Anton A Bukatov - Profile on Academia.edu (original) (raw)

Papers by Anton A Bukatov

Ukrainian Antarctic Journal, 2003

On a base of developed hydrodynamic models the reflecting capacities of edges, cracks and ice fie... more On a base of developed hydrodynamic models the reflecting capacities of edges, cracks and ice field breaks are studied when the surface waves pass through them. It was investigated the ice flexural rigidity and compression effects on the spatial distribution of wave disturbance amplitudes and bend stresses of the ice cover on both sides of the examined horizontal non-uniformity. Assessment of the ice breaking possibility within the edge-side zones was made. The surface wave propagation from the basin deep-water area through the bottom's step into the area of the finite depth is investigated. The spatial and temporal features of the formed dynamic frontal zones on both sides of the step are revealed. The dependence of the basin surface displacement amplitudes and wave current velocities on the ice thickness, incident wave periods, and depth of the step occurrence, is studied. The three-dimensional bending vibrations of floating ice cover induced by a moving vortex formation are studied. Dependence of the amplitude-phase vibration characteristics on the ice rigidity in bending, angular velocity and forward speed of the vortex is investigated. Spatial distribution of the flexural-gravity disturbances both in front of the moving pressure region and in the back wake is analyzed. A mathematical model of the non-linear dynamics of surface waves of finite amplitude in the ice floes seas was developed involving the method of multiscale expansions. Using the model, it was studied the dependence of the amplitude-phase structure of disturbances, formed by the propagating non-linear periodic waves, on the basin depth, ice thickness and non-linearity of its vertical acceleration, frequency and steepness of initial wave harmonics. The ice Stokes drift velocity was estimated as well as the ice induced non-linear mass transport analyzed.

Interaction of Finite Amplitude Surface Waves in a Basin with a Floating Elastic Plate

Lecture Notes in Control and Information Sciences - Proceedings, 2022

Physical Oceanography, 2011

By using the velocity potential obtained by the method of multiscale asymptotic expansions to wit... more By using the velocity potential obtained by the method of multiscale asymptotic expansions to within the quantities of the third order of smallness, we study the dependences of the components of the velocity of motion of a homogeneous liquid under the floating ice cover on the thickness of the cover and its modulus of elasticity in the process of propagation of periodic waves of finite amplitude. It is shown that the presence of broken ice leads to a decrease in the moduli of components of the velocity of liquid particles and the phase delay of generated oscillations. The effect of the elasticity of ice becomes more pronounced as the wavelength of the initial harmonic decreases and manifests itself in the increase in the maximum values of the components of velocity and in the phase shift of oscillations in the direction of propagation of waves.

Physical Oceanography, 2011

By the method of multiple scales, we obtain (to within the third order of smallness) the asymptot... more By the method of multiple scales, we obtain (to within the third order of smallness) the asymptotic expansions for the components of the velocity of motion of liquid under a floating ice cover in the process of propagation of periodic surface flexural gravity waves of finite amplitude under the conditions of ice compression. We study the dependences of the distributions of the velocity components along the wave profile on the compressive forces and the parameters of the initial harmonic. It is shown that the amplitude values of the velocity components decrease and the phase shift of oscillations increases as the compressive forces increase.

Finite-amplitude waves in a homogeneous fluid with a floating elastic plate

Journal of Applied Mechanics and Technical Physics, 2009

Equations for three nonlinear approximations of a wave perturbation in a homogeneous ideal incomp... more Equations for three nonlinear approximations of a wave perturbation in a homogeneous ideal incompressible fluid covered by a thin elastic plate are obtained using the method of multiple scales and taking into account that the acceleration of vertical flexural displacements of the plate is nonlinear. Based on the obtained equations, asymptotic expansions up third-order terms are constructed for the fluid velocity potential and the perturbations of the plate-fluid interface (plate bending) caused by a traveling periodic wave of finite amplitude. The wave characteristics are analyzed as functions of the elastic modulus and thickness of the plate and the length and tilt of the initial fundamental harmonic wave.

