UNESCO Equation Research Articles

New criterion for characterization of thermal-saline jets discharged from thermal desalination plants

• The hydrodynamic pattern of inclined thermal-saline jets was examined using LES. • Jets pattern depended only on the ratio of salinity to thermal Froude numbers ( R ρ ). • Jets with R ρ lower than 1.2 behaved similar to the negatively buoyant jet. • Jets with R ρ in a range of 1.2-1.3 achieved better mixing characteristics. • Geometrical characteristics of jets became asymptotic for R ρ less than 0.7. More than 80% of desalination plants use the multi-stage flash (MSF) technology in the Persian Gulf and hence may have a severe irreversible impact on the marine environment. In the present study, geometrical, mixing, and turbulence characteristics of thermal-saline jets, similar to MSF effluents, are numerically investigated using the dynamic Smagorinsky sub-grid scale (SGS) model and UNESCO equation of state. For this purpose, two affecting dimensionless parameters are considered: (1) density ratio, which is thermal flux to salinity flux ratio, and (2) salinity Froude number. Examining the effects of density ratio reveals that the jet flow pattern only depends on the density ratio with a separating range of 1.2-1.3. In addition, increasing the density ratio increases the geometrical values of descending jets, reduces the geometrical values of ascending ones, and increases the descending jet's dilution before returning to the bed. Furthermore, geometrical values of descending jets show asymptotic behavior for density ratios less than 0.7. Eventually, turbulence characteristics of different jet flow patterns show that large turbulence structures are more explicit for the quasi-neutral scenario. The current results recommend that thermal desalination discharges similar to quasi-neutral jets with density ratios in a range of 1.2-1.3 achieve better mixing characteristics.

Methods for calculating the speed of sound distribution by water temperature: case study for the Black Sea

The article presents the results of the research aimed at calculating the vertical speed of sound distribution in the active layer of the Black Sea based on water temperature readings. The research was carried out in the active layer of the deep-water section of the Black Sea at the depth range of 0 – 50 meters. The water temperature values taken at the hydrological stations or the shipboard measurements (OSD: Ocean Station Data) taken with the help of floats (PFL: Profiling Float Data) were used as initial data. The calculations were based on the identification of correlation relationships between the water temperature values at standard horizons of the Black Sea as per OSD data and the speed of sound calculated using the UNESCO equation. The calculation accuracy was estimated after comparing the speed of sound calculated by the established regression equations and by the UNESCO equation based on PFL data.
 The research allowed establishing the regression equations for calculating the vertical speed of sound distribution in the Black Sea up to the depth of 50 meters over the spring-autumn period. The possibility of calculating the vertical speed of sound distribution using the developed regression equations was also estimated.
 The calculations indicated statistically significant results over the spring-autumn period. Multiple correlation coefficients appeared to be significant and amounted to 0.99. The developed regression equations were efficient and reliable. Verification of effectiveness and reliability of the regression equations showed that the standard error was within ± 1 m s-1.
 In order to visualize the results the calculation of the vertical speed of sound distribution in the Black Sea using the regression equations was carried out for 6 hydrological sections (1 section for each of the months) introduced in 2018. The research showed that the isolines of the vertical speed of sound distribution calculated using the regression equations and the UNESCO equation are practically coherent.
 The studied equations can be used for calculating the vertical speed of sound profile distribution in the Black Sea up to the depth of 50 meters over the May-October period based on the measured or modeled data of water temperature variability. This calculation can be used for the purposes of scientific research and applied purposes in the field of hydrography, hydroacoustics, oceanology, marine ecology, navigation etc.

Direct numerical simulation of double-diffusive gravity currents

This paper presents three-dimensional direct numerical simulations of laboratory-scale double-diffusive gravity currents. Flow is governed by the incompressible Navier-Stokes equations under the Boussinesq approximation, with salinity and temperature coupled to the equations of motion using a nonlinear approximation to the UNESCO equation of state. The effects of vertical boundary conditions and current volume are examined, with focus on flow pattern development, current propagation speed, three-dimensionalization, dissipation, and stirring and mixing. It was observed that no-slip boundaries cause the gravity current head to take the standard lobe-and-cleft shape and encourage both a greater degree and an earlier onset of three-dimensionalization when compared to what occurs in the case of a free-slip boundary. Additionally, numerical simulations with no-slip boundary conditions experience greater viscous dissipation, stirring, and mixing when compared to similar configurations using free-slip conditions.

