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.

Introduction. The Azov Sea is a shallow semi-enclosed sea where satellite altimetry (SA) faces challenges in ensuring accurate sea level measurements. This study focuses on verifying Sentinel-3 altimetry data in the coastal areas of the Azov Sea using observational platform data and a three-dimensional hydrodynamic model. Materials and Methods. The study is based on a comparison of sea surface heights (SSH) obtained from the Sentinel-3 radar altimeter with tide gauge data and modelling results. A three-dimensional hydrodynamic model, adapted to the conditions of the Azov Sea, was used, along with satellite data processed considering atmospheric and tidal corrections. Results. The root mean square error (RMSE) between satellite-derived and reference data was found to be 85 mm. The analysis demonstrated that Sentinel-3 Doppler altimetry in SAR mode provides higher accuracy compared to traditional altimetry, particularly in coastal areas. Discussion and Conclusion. The assessment of Sentinel-3 data confirms their reliability in modeling water levels in the Azov Sea. The comparative analysis methodology proposed in this study enables the identification of systematic errors in satellite data and facilitates their integration with modelling and in situ observations. The study confirms the effectiveness of Sentinel-3 data in determining sea levels in complex coastal conditions. The developed methodology can be applied to other coastal areas to assess satellite altimetry performance.

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.

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.

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.

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.

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

This paper presents a parallel implementation of the wave hydrodynamics model and the modern SWAN wind-wave model. The results of the parameterization of the vertical turbulent exchange using filtered expedition data, which are included in the hydrodynamics model to clarify the coefficient of turbulent exchange, which is inhomogeneous vertically, are presented. The contours of the image of the Sea of Azov are used, determined by the method of a local binary template obtained from the WorldView satellite, as the input data in the models. The results of the numerical experiments obtained based on the SWAN model and a three-dimensional model of wave hydrodynamics are presented and compared. The article describes the parallel implementation of the SWAN model, calculates the indicators for evaluating its parallel computational efficiency, and determines the computational scalability of the SWAN model depending on the number of computational threads. The indicators for evaluating the parallel computational efficiency of a three-dimensional wave model of hydrodynamics are presented.

Introduction . Two-dimensional hydrodynamic models have proven their ability to adequately describe the processes of runoff and transportation in rivers, lakes, estuaries, deltas and seas. Practice shows that even where significant three-dimensional effects are expected, for example, with wind flows, a two-dimensional approach can work effectively. However, in some cases, the two-dimensional model does not accurately reflect the actual flow structures. For example, in shallow waters with complex bathymetry, heterogeneous terrain and dynamics can lead to a non-uniform velocity profile. The aim of the study is to develop a basis for determining in which cases a two-dimensional model averaged in depth is sufficient for modelling hydrodynamic processes in shallow waters like the Azov Sea, and in which cases it is advisable to use a three-dimensional model to obtain accurate results. Materials and Methods. Local analytical solutions have been obtained for the propagation of the predominant singular progressive wave in a shallow, well-mixed reservoir. Advective terms and Coriolis terms are neglected, the vortex viscosity is assumed to be constant, and the lower friction term is linearized. Special attention is paid to the latter, since the characteristics of the models significantly depend on the method of determining the coefficients of lower friction. The analytical method developed in the study shows that certain combinations of higher flow velocities (u ≈˃ 1 m/s) and water depths (d ˃ 50 m) can cause significant differences between the results of the depth-averaged model and the model containing vertical information. Results . The results obtained are verified by numerical simulation of stationary and non-stationary periodic flows in a schematized rectangular basin. The results obtained as a result of three-dimensional modelling are compared with the results of two-dimensional modelling averaged in depth. Both simulations show good compliance with analytical solutions. Discussion and Conclusions. 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.

The article is devoted to the construction and adaptation to natural and climatic conditions and geographical features of precision mathematical models of hydrodynamics of wave processes and relief formation. The incompleteness of data is characteristic of the new tasks considered in the article, the solution of this problem is carried out by involving remote sensing and cadastral survey data. It is essential to include in this complex algorithm for constructing raster models of dynamically changing bottom relief based on known cadastral survey data and remote sensing data. The software package described in this paper makes it possible to reduce the forecast time of hydrophysics processes, including dangerous and catastrophic phenomena. On the basis of the developed software package, prognostic calculations of the processes of coastal erosion and changes in the bottom relief were performed. Modeling of the state of a water body takes into account the characteristic features of natural processes, among which it is worth noting the spatial and temporal variability of relief formation.

Introduction. The work is devoted to the study of the generation and development of turbulent structures in shallow-water flows. For optimal water resource management, it is necessary to know what the consequences will be if the flow system changes as a result of human intervention. Basically, all fluid flows that relate to the practice of civil engineering are turbulent in nature. These are, for example, river and channel flows, tidal currents in the oceans and coastal seas. Shallow currents in the environment often include a wide range of vortex scales, ranging from micro-scale vortices to large-scale coherent structures with horizontal length scales that far exceed the depth of water ( L >> H ). The existence of such large structures is a typical characteristic of turbulence in shallow flow. This indicates the need for a systematic analysis of the problem, as well as modeling of such complex formalized systems. The purpose of this work is to model and analyze the dynamics of quasi-2D turbulence structures. Materials and Methods. Large-scale quasi-2D coherent structures (2 DCS) are investigated depending on the source and localization in the liquid column. Turbulent flows in the channel satisfying incompressible Navier-Stokes equations are considered. The numerical experiment was carried out on the basis of the “large eddy simulation” (LES) approach. The Results of the Study. Scenario of the dynamics of quasi-2D turbulence structures of the coastal zone is constructed, the formation of vortex structures is predicted. Discussion and Conclusions. The development of two-dimensional turbulence in shallow flows illustrates the processes that control quasi-two-dimensional turbulence, including the merging of individual vortices. The main mechanism controlling the decay of 2DCS is the loss of energy due to friction on the bottom, while the larger the size of the vortex relative to the depth, the faster the direct dissipation of its kinetic energy occurs.