International Applied Mechanics, 2011

The multi-scales method is used to derive third-order equations of gravitational bending oscillat... more The multi-scales method is used to derive third-order equations of gravitational bending oscillations of a thin elastic plate floating on the surface of a homogeneous perfect incompressible fluid of finite depth. The equations incorporate the compressive force and nonlinear acceleration of vertical displacements of the plate. Based on these equations, the deflection of the plate and the velocity potential of the fluid induced by a traveling periodic wave of finite amplitude are expanded into asymptotic series to terms of the third order of smallness. The dependence of the oscillation characteristics on the elastic modulus and thickness of the plate, compressive force, the initial length and steepness of the wave is analyzed

Physical Oceanography, 2019

Development of anoxia in marine basins leads to formation of hydrogen sulfide and the intermediat... more Development of anoxia in marine basins leads to formation of hydrogen sulfide and the intermediate reduced sulfur speciesthiosulfate, sulfite, zero-valent sulfur and sulfur of polysulfides. Except for thiosulfate, the data on the other reduced species of sulfur in the Black Sea water are scarce. The thiosulfate concentration in the papers of different authors varies from 20 to 40 μM; and it can be a consequence of hydrogen sulfide oxidation during sampling and analyzing. Data and methods. The previously proposed (by I. I. Volkov and N. N. Zhabina) method for determining the sulfur reduced species (sulfite + thiosulfate, zero-valent sulfur + sulfur of polysulfides) in the anaerobic basins' water has been re-evaluated and developed. Addition of suspension Zn 2 (OH) 2 CO 3 to a seawater sample destructs polysulfides and transfers the elemental sulfur to precipitation. The elemental sulfur, sulfur polysulfides and sulfides are separated from the sum of thiosulfate and sulfite by filtration. To analyze the reduced species of sulfur, we applied their reduction to hydrogen sulfide which is determined spectrophotometrically after its distillation in the argon stream and precipitation as ZnS. Results. The results of determining the sulfur species were tested by analyzing 2% solutions of NaCl with the introduced contents of thiosulfate (0.5-1.5 μmol), sulfite (< 1 μmol), elemental sulfur (< 1 μmol) against the background of much higher concentrations of hydrogen sulfide (60 µmol). Such ratios of concentrations of the sulfur reduced species and hydrogen sulfide are found in the Black Sea water. Discussion and conclusion. It is shown that the proposed method correctly reflects presence of the reduced species of sulfur in the solutions. To analyze the sulfur species, the Niskin bottles are necessarily filled with the inert gas and the samples are filtered in the inert atmosphere. The method for determining the sulfur reduced species is highly sensitive. The detection limit for ( -2 3 2 O S + -2 3 SO ) is 0.03 μM, for (S 0 + S 0 polysulfide) is 0.02 μM and for sulfide sulfur -0.01 μM.

Earth’s Insolation and Spatiotemporal Variability of Albedo in the Antarctic

Advances in Polar Ecology

Analysis of the phase structure of fluid vibrations with floating longitudinally compressed elastic plate in nonlinear interaction of the surface progressive waves

Based on the asymptotic expansions obtained by the multi-scale method up to the third order of sm... more 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 ...

On the basis of the data set of BADC HadISST ICE for the period of 1969-2002 years seasonal and i... more On the basis of the data set of BADC HadISST ICE for the period of 1969-2002 years seasonal and interannual variability of the Antarctic sea ice closeness is investigated. Interannual variations of the sea ice closeness on the climatic scale are estimated. The cross-correlation between the sea ice closeness, the air temperature at Antarctic stations and atmospheric circulation indices of SOI (Southern Oscillation) and AAO (Antarctic Oscillation) are obtained.

