Turbulent Exchange Coefficient Research Articles

Inverse problem for retrieving greenhouse gas fluxes at the non-uniform underlying surface from measurements of their concentrations at several levels

The study focuses on the formulation, analysis, and solution of the remote sensing inverse problem to retrieve surface carbon dioxide (CO2) fluxes from measurements of CO2 concentrations at different levels within the atmospheric boundary layer. A three-dimensional hydrodynamic model of turbulent greenhouse gas (GHG) transport was used as a forward model to link the surface GHG fluxes to the drone observations of GHG concentrations. The 3D model provides a GHG concentration distribution by solving the diffusion-advection equation using information on wind speed, its direction, and turbulent exchange coefficients. The surface GHG fluxes are considered as a boundary condition. The spatial distributions of wind speed and turbulence coefficient “for a moment in time” are computed from the relaxation problem for the averaged Navier-Stokes and continuity equations, using a 1.5 order closure scheme (E-ω model). The inverse problem is to retrieve a surface GHG flux by minimizing the difference between the measured and modelled concentrations at several levels. The algorithm was applied to estimate CO2 fluxes over a non-uniform forest canopy at the Roshny-Chu experimental site in the foothills of the Greater Caucasus (Chechen Republic). To test the forward numerical problem, data on surface topography, vegetation height and density, spatial distribution of photosynthetically active solar radiation, as well as data on plant photosynthesis and soil CO2 fluxes were used.

Complex turbulent exchange coefficient in Akerblom–Ekman model

Abstract The turbulent exchange in boundary layer models is usually characterized by a scalar eddy viscosity coefficient assumed to be a positive function of the vertical variable. We introduce a more general form for the turbulence exchange description, which includes two functions that describe the turbulence without any assumption about their positivity. We construct a model of the Akerblom–Ekman type, but with a complex coefficient of turbulent exchange. The basic quality criterion for these models and algorithms is the maximal agreement with meteorological observations. We optimize the agreement between the global meteorological archive of high-resolution wind observations that are provided by World Meteorological Organization (WMO) in Binary Universal Form for the Representation (BUFR). The main result of our work is that agreement between model solutions and observations will be much better if the turbulent exchange coefficient is optimized in the space of all complex-valued functions, and not limited to the cone of real positive functions.

Experimental and calculation investigations of hydrodynamics and heat exchange in liquid metal turbulent flows in fast reactor fuel assemblies

The formation of velocity and temperature fields in the fuel assemblies of fast reactor core occurs under the influence various factors. It is shown, that the most important factors include a complex multiply connected geometry, subject to deformation during the campaign under the influence of temperature non-uniformity and radiation effects. The results of studies of the velocity fields and shear stress, turbulence microstructure are presented. An intensification of turbulent momentum transfer in channels in azimuthal and radial directions in the area of gaps between the rods is demonstrated. The performed analysis is indicate that there are a significant difference between the experimental dependences for turbulent momentum transfer coefficients in the radial and azimuthal directions and calculated within the framework of semi-empirical models of turbulent momentum transfer as well as the anisotropy coefficients of the turbulent momentum transfer in rod bundles. The results of benchmark on the fuel assembly thermohydraulics showed that the common commercial codes describe experimental data only approximately. It is shown, that the intensification of turbulent momentum transfer in the channels of rod bundles is due to the appearance of large-scale turbulent momentum transfer (secondary flows). The contribution of large-scale turbulent momentum transfer to the turbulent momentum transfer coefficients in the channels of rod bundles is calculated. The dependence for coefficient of inter-channel turbulent exchange of momentum is obtained and the intensification of inter-channel turbulent exchange in close-packed rod lattices is explained. A dependence for the dissimilarity coefficients of forced inter-channel convective exchange of momentum and mass, as well as energy and mass in rod bundles spaced by wire winding is obtained. The calculation methods and the numerical modeling results for temperature regime of fuel assemblies with randomly distributed initial parameters by the Monte Carlo method are presented as well as the thermomechanical analysis of the temperature field in the fuel assemblies during the campaign. An idea about the equilibrium configuration of a rod bundle in a hexagonal jacket during irradiation, the stress–strain state of an individual fuel rod and a fuel assembly jacket is obtained. The tasks of further investigations discussed.

