara Sea – in July–September (≈ 0.055 s) and in November (≈ 0.058 s). In the same months, noted are the maximum values of the averaged natural frequencies and the minimum values of the averaged own period of the internal waves. Thus, for the wavelength 1000 m, the highest averaged own frequency and the smallest averaged own period of the first mode in the Barents Sea constitute 0.0025 s and 45 min., and those in the Kara Sea – 0.0038 s and 30 min, respectively.

Based on the asymptotic expansions obtained by the multi-scale method up to the third order of smallness for the potential velocity of liquid particles and the plate-fluid surface elevation, the dispersion properties of the vibrations generated by the interaction of progressive surface wave harmonics of finite amplitude are analyzed in the article. The effect of nonlinearity of acceleration of vertical displacements of an elastic plate on the dispersion characteristics of wave disturbances is studied. The dependence of the vibration frequency is estimated by taking into account the nonlinearity of the first and second approximations values, the plate thickness, and the longitudinal compressive force. It is shown that the sign of the amplitude of the second interacting harmonic and the nonlinearity of the acceleration of vertical displacements of the longitudinally compressed elastic plate affect the vibration phase. It was found that with a decrease in the wavelength of the initial harmonic, the influence of the plate’s nonlinearity vertical acceleration is enhanced. The presence of compressive force is manifested in a decrease in the frequency of vibrations of the wave disturbance in comparison with the frequency obtained in the absence of longitudinal compression, both with a positive and negative sign of the second interacting harmonic amplitude.

Research of annual total heat flow variability in the Arctic region formed by the interaction between Ocean and Atmosphere is executed. It's made on the basis of average monthly values of sea ice closeness and thickness, salinity and sea surface temperature and also air temperature at the level of weather shelter and skin temperature of a snow-ice cover, zonal and meridional wind velocity components during 1969–2012. Heat flow through a snow-ice cover is calculated in the assumption of linearity of a temperature profile between its upper and bottom boundaries. Heat exchange on the water surface is defined by the equation expressing proportionality of incoming and outgoing heat to product of wind velocity and difference between water and air temperature. The estimation error of the heat flow value at changing of the skin temperature of a snow-ice cover by the air temperature at the level of a weather shelter is made. The analysis of heat flow fluctuations correspondence with the Arctic Oscillation index is carried out.

Purpose. The aim of the paper is to study buoyancy frequency in the Laptev and East Siberian Seas and to assess correlation relations between the intra-year variability of the Vaisal - Brent frequency maximum and the climatic indices reflecting the atmosphere and hydrosphere state. Methods and Results. Based on the World Ocean Atlas 2013 for 1955-2012, the features of spatial and temporal variability of the buoyancy frequency distribution and its maximum depth in the Laptev and East Siberian seas are considered. It is found that the highest values of the Vaisal - Brent frequency are observed in the estuaries of the rivers Lena, Khatanga, Kolyma and Indigirka in summer where they attain 70-86 cycle/hour. In the deep-water northern areas of the seas under study, the majority of the water area is covered with ice throughout the whole year. As a consequence the surface layer of water is heated slightly and stability of stratification is much lower. The buoyancy frequency values in the seasonal pycnocline attain 24-46 cycle/hour. As a result of advection of the transformed Pacific waters in the northern and southeastern regions of the East Siberian Sea, on the depths 25-55 m observed is the layer of constant pycnocline where the Vaisal - Brent frequency values can mount to 21 cycles/hour. Correlation analysis is carried out for the relations between the intra-annual variability of the Vaisal - Brent frequency maximum and the climatic indices (North Atlantic Oscillation, Arctic Oscillation, Pacific Decadal Oscillation, Gulf Stream North Wall) reflecting the atmosphere and hydrosphere state. It is shown that relationship between the buoyancy frequency maximum and the two latter indices is the most pronounced. Conclusions. The results of the carried out investigations show that the features of spatial-temporal variability of the buoyancy frequency distribution and its maximum depth in the Laptev and East Siberian seas are conditioned by the river discharge and also by advection in the Arctic region of the Atlantic and transformed Pacific waters inflowing from the adjacent basins.

