This study presents a mathematical modeling framework to analyze extreme sea-level fluctuations in the Sea of Azov, driven by wind forcing, and enhances predictions through the integration of remote sensing data. The research addresses the critical need to improve the accuracy of surge and seiche predictions, phenomena that threaten coastal ecosystems and infrastructure in shallow basins. By solving shallow-water hydrodynamic equations and integrating satellite-derived observations with wind field data, we demonstrate that the combined use of numerical modeling and remote sensing significantly enhances the precision of extreme sea-level forecasts. Validation against in situ measurements confirms the model’s ability to accurately replicate observed water level variations. The results highlight the importance of localized geographical features and wind dynamics in governing hydrodynamic processes, providing a foundation for more reliable forecasting under changing climatic conditions. Ultimately, this work advances the development of science-based mitigation strategies to reduce the ecological and socioeconomic risks posed by wind-induced surge and seiche events in vulnerable coastal regions.

This paper provides an overview of the computational techniques and parallelization strategies employed within the FLOW-3D software for simulating hydrodynamic processes in complex environments. The study contrasts the outcomes of numerical simulations obtained via FLOW-3D and a 3D wave hydrodynamics model. The wave motion characteristics in the presence of four supports and the forces exerted on these supports were analyzed. The parallelization techniques in FLOW-3D, including spatial and temporal parallelization, as well as a hybrid approach, enable the efficient utilization of computing resources across multiple cores or network nodes. The numerical simulations highlight the effectiveness of the proposed algorithms, particularly in cases involving dynamically evolving free surfaces, underscoring the practical value of FLOW-3D for tackling complex hydrodynamic challenges.

The article is devoted to the study of the possibilities of the modern version of the third-generation wind-wave model WAVEWATCH III (WW3). The basic equations of the model are given and the software implementation is described. A retrospective analysis of the characteristics of wind waves in the Sea of Azov was carried out, and the simulation results were compared with the data from long-term observations of coastal hydrometeostations of the Sea of Azov, presented in the Unified Interdepartmental Federal Information System (ESIMO) databases. In the predictive model, the computational domains approximating the shoreline configuration and the bathymetry of real marine basins are regular latitude-longitude grids consisting of elements of size 1.2 x 1.2 degree (about 2 x 2 km). The bathymetry and the corresponding land-sea mask (a two-dimensional array with values determining the belongingness of an element to ground or sea) required to do calculations for each of the basins were constructed using navigation maps. In the retrospective analysis, climatic data for a multi-year month (2008-2023) on wind speed were used to generate input wind data at grid nodes. Based on the WW3 spectral model, the forecast of wind wave parameters in the Sea of Azov was carried out. Prognostic maps of the average period, average length and heights of the waves prevailing at different points in time were constructed. The meteorological fields (wind speed, water and air temperature) necessary for calculations were taken from the databases of the Hydrometeorological Center of Russia and NCEP/NOAA. Parallel efficiency indicators for hybrid parallelization (MPI-OpenMP) were calculated, and scalability was determined for both MPI and hybrid launches.