Äîñë³äaeåíî êë³ìàòè÷íó åâîëþö³þ ðåã³îíàëüíîãî ðîçïîä³ëó çãóðòîâàíîñò³ ìîðñüêîãî ëüîäó â Àíòàðêòè÷... more Äîñë³äaeåíî êë³ìàòè÷íó åâîëþö³þ ðåã³îíàëüíîãî ðîçïîä³ëó çãóðòîâàíîñò³ ìîðñüêîãî ëüîäó â Àíòàðêòè÷í³é îá-ëàñò³ ϳâäåííîãî îêåàíó çà ïåð³îä 1969-2010 ðð. Ïðîâåäåíî àíàë³ç ïðîñòîðîâî-÷àñîâî¿ ì³íëèâîñò³ ãåîãðàô³÷íîãî ïîëîaeåííÿ çîâí³øíüî¿ ìåae³ ëüîäîâîãî ïîÿñó íàâêîëî Àíòàðêòèäè. Âèêîíàíî îö³íêó âçàºìíîãî êîðåëÿö³éíîãî çâ'ÿçêó øèðîòíèõ çì³ùåíü êðîìêè ëüîäó ³ ÷èñåë Âîëüôà ñîíÿ÷íî¿ àêòèâíîñò³. Êëþ÷îâ³ ñëîâà: àíòàðêòè÷íèé ìîðñüêèé ë³ä, çãóðòîâàí³ñòü ìîðñüêîãî ëüîäó, êðîìêà ìîðñüêîãî ëüîäó, äèíàì³êà êðîìêè ëüîäó.

Propagation of Surface Waves of Finite Amplitude In a Basin With Floating Broken Ice

International Journal of Offshore and Polar Engineering

Gravity Force Anomalies Caused by Tidal Deformations of the Earth's Surface

Generation of long waves in a basin of variable depth in the process of formation of a region of perturbations of atmospheric pressure

ABSTRACT

Nonlinear elastic plate fluctuations on a fluid surface

2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP), 2015

Asymptotic expansions to within the third order of smallness for flexural displacements of the fl... more Asymptotic expansions to within the third order of smallness for flexural displacements of the floating plate and the fluid velocity potential under plate are obtained using the method of multiple scales. They are formed by a propagating periodic wave of finite--amplitude. In case of an ice plate the analysis of influence of the elastic modulus, the longitudinal compression value and nonlinearity of a plate vertical displacement acceleration on its flexural fluctuations characteristics and distribution of orbital velocity components of fluid particles movement along a flexural-gravitational wave profile under the plate is done.

Прикладная механика и техническая физика, 2018

На основе метода многих масштабов построены асимптотические разложения до величин третьего порядк... more На основе метода многих масштабов построены асимптотические разложения до величин третьего порядка малости для потенциала скорости движения жидкости конечной глубины и изгибных деформаций плавающей упругой пластины, возникающих при взаимодействии гармоник прогрессивных поверхностных волн конечной амплитуды. Получено выражение для амплитуды второй гармоники и определены критические значения волнового числа. Выполнен анализ колебаний пластины при различных значениях ее толщины и модуля упругости. Исследованы вертикальные смещения пластины при ее изгибной деформации.

PHYSICAL OCEANOGRAPHY, 2018

Asymptotic expansions up to the third-order terms are constructed based on the multiple scales me... more 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.

Выполнено исследование внутригодовой изменчивости распределения сплоченности морского льда в Аркт... more Выполнено исследование внутригодовой изменчивости распределения сплоченности морского льда в Арктике за период 1969 – 2012 гг. Проведен анализ динамики географического положения кромки льда. Дана оценка среднемесячных значений скорости смещения кромки льда в широтном направлении на каждой долготе вдоль периметра кромки. Выполнен анализ отклонений среднемесячных значений широты положения кромки льда от своего линейного тренда.

Inter-annual climatic response of the sea ice edge latitudinal displacement in the Arctic to vari... more Inter-annual climatic response of the sea ice edge latitudinal displacement in the Arctic to variability of the large-scale atmospheric circulation (the Arctic Oscillation and North Atlantic Oscillation), location of the Gulf Stream northern boundary and solar activity in 1969–2012 is studied. It is noted that the most significant ice edge latitudinal displacements in the intra-annual cycle were observed westward of Novaya Zemlya and in the Bering Strait area. It is shown that, depending on the longitudinal sector, response of the edge geographical position to changes of the atmospheric circulation and the Gulf Stream indices can be manifested both quasi-synchronously and with a delay. Exceptions are the Greenland Sea and the Norwegian Sea areas as well as the Barents Sea western part where ice edge displacements advance the Gulf Stream index variation. The correlation between the edge latitudinal displacement along its perimeter and the Wolf numbers variation is assessed. It is received that the oscillations of cross-correlation functions with a period which is close to 11-year one (Schwabe Cycle) are observed on each longitude at that. In the variations of cross-correlation functions from their average position, solar activity variation is manifested in the edge position displacement with up to two-year delay.