The equations for three nonlinear approximations of flexural-gravity vibrations of a longitudinally compressed elastic plate which take into account the nonlinearity of acceleration of vertical plate displacements are obtained using the method of multiple scales. The ice plate unbounded in horizontal directions floats on the surface of a homogeneous ideal fluid. Asymptotic expansions up to the third order of smallness are constructed on the basis of the obtained equations for the plate-fluid surface elevation and the velocity potential of the liquid particles formed in the nonlinear interaction of two harmonics of progressive periodic surface waves. The amplitude-phase characteristics of the formed elevation of the fluid surface (bending of the plate) are analyzed as functions of the basin depth, the parameters of ice plate and interacting harmonics, and the nonlinearity of acceleration of vertical ice displacements.

The method of many scales was used to construct an asymptotic expansion up to thirdorder terms for the velocity potential of a fluid of finite depth and the flexural deformations of a floating elastic plate arising from the interaction of harmonics of finite-amplitude progressive surface waves. An expression for the second-harmonic amplitude was obtained, and critical values of the wavenumber were determined. Vibrations of plates with different thicknesses and elastic modulus were analyzed. Vertical displacements of the plate under flexural deformation were studied.

Asymptotic expansions up to the third-order terms are constructed based on the multiple scales method for the fluid velocity potential of the finite-depth homogeneous fluid and elevation of the plate-fluid surface (ice-water surface). The obtained expansions constitute a foundation for analyzing dispersive properties of the fluctuations formed under interaction of progressive harmonics of the finite-amplitude surface waves. Changes of the fluctuation frequency taking place due to the contribution of the values of the first and second approximations conditioned by the taken into account non-linearity are considered. The effect of non-linearity of the ice plate vertical displacement acceleration on the amplitude, frequency and phase velocity of the wave disturbances is studied. It is shown that at the wave numbers exceeding the maximum resonance value, the oscillation frequency increases in case non-linearity of the plate vertical displacement acceleration is taken into account. It also grows with the plate thickness, and change of a sign (plus into minus) of the second interacting harmonic amplitude reduces the frequency value if the wave number is fixed. The phase velocity increase with allowance for the acceleration nonlinearity is more significant than without considering it. Under a negative amplitude of the second interacting harmonic, if the acceleration nonlinearity is taken into account, the phase velocity is less than when it is not.

The one-dimensional thermodynamic model adapted to the physiographic conditions of the Kerch Strait was used to study the seasonal evolution of sea ice thickness in the Kerch and Kamysh-Burun bays in the winter of 2007/2008. The dependence of the regional variability of ice thickness on hydrometeorological conditions is analyzed.

В Атласе представлены климатические карты структуры поля приземного ветра и ветра в тропосфере на 11-ти уровнях от 100 до 925 гПа.Для приземного ветра также приведены карты трендов скорости ветра, карты ее среднеквадратичного отклонения, коэффициента корреляции компонент скорости, карты кинематических характеристик ветра: дивергенции, угловой скорости вращения относительного вихря, дилатации и угла дилатации.Карты построены на основе данных NCEP/NCAR за период 1948 -2012 гг.Атлас может быть полезен специалистам в области климата, метеорологии, океанографии, экологии.Ключевые слова: ветер, поле ветра, кинематические характеристики ветра, тренд скорости ветра, приземный ветер, ветер в тропосфере.The atlas presents the climatic maps of the wind above-ground level and wind in the troposphere on 11 levels from 100 to 925 hPа.For the wind above-ground level it is shown the trend maps of the wind velocity, maps of its standard deviation, maps of correlation coefficient of velocity components, maps of the wind kinematics parameters: divergence, angular rotation velocity of relative vortex, dilatation and dilatation angle.Maps are built on the basis of NCEP/NCAR data for period 1948 -2012.The atlas is intended for specialists in the field of climate research, meteorology, oceanography and ecology.

Investigation of intra-annual variability of sea-ice concentration distribution in the Arctic in the period of 1969–2012 with the analysis of ice edge geographical position dynamics have been conducted. Monthly average velocity of the sea-ice edge displacement in latitudinal direction is estimated for every degree of longitude along the ice edge perimeter. Deviations of monthly mean latitudes of the ice edge position from its linear trend have been analyzed.