3D-гидродинамическое моделирование потоков СО2 и CH4 в приземном слое атмосферы (На примере лесного участка «Рошни-Чу»)

Introduction: The aim of this study is to evaluate the spatial variability of carbon dioxide (CO2) and methane (CH4) fluxes at the reference site "Roshni-Chu" of the carbon measurement megasites of the Chechen Republic using modeling experiments with in-situ measurements and remote sensing data. Methods and materials: Measurements of carbon dioxide (CO2) and methane (CH4) fluxes at the soil surface at the "Roshni Chu" forest site in the mountainous forest region of the Chechen Republic were conducted using a dynamic closed chamber connected to a portable gas analyzer G4301 (Picarro, USA). Leaf photosynthesis and respiration parameters of the main edificators and sub-edificators of premontane broadleaf forests were measured using the portable photosynthetic system LI-6800 (LI-COR, USA). Landsat 8 data were used to produce digital maps of surface topography and Nor-malized Difference Vegetation Index (NDVI). A 3D process-based atmospheric transfer model was chosen to describe the spatial variability of carbon dioxide and methane fluxes within the atmospheric boundary layer. The model is based on a one-and-a-half closure scheme for the Navier-Stokes and continuity equations, solved using Reynolds averaging and the Bussiness conjecture. Results: It was shown that a three-dimensional (3D) mathematical transfer models based on the solution of the equations of thermo-hydrodynamics are among the most effective methods for estimating vertical and horizontal fluxes of greenhouse gases in the atmosphere, taking into account the heterogeneous vegetation structure and surface topography. Based on the modeling results, maps of spatial distribution of turbulent exchange coefficient and horizontal wind speed at 5 m height, and maps of spatial distribution of CO2 and CH4 methane fluxes at 5, 25 and 50 m height were created. It was revealed that the "Roshni-Chu" forest area serves as a CO2 sink from the atmosphere under warm sunny weather in summer. The greatest uptake is detected near the local elevations. The fluxes of CH4 are almost negative, the lowest values of CH4 uptake are connected with uneven topography and are observed in small depressions between the hills. Conclusions: Based on the study of the wind field and the greenhouse gas fluxes at the carbon experimental site "Roshni-Chu" in the Chechen Republic, a significant spatial heterogeneity of the vertical CO2 and CH4 fluxes was revealed. The model approach, together with field measurements and remote sensing data, can be very effective for assessing the spatial heterogeneity of greenhouse gas fluxes at sites with non-uniform topography and vegetation. The method of modeling the spatial distribution of CO2 and CH4 fluxes within the atmospheric boundary layer can be used in different forest regions of the North Caucasus to describe the regional greenhouse gas balance.

Estimating turbulent energy flux vertical profiles from uncrewed aircraft system measurements: exemplary results for the MOSAiC campaign

Abstract. This study analyzes turbulent energy fluxes in the Arctic atmospheric boundary layer (ABL) using measurements with a small uncrewed aircraft system (sUAS). Turbulent fluxes constitute a major part of the atmospheric energy budget and influence the surface heat balance by distributing energy vertically in the atmosphere. However, only few in situ measurements of the vertical profile of turbulent fluxes in the Arctic ABL exist. The study presents a method to derive turbulent heat fluxes from DataHawk2 sUAS turbulence measurements, based on the flux gradient method with a parameterization of the turbulent exchange coefficient. This parameterization is derived from high-resolution horizontal wind speed measurements in combination with formulations for the turbulent Prandtl number and anisotropy depending on stability. Measurements were taken during the MOSAiC (Multidisciplinary drifting Observatory for the Study of Arctic Climate) expedition in the Arctic sea ice during the melt season of 2020. For three example cases from this campaign, vertical profiles of turbulence parameters and turbulent heat fluxes are presented and compared to balloon-borne, radar, and near-surface measurements. The combination of all measurements draws a consistent picture of ABL conditions and demonstrates the unique potential of the presented method for studying turbulent exchange processes in the vertical ABL profile with sUAS measurements.