Ukrainian Antarctic Journal, 2003

On a base of developed hydrodynamic models the reflecting capacities of edges, cracks and ice fie... more On a base of developed hydrodynamic models the reflecting capacities of edges, cracks and ice field breaks are studied when the surface waves pass through them. It was investigated the ice flexural rigidity and compression effects on the spatial distribution of wave disturbance amplitudes and bend stresses of the ice cover on both sides of the examined horizontal non-uniformity. Assessment of the ice breaking possibility within the edge-side zones was made. The surface wave propagation from the basin deep-water area through the bottom's step into the area of the finite depth is investigated. The spatial and temporal features of the formed dynamic frontal zones on both sides of the step are revealed. The dependence of the basin surface displacement amplitudes and wave current velocities on the ice thickness, incident wave periods, and depth of the step occurrence, is studied. The three-dimensional bending vibrations of floating ice cover induced by a moving vortex formation are studied. Dependence of the amplitude-phase vibration characteristics on the ice rigidity in bending, angular velocity and forward speed of the vortex is investigated. Spatial distribution of the flexural-gravity disturbances both in front of the moving pressure region and in the back wake is analyzed. A mathematical model of the non-linear dynamics of surface waves of finite amplitude in the ice floes seas was developed involving the method of multiscale expansions. Using the model, it was studied the dependence of the amplitude-phase structure of disturbances, formed by the propagating non-linear periodic waves, on the basin depth, ice thickness and non-linearity of its vertical acceleration, frequency and steepness of initial wave harmonics. The ice Stokes drift velocity was estimated as well as the ice induced non-linear mass transport analyzed.

Interaction of Finite Amplitude Surface Waves in a Basin with a Floating Elastic Plate

Lecture Notes in Control and Information Sciences - Proceedings, 2022

Physical Oceanography, 2011

By using the velocity potential obtained by the method of multiscale asymptotic expansions to wit... more By using the velocity potential obtained by the method of multiscale asymptotic expansions to within the quantities of the third order of smallness, we study the dependences of the components of the velocity of motion of a homogeneous liquid under the floating ice cover on the thickness of the cover and its modulus of elasticity in the process of propagation of periodic waves of finite amplitude. It is shown that the presence of broken ice leads to a decrease in the moduli of components of the velocity of liquid particles and the phase delay of generated oscillations. The effect of the elasticity of ice becomes more pronounced as the wavelength of the initial harmonic decreases and manifests itself in the increase in the maximum values of the components of velocity and in the phase shift of oscillations in the direction of propagation of waves.

Physical Oceanography, 2011

By the method of multiple scales, we obtain (to within the third order of smallness) the asymptot... more By the method of multiple scales, we obtain (to within the third order of smallness) the asymptotic expansions for the components of the velocity of motion of liquid under a floating ice cover in the process of propagation of periodic surface flexural gravity waves of finite amplitude under the conditions of ice compression. We study the dependences of the distributions of the velocity components along the wave profile on the compressive forces and the parameters of the initial harmonic. It is shown that the amplitude values of the velocity components decrease and the phase shift of oscillations increases as the compressive forces increase.

Finite-amplitude waves in a homogeneous fluid with a floating elastic plate

Journal of Applied Mechanics and Technical Physics, 2009

Equations for three nonlinear approximations of a wave perturbation in a homogeneous ideal incomp... more Equations for three nonlinear approximations of a wave perturbation in a homogeneous ideal incompressible fluid covered by a thin elastic plate are obtained using the method of multiple scales and taking into account that the acceleration of vertical flexural displacements of the plate is nonlinear. Based on the obtained equations, asymptotic expansions up third-order terms are constructed for the fluid velocity potential and the perturbations of the plate-fluid interface (plate bending) caused by a traveling periodic wave of finite amplitude. The wave characteristics are analyzed as functions of the elastic modulus and thickness of the plate and the length and tilt of the initial fundamental harmonic wave.