Introduction. Mathematical modelling of currents is an urgent research topic in the field of hydrodynamics and oceanography. Despite ongoing research in the field of developing accurate and efficient numerical methods for solving Navier-Stokes equations that take into account vortex viscosity, the problems of accurate prediction and control of turbulence remain unresolved. The influence of nonlinear effects in vortex viscosity models on the accuracy of forecasts and their applicability to various flow conditions also remains relevant. The aim of the study is to study the influence of linearized and quadratic bottom friction and two turbulence models on the numerical solution of stationary and non-stationary periodic flows. Special emphasis is placed on comparing numerical results with analytical solutions within the framework of using various models of bottom friction.Materials and Methods. The computational models used in this study are based on a simplified two-dimensional wave model and full three-dimensional Navier-Stokes equations. The classical model of shallow water motion and the 2D model without taking into account dynamic changes in the geometry of the reservoir surface are derived from a system of equations for a spatially inhomogeneous three-dimensional mathematical model of wave hydrodynamics of a shallow reservoir. Analytical solutions were found by linearization of the equations, which obviously has its limitations. A distinction is made between two types of nonlinear effects – nonlinearities caused by higher-order terms in the equations of motion, i. e. terms of advective acceleration and friction, and nonlinear effects caused by geometric nonlinearities, this is due, for example, to different water depths and reservoir widths, which will be important when modelling a real sea.Results. The results of modeling stationary and non-stationary periodic flows in a schematized rectangular basin using linearized bottom friction are presented. The influence of linearization on the numerical solution is investigated in comparison with analytical profiles using models calculating bottom friction in a quadratic formulation. In combination with quadratic bottom friction, two turbulence models are studied: the constant vortex viscosity and the Prandtl mixing length model. The results obtained as a result of three-dimensional modelling are compared with the results of two-dimensional modeling and analytical solutions averaged in depth.Discussion and Conclusion. New approaches to modelling and studying flows with variable vortex viscosity are proposed, including analysis of the influence of linearization and the use of various turbulence models. For the linearized and quadratic formulations of bottom friction, it is proved that the numerical results for the case of stationary flow show great similarity with analytical solutions, since the surface height is much less than the water depth and advection can be neglected. The numerical results for the unsteady flow also show a good agreement with the theory. Unlike analytical solutions, numerical modelling has minor deviations in the long run. The study of flows, within the framework of using various turbulence models, will make it possible to take into account the influence of nonlinear effects in vortex viscosity models on the accuracy of forecasts and their applicability to various flow conditions. The results obtained make it possible to better understand and describe the physical processes occurring in shallow waters. This opens up new possibilities for applying mathematical modelling to predict and analyze the impact of human activities on the marine environment and to solve other problems in the field of oceanology and geophysics.

We use the complex model combining the spatially 2D bottom material transport model, the 3D suspension transport model, and the 3D hydrodynamics model. The results of numerical experiments obtained on the basis of a complex model for calculating sedimentation and changes in the relief of the bottom surface are presented, and the intensity of abrasion for the coastal zones of the Tsimlyansk reservoir with the most intense geoecological situation is estimated. Based on the developed software package, calculations of the processes of coastal erosion and changes in the bottom relief were performed, taking into account the spatial and temporal variability of relief formation.

The article presents the results of a study of alcoholysis of fiberglass reinforced epoxy resin composites obtained by vacuum infusion. To intensify alcoholysis, chlorides, nitrates and sulfates of cobalt (II) and copper (II) were introduced into the reaction medium in an amount of 5% of the mass of ethyl alcohol for each system. The efficiency of the system was assessed based on data from the analysis of mass change of composite samples during alcoholysis, thermogravimetric analysis and scanning electron microscopy. It was found that the presence of metal chlorides contributes to 5 times increase of the alcoholysis velocity. The residual strength of the recovered fiber samples obtained is at least 95%.

Wind-wave models of the third generation WAM, SWAN, WaveWatch give realistic forecasts consistent with the data obtained on the basis of analytical, numerical, experimental approaches, but they also have a number of significant drawbacks. The paper presents a model of wave hydrodynamics that takes into account advective and microturbulent transport in the vertical direction in the coastal zone, and, as a result, is devoid of a number of disadvantages that limit the possibilities of using SWAN-type models. The contours of the image of the Azov Sea obtained from the WorldView satellite, determined by the method of a local binary template, are presented, which are used in the models as input data. As input data in the models, the contours of the image of the Azov Sea are used, determined by the method of a local binary template obtained from the WorldView satellite. The results of numerical experiments obtained on the basis of SWAN and a three-dimensional model of wave hydrodynamics are presented, and their comparison is carried out.

The distribution and movement of microparticles of plastic (MP) in freshwater and marine environments are determined by the characteristics of both MP and the surrounding flow. The most common plastic polymers in the aquatic environment, such as polyethylene and polypropylene, have a density lower than the density of water. Therefore, based only on buoyancy, it is expected that most MP will be present in the surface layers of the aquatic environment. In both freshwater and marine environments, turbulence-induced mixing depends on factors such as velocity gradient and convective flow. Consequently, the surface wind, the deep temperature gradient and the breaking of waves in the surf zone can lead to the formation of turbulence and deep vertical mixing. In such conditions, in addition to gravity and buoyancy, the motion caused by turbulent mixing can affect the vertical transport and distribution of particles. The paper presents the results of modeling Lagrangian trajectories for floating particles and non-floating particles, under wave conditions they correspond to regular waves, while the particle sizes range from 10 microns to 5 mm, and the density ranges from 0.88 to 2.80 g/cm3, which is within some of the most common densities of microplastic particles.