Modeling Tool for Estimating Carbon Dioxide Fluxes over a Non-Uniform Boreal Peatland

We present a modeling tool capable of computing carbon dioxide (CO2) fluxes over a non-uniform boreal peatland. The three-dimensional (3D) hydrodynamic model is based on the “one-and-a-half” closure scheme of the system of the Reynolds-Averaged Navier–Stokes and continuity equations. Despite simplifications used in the turbulence description, the model allowed obtaining the spatial steady-state distribution of the averaged wind velocities and coefficients of turbulent exchange within the atmospheric surface layer, taking into account the surface heterogeneity. The spatial pattern of CO2 fluxes within and above a plant canopy is derived using the “diffusion–reaction–advection” equation. The model was applied to estimate the spatial heterogeneity of CO2 fluxes over a non-uniform boreal ombrotrophic peatland, Staroselsky Moch, in the Tver region of European Russia. The modeling results showed a significant effect of vegetation heterogeneity on the spatial pattern of vertical and horizontal wind components and on vertical and horizontal CO2 flux distributions. Maximal airflow disturbances were detected in the near-surface layer at the windward and leeward forest edges. The forest edges were also characterized by maximum rates of horizontal CO2 fluxes. Modeled turbulent CO2 fluxes were compared with the mid-day eddy covariance flux measurements in the southern part of the peatland. A very good agreement of modeled and measured fluxes (R2 = 0.86, p < 0.05) was found. Comparisons of the vertical profiles of CO2 fluxes over the entire peatland area and at the flux tower location showed significant differences between these fluxes, depending on the prevailing wind direction and the height above the ground.

Fine Structure of Vertical Density Distribution in the Black Sea and Its Relationship with Vertical Turbulent Exchange

This paper is concerned with the analysis of the long-term regular time series of current velocity and conductivity, temperature, and depth (CTD) profiles, measured with the moored autonomous profiler Aqualog over the upper part of the continental slope at a fixed geographical location in the Northeastern Black Sea. This study focuses on the fine structure of the density profiles to show that the fine-structure Cox number (C) is a power function of the Richardson number (Ri). A similar inverse power relationship with the same exponent was found earlier for the coefficient of vertical turbulent mass exchange (Kρ) and Ri. Based on those results, the analysis indicated a statistically significant correlation between C and Kρ, which suggests that the estimations of Kρ could be conducted from the CTD data only.

Dispersion of conservative impurities in rivers: implications for compliance with environmental standards

The research goal is to understand the mechanisms of transport and transformation of conservative impurities in river flows and provide practical solutions to ensure compliance with environmental standards. The need to close the system of equations and make it suitable for solving practical problems caused the addition of equations of motion with empirical regularities. We use an approach based on fundamental equations of hydrodynamics. The main task of mathematical transformations of the fundamental equations was: a) considering the variability of the turbulent exchange coefficients along the flow cross-section. b) addition of the obtained equations with empirical regularities linking the flow characteristics with the turbulent exchange coefficients. c) mathematical transformations were performed to obtain a group of closed equations for which approximate solution methods are known and developed. The best empirical regularities in determining the turbulent exchange coefficients were selected by applying a closed mathematical model. For each desired variable, we obtained an equation of the evolutionary type, which lends itself well to algorithmization. The schemes presented in the article allow us to design computational algorithms using classical approaches to solving impurity transfer equations with variable coefficients of turbulent exchange.

Improved parametrization of the vertical turbulent exchange coefficient, taking into account the shallow water bodies specifics

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.