Modeling Geochemically Caused Permanent Stratification in Lake Waldsee (Germany)

A geochemical model was incorporated into a stratification model for lakes to create the model package: DYCD-CORE, a numerical code that couples the thermal and hydrodynamic capabilities of DYRESM and the geochemical capabilities of the reactive transport model CORE2D V4. Based on the chemical composition of solutes calculated in each node for each time step, density was computed using specific partial molal volumes of all considered solutes and fed back into the stratification module of the program package. The density calculated each time step leads to a strong coupling of hydrodynamics and hydrogeochemistry and reflects the complex interaction as it is present in all lakes. To demonstrate the functionality of the numerical approach, an example of an iron-meromictic lake was chosen, where the reactivity of the dissolved iron kept the water body perennially stratified. To critically validate the model results, temperatures were continously measured at high vertical and temporal resolution in a field investigation of Waldsee (near Dobern, Germany). Multiparameterprobe profiles and water samples confirmed the continous chemical stratification and served as initial and boundary conditions for the simulation period. The model package DYCD-CORE could reproduce the permanent stratification as it were in the lake. A demonstration run using the standard UNESCO equation for density, and hence assuming non-reactive solutes, failed entirely. Hence, stratification models using salinity for density are not suited for simulating density created by lake-internal geochemical transformation of solutes. However, density can be based directly on the simultaneous numerical simulation of lake geochemistry. Predictive modeling of changing lake circulation in a variable climate or considering change of use will require a proper inclusion of the geochemistry as demonstrated in this paper.

Acoustic wave propagation in high-pressure system

Recently, substantial attention is paid to the development of methods of generation of pulsations in high-pressure systems to produce pulsating high-speed water jets. The reason is that the introduction of pulsations into the water jets enables to increase their cutting efficiency due to the fact that the impact pressure (so-called water-hammer pressure) generated by an impact of slug of water on the target material is considerably higher than the stagnation pressure generated by corresponding continuous jet. Special method of pulsating jet generation was developed and tested extensively under the laboratory conditions at the Institute of Geonics in Ostrava. The method is based on the action of acoustic transducer on the pressure liquid and transmission of generated acoustic waves via pressure system to the nozzle. The purpose of the paper is to present results obtained during the research oriented at the determination of acoustic wave propagation in high-pressure system. The final objective of the research is to solve the problem of transmission of acoustic waves through high-pressure water to generate pulsating jet effectively even at larger distances from the acoustic source. In order to be able to simulate numerically acoustic wave propagation in the system, it is necessary among others to determine dependence of the sound speed and second kinematical viscosity on operating pressure. Method of determination of the second kinematical viscosity and speed of sound in liquid using modal analysis of response of the tube filled with liquid to the impact was developed. The response was measured by pressure sensors placed at both ends of the tube. Results obtained and presented in the paper indicate good agreement between experimental data and values of speed of sound calculated from so-called “UNESCO equation”. They also show that the value of the second kinematical viscosity of water depends on the pressure.

Some neural network applications in environmental sciences. Part II: advancing computational efficiency of environmental numerical models

A new generic neural network (NN) application—improving computational efficiency of certain processes in numerical environmental models—is considered. This approach can be used to accelerate the calculations and improve the accuracy of the parameterizations of several types of physical processes which generally require computations involving complex mathematical expressions, including differential and integral equations, rules, restrictions and highly nonlinear empirical relations based on physical or statistical models. It is shown that, from a mathematical point of view, such parameterizations can usually be considered as continuous mappings (continuous dependencies between two vectors) and, therefore, NNs can be used to replace primary parameterization algorithms. In addition to fast and accurate approximation of the primary parameterization, NN also provides the entire Jacobian for very little computation cost. Four particular real-life applications of the NN approach are presented here: for oceanic numerical models, a NN approximation of the UNESCO equation of state of the sea water (NN for the density of the seawater) and an inversion of this equation (NN for the salinity of the seawater); for atmospheric numerical models, a NN approximation for long wave radiative transfer code; and for wave models, a NN approximation for the nonlinear wave–wave interaction. In all considered applications a significant acceleration of numerical computations has been achieved. The first two of these NN applications have already been implemented in the multi-scale ocean forecast system at NCEP. The NN approach introduced in this paper can provide numerically efficient solutions to a wide range of problems in numerical models where lengthy, complicated calculations, which describe physical, chemical and/or biological processes, must be repeated frequently.