International Applied Mechanics, 2011

The multi-scales method is used to derive third-order equations of gravitational bending oscillat... more The multi-scales method is used to derive third-order equations of gravitational bending oscillations of a thin elastic plate floating on the surface of a homogeneous perfect incompressible fluid of finite depth. The equations incorporate the compressive force and nonlinear acceleration of vertical displacements of the plate. Based on these equations, the deflection of the plate and the velocity potential of the fluid induced by a traveling periodic wave of finite amplitude are expanded into asymptotic series to terms of the third order of smallness. The dependence of the oscillation characteristics on the elastic modulus and thickness of the plate, compressive force, the initial length and steepness of the wave is analyzed

Physical Oceanography, 2019

Development of anoxia in marine basins leads to formation of hydrogen sulfide and the intermediat... more Development of anoxia in marine basins leads to formation of hydrogen sulfide and the intermediate reduced sulfur speciesthiosulfate, sulfite, zero-valent sulfur and sulfur of polysulfides. Except for thiosulfate, the data on the other reduced species of sulfur in the Black Sea water are scarce. The thiosulfate concentration in the papers of different authors varies from 20 to 40 μM; and it can be a consequence of hydrogen sulfide oxidation during sampling and analyzing. Data and methods. The previously proposed (by I. I. Volkov and N. N. Zhabina) method for determining the sulfur reduced species (sulfite + thiosulfate, zero-valent sulfur + sulfur of polysulfides) in the anaerobic basins' water has been re-evaluated and developed. Addition of suspension Zn 2 (OH) 2 CO 3 to a seawater sample destructs polysulfides and transfers the elemental sulfur to precipitation. The elemental sulfur, sulfur polysulfides and sulfides are separated from the sum of thiosulfate and sulfite by filtration. To analyze the reduced species of sulfur, we applied their reduction to hydrogen sulfide which is determined spectrophotometrically after its distillation in the argon stream and precipitation as ZnS. Results. The results of determining the sulfur species were tested by analyzing 2% solutions of NaCl with the introduced contents of thiosulfate (0.5-1.5 μmol), sulfite (< 1 μmol), elemental sulfur (< 1 μmol) against the background of much higher concentrations of hydrogen sulfide (60 µmol). Such ratios of concentrations of the sulfur reduced species and hydrogen sulfide are found in the Black Sea water. Discussion and conclusion. It is shown that the proposed method correctly reflects presence of the reduced species of sulfur in the solutions. To analyze the sulfur species, the Niskin bottles are necessarily filled with the inert gas and the samples are filtered in the inert atmosphere. The method for determining the sulfur reduced species is highly sensitive. The detection limit for ( -2 3 2 O S + -2 3 SO ) is 0.03 μM, for (S 0 + S 0 polysulfide) is 0.02 μM and for sulfide sulfur -0.01 μM.

Earth’s Insolation and Spatiotemporal Variability of Albedo in the Antarctic

Advances in Polar Ecology

Analysis of the phase structure of fluid vibrations with floating longitudinally compressed elastic plate in nonlinear interaction of the surface progressive waves

Based on the asymptotic expansions obtained by the multi-scale method up to the third order of sm... more 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 ...

On the basis of the data set of BADC HadISST ICE for the period of 1969-2002 years seasonal and i... more On the basis of the data set of BADC HadISST ICE for the period of 1969-2002 years seasonal and interannual variability of the Antarctic sea ice closeness is investigated. Interannual variations of the sea ice closeness on the climatic scale are estimated. The cross-correlation between the sea ice closeness, the air temperature at Antarctic stations and atmospheric circulation indices of SOI (Southern Oscillation) and AAO (Antarctic Oscillation) are obtained.

Äîñë³äaeåíî êë³ìàòè÷íó åâîëþö³þ ðåã³îíàëüíîãî ðîçïîä³ëó çãóðòîâàíîñò³ ìîðñüêîãî ëüîäó â Àíòàðêòè÷... more Äîñë³äaeåíî êë³ìàòè÷íó åâîëþö³þ ðåã³îíàëüíîãî ðîçïîä³ëó çãóðòîâàíîñò³ ìîðñüêîãî ëüîäó â Àíòàðêòè÷í³é îá-ëàñò³ ϳâäåííîãî îêåàíó çà ïåð³îä 1969-2010 ðð. Ïðîâåäåíî àíàë³ç ïðîñòîðîâî-÷àñîâî¿ ì³íëèâîñò³ ãåîãðàô³÷íîãî ïîëîaeåííÿ çîâí³øíüî¿ ìåae³ ëüîäîâîãî ïîÿñó íàâêîëî Àíòàðêòèäè. Âèêîíàíî îö³íêó âçàºìíîãî êîðåëÿö³éíîãî çâ'ÿçêó øèðîòíèõ çì³ùåíü êðîìêè ëüîäó ³ ÷èñåë Âîëüôà ñîíÿ÷íî¿ àêòèâíîñò³. Êëþ÷îâ³ ñëîâà: àíòàðêòè÷íèé ìîðñüêèé ë³ä, çãóðòîâàí³ñòü ìîðñüêîãî ëüîäó, êðîìêà ìîðñüêîãî ëüîäó, äèíàì³êà êðîìêè ëüîäó.