Multi-scale flow structure and its effect on momentum flux in the coastal marine atmospheric boundary layer

To accurately calculate the turbulent exchange coefficient, the contribution of multi-scale turbulent transportation needs to be considered, especially in the complex terrain of the coastal area. In September 2019, a comprehensive observation experiment on the offshore atmospheric boundary layer was carried out at the Yangmeikeng Ecological Monitoring Station and Sai Chung Gulf. Through scale decomposition, it is shown that the turbulent motion in the atmospheric boundary layer in the coastal area is affected by the underlying surface, such as that of the coastal land or the sea–land boundary. This is the main reason behind the phenomenon whereby different scales make different contributions to momentum flux. Different multi-scale characteristics of turbulent structures on the underlying surface affect the drag coefficient. Through wavelet transform and finite element method, the characteristics of the multi-scale flow structures produced by the complicated offshore terrain are analysed. It is found that large-scale flow structures enhance the pulsating intensity at the small scale, but the large-scale coherence characteristics are different from those at the small scale. In summary, in comparing these three sites, the flux exchange on the roof is greatest, followed by that on the tower. In the Gulf, the flux exchange is mainly dependent on small-scale structures, which are linked with the smallest values.

MATHEMATICAL MODELING AND ECOLOGICAL DESIGN OF THE MARINE SYSTEMS TAKING INTO ACCOUNT MULTI-SCALE TURBULENCE USING REMOTE SENSING DATA

The paper considers a mathematical model of biological kinetics and geochemical cycles based on a system of convection-diffusion equations with nonlinear coefficients, supplemented by a spatially inhomogeneous three-dimensional mathematical model of wave hydrodynamics of a shallow reservoir, with a refined coefficient of turbulent vertical exchange. The task of monitoring the water surface in order to detect phytoplankton spots involves the creation and verification of effective methods for clustering these objects on the surface of reservoirs, in particular, restoring their boundaries based on remote sensing data. The article uses multispectral satellite images as sounding data. Based on the obtained images of plankton populations, the initial conditions for mathematical models of biogeochemical cycles can be determined, on the basis of which prognostic calculations are performed.

Spatializing the roughness length of heterogeneous urban surfaces to improve the WRF simulation-Part 2: Impacts on the thermodynamic environment

Roughness length (Z0) is a fundamental parameter in atmospheric boundary layer theory that affects the transfer of momentum and heat. However, this parameter in urban areas in the WRF model is typically assigned a fixed value. In a previous study, we developed a Z0 database for the heterogeneous urban underlying surface of Guangzhou and demonstrated that its application in the WRF model had significantly improved the simulations of wind speed. In this study, the impact of Z0 update on the dynamic and thermal environment in Guangzhou urban areas is investigated through two numerical experiments: the base experiment applies the model-default Z0 value (0.5 m) for the urban areas and the sensitivity one uses a heterogeneous Z0 map (with higher Z0 values in most urban areas) estimated in the previous study. The results show that the temperature and relative humidity at 2 m height are not sensitive to this Z0 modification. For the dynamic environment, the modification of Z0 decreases the wind speed at 10 m height and increases the friction velocity. The reduction of horizontal wind speed due to Z0 increases reaches heights of several hundred meters, especially below a height of 400 m (950 hPa). Additionally, the updated Z0 leads to an increase in the turbulent momentum exchange coefficient over the urban underlying surface, resulting in a more vigorous turbulent mixing and elevated planetary boundary layer height. For the thermal environment, the Z0 increases result in a higher turbulent heat exchange coefficient near the surface layer, which contributes to the vertical heat flux transport. Moreover, the Z0 increase enhances the sensible heat flux during daytime and reduces the land surface temperature and ground heat flux in Guangzhou central urban area. Due to the reduced heat storage during the daytime, the amount of heat released at night decreases accordingly, thus causing a reduction in the land surface temperature at night and a decrease in the sensible heat flux. This study provides a comprehensive understanding of the sensitivity of the thermodynamic environment to the urban Z0 increase and reconfirms the significance of a realistic Z0 dataset in atmospheric modeling.

Stable Numerical Implementation of a Turbulence Scheme with Two Prognostic Turbulence Energies