A neural network technique to improve computational efficiency of numerical oceanic models

A new generic approach to improve computational efficiency of certain processes in numerical environmental models is formulated. This approach is based on the application of neural network (NN) techniques. It can be used to accelerate the calculations and improve the accuracy of the parameterizations of several types of physical processes which generally require computations involving complex mathematical expressions, including differential and integral equations, rules, restrictions and highly nonlinear empirical relations based on physical or statistical models. It is shown that, from a mathematical point of view, such parameterizations can usually be considered as continuous mappings (continuous dependencies between two vectors). It is also shown that NNs are a generic tool for fast and accurate approximation of continuous mappings and, therefore, can be used to replace primary parameterization algorithms. In addition to fast and accurate approximation of the primary parameterization, NN also provides the entire Jacobian for very little computation cost. Three successful particular applications of the NN approach are presented here: (1) a NN approximation of the UNESCO equation of state of the seawater (density of the seawater); (2) an inversion of this equation (salinity of the seawater); and (3) a NN approximation for the nonlinear wave–wave interaction. The first application has been implemented in the National Centers for Environmental Prediction multi-scale oceanic forecast system, and the second one is being developed for wind wave models. The NN approach introduced in this paper can provide numerically efficient solutions to a wide range of problems in environmental numerical models where lengthy, complicated calculations, which describe physical processes, must be repeated frequently.

An oceanic general circulation model in pressure coordinates

A new oceanic general circulation model in pressure coordinates is formulated. Since the bottom pressure changes with time, the vertical coordinate is actually a pressure-σ coordinate. The numerical solution of the model is based on an energy—conservation scheme of finite difference. The most important new feature of the model is that it is a truly compressible ocean model and it is free of the Boussinesq approximations. Thus, the new model is quite different from many existing models in the following ways: 1) the exact form of mass conservation, 2) the in—situ instantaneous pressure and the UNESCO equation of state to calculate density, 3) the in—situ density in the momentum equations, 4) finite difference schemes that conserve the total energy.

A new approximation of the equation of state for seawater, suitable for numerical ocean models

An approximation to the UNESCO equation of state for seawater is obtained in the form of a polynomial that is cubic in potential temperature, quadratic in pressure, and linear in salinity. The polynomial represents a reasonable compromise between accuracy and computational economy; it also allows potential temperature to be obtained analytically from given values of density, salinity, and pressure.

Evolution of temperature and salt structure of Lake Bonney, a chemically stratified Antarctic lake

A resurgence of interest in the ecology of perennially ice-covered lakes in the McMurdo dry valleys has necessitated a review of our knowledge of the physical and chemical properties of these unusual lakes. Salinities in the ice-covered lakes cover a range from freshwater to hypersaline brines. Recent measurements of salt composition and concentrations in Lake Bonney reveal little change below the chemocline since extensive measurements made in 1960–1961, although lake level has risen by approximately 5 m since that time. The rise in lake level has resulted in a thickening of the freshwater layer above the chemocline. Temperature structure has adjusted to the effects of increased lake level on heat transfer processes such as transmission and absorption of solar radiation in the water column. Questions about how water-column stability affects biology in Lake Bonney have motivated the formulation of a method to compute density from in situ measurements of temperature, conductivity and pressure. Owing to high salt concentration and unique ion ratios, we modified the UNESCO Equation of State for seawater to predict density at salinities greater than 42. The modifications merge smoothly with the UNESCO equations at a salinity of 42. At salinities below 42 the UNESCO equations give excellent predictions of density.

The densities of Changjiang estuarine waters

In order to check the validity of the International Equation of State of Seawater set up by the UNESCO in 1980 for application to China coastal waters, the authors measured the relative density of Changjiang estuarine seawater and seawater solutions diluted with the Changjiang River water at one atmosphere from 5–35 salinity under 15–24°C with a high precision magnetic float densimeter designed by them. The average standard deviation of measured values was ±2.3×10−3 kgm−3. the statistical results showed that for all samples from the Changjiang estuary, the measured density with the densimeter was always higher than the density calculated by the UNESCO equation. The average differences, for dry season and flood season seawater samples were (+6.3±2.3)×10−3kgm−3 and (+8.1±2.3)×10−3kgm−3, respectively. The average difference between the measured and calculated (from the UNESCO equation) density increased linearly as salinity decreased and became +47.2×10−3 kgm−3 at the Changjiang River water salinity limit of around 0.134. A linear correlation was found between this average difference and the [Ca2+]/s ratio value. The experimental average values of [Ca2+]/s, [SO42−]/s, [Mg2+]/s, and [Sr2+]/s were 0.01183±1.0×10−4, 0.07698±1.7×10−4, 0.03743±8.1×10−5 and 2.26×10−4, respectively, at sample salinities of 30 to 35. The experimental value of [Ca2+]/s for the Wuhu Changjiang River water was 0.2597. The resulting densities of all samples were then fitted to an equation of the formd−dw=B1s1/2+B2s+B3s3/2+B4s2 wheredw is the density of SMOW andB1,B2,B3 andB4 are temperature-dependent parameters. The average standard deviation between calculated densities of this equation and experimental values was ±3.9×10−3 kgm−3.