Propagation of Surface Waves of Finite Amplitude In a Basin With Floating Broken Ice

International Journal of Offshore and Polar Engineering

Gravity Force Anomalies Caused by Tidal Deformations of the Earth's Surface

Generation of long waves in a basin of variable depth in the process of formation of a region of perturbations of atmospheric pressure

ABSTRACT

Nonlinear elastic plate fluctuations on a fluid surface

2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP), 2015

Asymptotic expansions to within the third order of smallness for flexural displacements of the fl... more Asymptotic expansions to within the third order of smallness for flexural displacements of the floating plate and the fluid velocity potential under plate are obtained using the method of multiple scales. They are formed by a propagating periodic wave of finite--amplitude. In case of an ice plate the analysis of influence of the elastic modulus, the longitudinal compression value and nonlinearity of a plate vertical displacement acceleration on its flexural fluctuations characteristics and distribution of orbital velocity components of fluid particles movement along a flexural-gravitational wave profile under the plate is done.

Прикладная механика и техническая физика, 2018

На основе метода многих масштабов построены асимптотические разложения до величин третьего порядк... more На основе метода многих масштабов построены асимптотические разложения до величин третьего порядка малости для потенциала скорости движения жидкости конечной глубины и изгибных деформаций плавающей упругой пластины, возникающих при взаимодействии гармоник прогрессивных поверхностных волн конечной амплитуды. Получено выражение для амплитуды второй гармоники и определены критические значения волнового числа. Выполнен анализ колебаний пластины при различных значениях ее толщины и модуля упругости. Исследованы вертикальные смещения пластины при ее изгибной деформации.

PHYSICAL OCEANOGRAPHY, 2018

Asymptotic expansions up to the third-order terms are constructed based on the multiple scales me... more 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.

Выполнено исследование внутригодовой изменчивости распределения сплоченности морского льда в Аркт... more Выполнено исследование внутригодовой изменчивости распределения сплоченности морского льда в Арктике за период 1969 – 2012 гг. Проведен анализ динамики географического положения кромки льда. Дана оценка среднемесячных значений скорости смещения кромки льда в широтном направлении на каждой долготе вдоль периметра кромки. Выполнен анализ отклонений среднемесячных значений широты положения кромки льда от своего линейного тренда.

Inter-annual climatic response of the sea ice edge latitudinal displacement in the Arctic to vari... more Inter-annual climatic response of the sea ice edge latitudinal displacement in the Arctic to variability of the large-scale atmospheric circulation (the Arctic Oscillation and North Atlantic Oscillation), location of the Gulf Stream northern boundary and solar activity in 1969–2012 is studied. It is noted that the most significant ice edge latitudinal displacements in the intra-annual cycle were observed westward of Novaya Zemlya and in the Bering Strait area. It is shown that, depending on the longitudinal sector, response of the edge geographical position to changes of the atmospheric circulation and the Gulf Stream indices can be manifested both quasi-synchronously and with a delay. Exceptions are the Greenland Sea and the Norwegian Sea areas as well as the Barents Sea western part where ice edge displacements advance the Gulf Stream index variation. The correlation between the edge latitudinal displacement along its perimeter and the Wolf numbers variation is assessed. It is received that the oscillations of cross-correlation functions with a period which is close to 11-year one (Schwabe Cycle) are observed on each longitude at that. In the variations of cross-correlation functions from their average position, solar activity variation is manifested in the edge position displacement with up to two-year delay.