Abstract In this paper, we present a new and more stable numerical implementation of the two-energy configuration of the Third Order Moments Unified Condensation and N-dependent Solver (TOUCANS) turbulence scheme. The original time-stepping scheme in TOUCANS tends to suffer from spurious oscillations in stably stratified turbulent flows. Because of their high frequency, the oscillations resemble the so-called fibrillations that are caused by the coupling between turbulent exchange coefficients and the stability parameter. However, our analysis and simulations show that the oscillations in the two-energy scheme are caused by the usage of a specific implicit–explicit temporal discretization for the relaxation terms. In TOUCANS, the relaxation technique is used on source and dissipation terms in prognostic turbulence energy equations to ensure numerical stability for relatively long time steps. We present both a detailed linear stability analysis and a bifurcation analysis, which indicate that the temporal discretization is oscillatory for time steps exceeding a critical time-step length. Based on these findings, we propose a new affordable time discretization of the involved terms that makes the scheme more implicit. This ensures stable solutions with enough accuracy for a wider range of time-step lengths. We confirm the analytical outcomes in both idealized 1D and full 3D model experiments. Significance Statement The vertical turbulent transport of momentum, heat, and moisture has to be parameterized in numerical weather prediction models. The parameterization typically employs nonlinear damping equations, whose numerical integration can lead to unphysical, time-oscillating solutions. In general, a presence of such numerical noise negatively affects the model performance. In our work, we address numerical issues of the recently developed scheme with two prognostic turbulence energies that have more realism and physical complexity. Specifically, we detect, explain, and design a numerical treatment for a new type of spurious oscillations that is connected to the temporal discretization. The treatment suppresses the oscillations and allows us to increase the model time step more than 4 times while keeping an essentially non-oscillatory solution.

3D turbulent currents simulation in the coastal zone using the LES approach based on filtered ADCP data

The interest in turbulence in shallow waters, such as the Azov Sea, is caused by the fact that in the places of its existence there is an intensive transfer of the amount of motion and heat, the spread of passive impurities, the transfer of suspended particles. These processes significantly affect the formation and spatial structure of physical, chemical and biological fields of reservoirs and their spatial and temporal changes. Depending on the smoothing scale of the series of initial readings of the flow meters, the pulsation characteristics of the flow velocity were determined, which were processed in order to obtain data on turbulence and its scales. The research results provided empirical data on the conditions of generation and existence of small-scale turbulence. The collected empirical material is currently being processed to study the internal structure of the recorded disturbances of small-scale turbulence. In this paper, small-scale motion is excluded from the Navier-Stokes equations by applying the filtration operation and is modeled using subgrid models. To do this, in two-dimensional and three-dimensional cases, various types of filters are used: a box filter, a Gaussian filter and a Fourier filter, with a gradual decrease in the filter width, which allows you to reproduce a wider frequency range of fluctuations of the solution. The obtained data are planned to be used for numerical simulation of three-dimensional turbulent flows using the LES approach and comparison with the results of averaging by RANS. The article considers the possibilities of using various types of approximations for parametrization of vertical turbulent exchange. Algebraic models for calculating the coefficient of vertical turbulent exchange and semi-empirical turbulence models are compared.

Algorithms for calculating the microturbulent exchange coefficient for a three-dimensional mathematical model of hydrodynamics of coastal systems

The work is devoted to the construction of a model of turbulent exchange in shallow water bodies using the results of expeditionary measurements. The Kalman filter algorithm was used to filter field data. An algorithm for calculating the coefficient of vertical turbulent exchange, which decisively affects the heat and gas exchange of the coastal system, has been developed, which has made it possible to significantly reduce the effect f noise in the experimental data used. As a result of the numerical implementation of the developed algorithm, the coefficient of microturbulent exchange in the vertical direction was obtained for a three-dimensional mathematical model of hydrodynamics of coastal systems.

Vertical turbulent exchange structure and parametrization for 3D shallow water hydrodynamics models

The work describes research of vertical turbulent exchange structure and parametrization for 3D shallow water hydrodynamics models. In this paper, the coefficients of horizontal turbulent exchange are calculated using a whole set of averaging periods of turbulent velocity pulsations. Using experimental data on the pulsations of the velocity components, the coefficient of vertical turbulent exchange was calculated on the basis of various approaches to its parameterization, based on the analysis of the obtained coefficient distributions, the most adequate parameterization of the coefficient was selected, which is used in the software package. The distribution of the vertical turbulent exchange coefficient obtained in a numerical experiment was compared with the results of full-scale measurements, and the calculation results obtained using the mathematical statistics apparatus were analysed.