The article examines potential applications of WAVEWATCH III (WW3), the thirdgeneration wind-wave model. This study delves into the implementation of hybrid parallelization (MPI-OpenMP) and the development of multiple-cell grids tailored for the Azov Sea region. It elucidates fundamental equations of the model, their discretization, and software execution. The multiple-cell grid strategy employs high-resolution cells within the region of interest, gradually increasing cell density in other areas to optimize memory consumption. A 6-level multiple-cell grid was specifically crafted for the Azov Sea, with an algorithm outlined for its generation incorporating two refinement methods. This algorithm enables the creation of refined multiple-cell grids near shorelines at varying levels, along with the capability to refine grid structures in arbitrary zones. Additionally, the article presents hybrid parallelization techniques for the wave spectral component (MPI-OpenMP), assessing scalability in both MPI and hybrid deployments. The WW3 model offers a multigrid option facilitating parallel operation of subdomains akin to domain decomposition, while ensuring parallelization of each subnet via the component decomposition method.

The work is devoted to the parallel implementation of the wave hydrodynamics model and the modern SWAN wind-wave model. To determine the indicators of parallel efficiency of models, the model problem of hydrodynamics was solved. The calculation of water flow rates for the area of a shallow reservoir was carried out, while using a grid with steps differing by orders of magnitude in the horizontal and vertical coordinate directions. Two parallelization strategies SWAN OpenMP and MPI are compared. The indicators of parallel implementation are determined: computing time, speed-up radio, efficiency ratio. It is shown that the MPI version is more efficient than OpenMP. The indicators for evaluating the parallel computational efficiency of a three-dimensional wave model of hydrodynamics are presented. The dependence of computational efficiency indicators on the number of processors required to solve hydrodynamic problems using MPI is shown. It was revealed that the speed-up radio reaches the highest value at 128 cores, and with a further increase in the number of computing cores, the acceleration only decreases, which is associated with an increase in the time spent on data exchange between nodes. The spatial distribution algorithm for individual processors provides load balancing for each time step, but does not guarantee that communication is synchronized, since not every calculation on each processor will require the same effort.

The article studies and calibrates semi-empirical models of turbulent exchange for the Azov Sea using expedition data for vortex-resolving methods. To solve the problem of constructing adequate models of vortex resolution, the data obtained during the expedition in the Central-Eastern part of the Azov Sea were used. The hydrophysical ADCP probe was used to measure the three-dimensional velocity vector of the water medium. The measured water flow currents fields were filtered using box, Gauss and Fourier filter with different filter widths. In these calculations, the filter width was set based on the dimension of the hydrodynamics problem to be solved and the grid scale corresponding to this dimension. Then, using filtered data, the parameterization of the vertical turbulent exchange coefficient was carried out. Parameterization of the turbulent exchange process in discrete for the vertical coordinate direction is performed on the basis of subgrid models. To assess the quality of parametrization, an analysis was carried out using methods of mathematical statistics and quality functional. The optimal parameterization is selected. The modeling of the velocity vector of the aqueous medium obtained as a result of the application of the RANS and LES approaches is carried out. The key differences of modeling results are revealed. The analysis of the influence of regular waves on the turbulent vertical exchange is presented.

A detailed three-dimensional simulation of large vortices (LES) was performed on a parallel cluster. It provided useful 3D data on currents at various bottom geometries, in the cases of Shallow Mixing Layer (SML) and Shallow Lateral Expansion (SLE). The basic LES approach is derived directly from the Navier-Stokes equations. The paper studies the evolution of large-scale horizontal turbulence structures in shallow-water systems. We investigate how the three-dimensionality of the flow affects the quasi-two-dimensional turbulence pattern of the SLE mixing layer using numerical methods. The development of the SLE mixing layer, including the dynamics of large-scale quasi-2D coherent structures (2DCS) and their interaction with steady-state cycles has a quasi-two-dimensional character, but the influence of the third dimension is obvious. Consequently, the dynamics of three-dimensional turbulence should be taken into account in the numerical study of quasi-2D turbulence. In both cases, sequences of large-scale vortex structures are induced by a lateral shift along the mixing layer, which is caused by a difference in velocities upstream. In both cases, the transverse shift decreases with increasing distance downstream, while the momentum downstream is transferred from the high velocity side to the low velocity side due to the momentum advection of large-scale quasi-2D coherent structures. The difference in the configuration of the side walls affects the overall flow pattern.