Osnovnyye zakonomernosti vertikal'nogo turbulentnogo obmena v kvaziodnorodnykh i stratifitsirovannykh sloyakh Chernogo morya

Purpose. The purpose of the study is to assess the coefficient of vertical turbulent exchange for different layers of the Black Sea basin based on the experimental data on microstructure of the physical fields obtained for the period 2004–2019 in the Black Sea and using the semi-empirical models. Methods and Results. For the upper mixed layer, the turbulent energy dissipation rate ɛ and the exchange coefficient were calculated using the velocity fluctuation spectra based on the Kolmogorov hypotheses on the turbulence spectrum inertial range. In the stratified layers, the turbulence coefficient and the dissipation rate were experimentally determined both from the spectra of the velocity horizontal fluctuations’ gradients and the vertical spectra of temperature fluctuations using the concept of the effective scale of turbulent spots. Depending on the features of the hydrological regime and the prevailing energy contributors to turbulence generation, five layers were identified and described (including their characteristic power dependences of the vertical turbulent diffusion coefficients K on the buoyancy frequency N) using the 1.5D-model of vertical turbulent exchange for the basin under study. For the stratified layers, the 1.5D-model results were comparatively analyzed with those of the other semi-empirical and theoretical models describing the most probable hydrophysical processes in each specific layer; the relations for the vertical turbulent exchange coefficient were obtained depending on the buoyancy frequency. Conclusions. Comparison of the experimental data collected under different hydrometeorological conditions with the simulations resulted from the known turbulence models for the sea upper layer showed that the best agreement between the simulation and measurement data was provided by a multiscale model taking into account three basic mechanisms of turbulence generation: current velocity shear, instability of wave motions, and wave breaking. The turbulent exchange coefficient dependencies on depth are conditioned by the affect of the turbulence dominant source at a given level. In the stratified layers, the exchange coefficient dependence on buoyancy frequency is determined by the hydrophysical processes in each layer; the relations obtained for individual layers indicate intensity of the contributions of vertical advection, internal wave breakings, turbulence diffusion and geothermal flux.

Basic Regularities of Vertical Turbulent Exchange in the Mixed and Stratified Layers of the Black Sea

Purpose. The purpose of the study is to assess the coefficient of vertical turbulent exchange for different layers of the Black Sea basin based on the experimental data on microstructure of the physical fields obtained for the period 2004–2019 in the Black Sea and using the semi-empirical models. Methods and Results. For the upper mixed layer, the turbulent energy dissipation rate ɛ and the exchange coefficient were calculated using the velocity fluctuation spectra based on the Kolmogorov hypotheses on the turbulence spectrum inertial range. In the stratified layers, the turbulence coefficient and the dissipation rate were experimentally determined both from the spectra of the velocity horizontal fluctuations’ gradients and the vertical spectra of temperature fluctuations using the concept of the effective scale of turbulent patches. Depending on the features of the hydrological regime and the prevailing energy contributors to turbulence generation, five layers were identified and described (including their characteristic power dependences of the vertical turbulent diffusion coefficients K on the buoyancy frequency N) using the 1.5D-model of vertical turbulent exchange for the basin under study. For the stratified layers, the 1.5D-model results were comparatively analyzed with those of the other semi-empirical and theoretical models describing the most probable hydrophysical processes in each specific layer; the relations for the vertical turbulent exchange coefficient were obtained depending on the buoyancy frequency. Conclusions. Comparison of the experimental data collected under different hydrometeorological conditions with the simulations resulted from the known turbulence models for the sea upper layer showed that the best agreement between the simulation and measurement data was provided by a multiscale model taking into account three basic mechanisms of turbulence generation: current velocity shear, instability of wave motions, and wave breaking. The turbulent exchange coefficient dependencies on depth are conditioned by the effect of the turbulence dominant source at a given level. In the stratified layers, the exchange coefficient dependence on buoyancy frequency is determined by the hydrophysical processes in each layer; the relations obtained for individual layers indicate intensity of the contributions of vertical advection, internal wave breakings, turbulence diffusion and geothermal flux.

Assessment of the Black Sea Temperature and Salinity Climatic Fields for the Recent Climatological Period (1991–2020)

Purpose. The purpose of the study is to assess the coefficient of vertical turbulent exchange for different layers of the Black Sea basin based on the experimental data on microstructure of the physical fields obtained for the period 2004–2019 in the Black Sea and using the semi-empirical models. Methods and Results. New array of the temperature and salinity climatic fields was assessed by the results of numerical experiments. In the experiment, annual variation of the Black Sea hydrophysical parameters was reconstructed by the numerical model. Modeling included the scheme of assimilating the data of the climatic temperature and salinity array assessed. In contrast to the averaged data of the field observations, the modeled fields are compliant with equations of motion. Besides the temperature and salinity three-dimensional fields, the three-dimensional climatic fields of the Black Sea currents were also reconstructed for each day of a climatic year that is quite impossible using the observational data only. Spatial-temporal variability of the modeled three-dimensional fields was analyzed. The integral characteristics of the Black Sea water dynamics for the recent 30-year climatic period were studied and compared with the analogous ones for the previous century. Simulation was carried out by three-dimensional non-linear model of the Black Sea dynamics developed in Marine Hydrophysical Institute. The horizontal resolution of the model was 5 km, and the EMODNet bathymetry was used. The performed calculations showed that the increased spatial resolution of the temperature and salinity climatic array for the recent period made it possible to reconstruct the dynamics of the Black Sea in all layers in more detail. At the same time, significant small-scale variability of salinity fields was revealed. It was most pronounced at the deep-water horizons. Conclusions. Modeling using a new array of thermohaline fields revealed an increase in the integral temperature of the upper mixed layer in comparison with the experiment with assimilation of the previous version of the climatic array. At that, thinning and «break» of the cold intermediate layer found in the central part of the sea, indicates warming of the sea upper layer during the last 30 years. The highest noise detected at the deep-water horizons in the modeled salinity fields is related to quantity and quality of the salinity data resulted from the field observations. Taking into account insufficient calibration facilities for measuring seawater electrical conductivity, the next version of climatic TS-array requires a more strict procedure for verifying and processing the observation data obtained in the deep-sea layers.

Локально-двумерные схемы расщепления для параллельного решения трехмерной задачи транспорта взвешенного вещества

A 3D model of suspended matter transport in coastal marine systems is considered, which takes into account many factors, including the hydraulic size or the rate of particle deposition, the propagation of suspended matter, sedimentation, the intensity of distribution of suspended matter sources, etc. The difference operators of diffusion transport in the horizontal and vertical directions for this problem have significantly different characteristic spatiotemporal scales of processes, as well as spectra. With typical sampling, applied to shallow-water systems in the South of Russia (the Sea of Azov, the Tsimlyansk reservoir), the steps in horizontal directions are 200-1000 meters, the coefficients of turbulent exchange (turbulent diffusion) are (103-104) m2/sec; in the vertical direction - - - steps of 0.1 m-1 m, and the coefficients of microturbulent exchange in the vertical — (0.1-1) m2/sec. If we focus on the use of explicit locally twodimensional - - - locally one-dimensional splitting schemes, then the permissible values of the time step for a two-dimensional problem will be about 10-100 seconds, and for a one-dimensional problem in the vertical direction - - - 0.1 – 1 sec. This motivates us to construct an additive locally-two-dimensional-locallyonedimensional splitting scheme in geometric directions. The paper describes a parallel algorithm that uses both explicit and implicit schemes to approximate the two-dimensional diffusion-convection problem in horizontal directions and the one-dimensional diffusion-convection problem in the vertical direction. The two-dimensional implicit diffusion-convection problem in horizontal directions is numerically solved by the adaptive alternating-triangular method. The numerical implementation of the one-dimensional diffusion-convection problem in the vertical direction is carried out by a sequential run-through method for a series of independent one-dimensional three-point problems in the vertical direction on a given layer. To increase the efficiency of parallel calculations, the decomposition of the calculated spatial grid and all grid data in one or two spatial directions - in horizontal directions-is also performed. The obtained algorithms are compared taking into account the permissible values of time steps and the actual time spent on performing calculations and exchanging information on each time layer.