Introduction. This work is devoted to the mathematical modelling of extreme sea level fluctuations in the Azov Sea using remote sensing data. The aim of the study is to develop and apply a mathematical model that allows more accurate prediction of surge and seiche events caused by extreme wind conditions. The relevance of the work is due to the need to improve the forecasts of hydrodynamic processes in shallow water bodies (such as the Azov Sea), where such phenomena can have significant economic and ecological consequences. The goal of this work is to develop and apply a mathematical model for predicting extreme sea level fluctuations in the Azov Sea caused by wind conditions.Materials and Methods. The study is based on the analysis of remote sensing data and observations of wind speed and direction over the Azov Sea. The primary method used is mathematical modelling, which includes solving the system of shallow water hydrodynamics equations. Wind condition data were collected from November 20 to 25, 2019, during which catastrophic sea level fluctuations were observed. The model considers the components of water flow velocity, water density, hydrodynamic pressure, gravitational acceleration, and turbulence exchange coefficients.Results. The modelling showed that prolonged easterly winds with speeds up to 22 m/s led to significant surge and seiche fluctuations in sea level. The maximum amplitudes of fluctuations were recorded in the central part of the Taganrog Bay, where the wind direction and speed remained almost constant throughout the observation period. Data from various platforms located in different parts of the Azov Sea confirmed a significant decrease in water level in the northeast and an increase in the southwest.Discussion and Conclusions. The study results confirm that using mathematical models in combination with remote sensing data allows more accurate predictions of extreme sea level fluctuations. This is important for developing measures to prevent and mitigate the consequences of surge and seiche events in coastal areas. In the future, it is necessary to improve models by including additional factors such as climate change and anthropogenic impact on the Azov Sea ecosystem.

Introduction. Reliable prediction of indicators of turbulent flows is a very difficult task, which is explained by the exceptional physical complexity of turbulence, in particular its probabilistic nature, a wide space-time spectrum and a fundamentally three-dimensional non-stationary nature. Despite conducting a wide range of studies focused on the problem under consideration, they did not fully reflect the totality of various factors and processes affecting the structure and parameters of vertical turbulent mixing. Materials and methods. The article is devoted to the study of spatial- three-dimensional wave processes in shallow water bodies, taking into account the features of turbulent exchange depending on the source and localization in the column of liquid, as well as the study of the influence of regular wave processes on turbulent exchange and vertically using a mathematical model of wave processes based on the system of Navier-Stokes equations, including three equations of motion in the with dynamically changing geometry of the computational domain. Results. Based on the developed software package, a scenario of changes in hydrodynamic wave processes of the coastal zone is constructed. Discussions and conclusions. The separation of the wave flow into a near-surface macroturbulent layer caused by wave motion and a lower layer with background hydrodynamic turbulence is proved, the strength and intensity of turbulence changed synchronously with wave oscillations, demonstrating a pronounced asymmetry of turbulence generation throughout the water column.

The article is devoted to the problem of improving the parameterization of the coefficient of turbulent exchange in shallow water bodies with significant depth differences and intensive vertical mixing. The article presents the basic equations of the model of taking into account the wave effect on the inhomogeneous vertical coefficient of turbulent exchange. This model is integrated into the system of Navier-Stokes equations taking into account the variable density, temperature and salinity, which describes the movement of a liquid under the influence of various forces, including pressure and viscosity, as well as forces caused by the action of waves. The article presents the discretization of the Navier-Stokes equations and the transfer equations by the finite difference method in three measurement directions. The additional term describing the wave effect on the vertical velocity in a shallow-water reservoir depends on the characteristics of the wave field: amplitude, angular frequency, wave number and coordinates. Using a model that takes into account the wave effect in three measuring directions and inhomogeneous turbulent exchange in the vertical direction, detailed information about the dynamics of waves in the simulated section of a shallow reservoir was obtained. The forecast of changes in hydrodynamic wave processes of the coastal zone is constructed. Inhomogeneous vertical turbulent exchange can vary significantly in different parts of a shallow reservoir and affect wave activity. Taking into account these changes makes the model more accurate and relevant to real conditions.

Benthal deposits form under climatic, chemical, physical, biological, mechanical, and hydrological influences in water bodies and their surfaces. An analysis of the benthal deposits is integral for assessing the pollution rate in a water body as it indicates the extent of an anthropogenic impact on it. However, the existing methods of benthal deposit analysis are highly underdeveloped. This research aims to estimate the heavy metal pollution in benthal deposits of the Zheleznogorsk region headwaters, Kursk Region. In order to achieve the set goal, the authors formulated the following objectives: (1) to assess the benthal deposit pollution rate via the regional St. Petersburg assessment method (1996); (2) to assess the benthal deposit pollution rate via pollutant threshold limit values for soils; (3) to identify the top priority pollutants of the benthal deposits in the researched headwaters; and (4) to identify factors of heavy metal flow in benthal deposits. The research results revealed the inadequacy of soil sanitary norms applied to benthal deposits. At the same time, the regional St.Petersburg method has broader possibilities of application in the assessment of benthal deposits. However, it requires adjustment to the environmental conditions of the Central Black Earth zone due to composition differences between soils and benthal deposits. The following metals exceeded the ambient content level in the benthal deposits of Zheleznogorsk region headwaters, Kursk Region: chrome, nickel, iron, and zinc. High iron content in rivers has been registered both in the proximity of the Mikhailovsky mining and processing plant [MMPP] and quarry and in headwaters located near the living areas of Zheleznogorsk far higher than the MMPP. All the water collection basins reviewed in this study demonstrated an even distribution of pollutants with no major divergence from the norm around the MMPP-related objects. However, the pollutant concentration exceeded the limit near all the living areas.

Работа посвящена параллельной реализации модели волновой гидродинамики и современной ветро-волновой модели SWAN. Представлены результаты параметризации вертикального турбулентного обмена с применением отфильтрованных экспедиционных данных, которые включены в модель гидродинамики для уточнения коэффициента турбулентного обмена, неоднородного по вертикали. В качестве входных данных в моделях использованы контуры полученного со спутника WorldView изображения Азовского моря, определенные методом локального бинарного шаблона. Представлены результаты численных экспериментов, полученные на основе SWAN и трехмерной модели волновой гидродинамики, проведено их сравнение. Описана параллельная реализация SWAN, рассчитаны показатели оценки параллельной вычислительной эффективности SWAN, определена вычислительная масштабируемость SWAN в зависимости от количества вычислительных потоков. Представлены показатели оценки параллельной вычислительной эффективности трехмерной волновой модели гидродинамики.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Elena Protsenko, Aleksandr Strazhko, Sofya Protsenko; The possibilities of using various types of approximations for vertical turbulent exchange parametrization. AIP Conference Proceedings 14 June 2023; 2507 (1): 040004. https://doi.org/10.1063/5.0109352 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

Introduction. Reliable prediction of indicators of turbulent flows is a very difficult task, which is explained by the exceptional physical complexity of turbulence, in particular its probabilistic nature, a wide space-time spectrum and a fundamentally three-dimensional non-stationary nature. Despite conducting a wide range of studies focused on the problem under consideration, they did not fully reflect the totality of various factors and processes affecting the structure and parameters of vertical turbulent mixing. This indicates the need for a systematic analysis of the problem and modeling of such complex formalized systems. The aim of the work is to construct a scenario of changes in hydrodynamic wave processes of the coastal zone, based on an improved mathematical model of wave processes. Materials and methods . The article is devoted to the study of spatial-three-dimensional wave processes in shallow water bodies, taking into account the features of turbulent exchange depending on the source and localization in the column of liquid, as well as the study of the influence of regular wave processes on turbulent exchange and vertically using a mathematical model of wave processes based on the system of Navier-Stokes equations, including three equations of motion in the with dynamically changing geometry of the computational domain. The results of the study. Based on the developed software package, a scenario of changes in hydrodynamic wave processes of the coastal zone is constructed, the formation of vortex structures is predicted. Discussion and conclusions. The separation of the wave flow into a near-surface macroturbulent layer caused by wave motion and a lower layer with background hydrodynamic turbulence is proved, the strength and intensity of turbulence changed synchronously with wave oscillations, demonstrating a pronounced asymmetry of turbulence generation throughout the water column.