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.

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.

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 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.

VERTICAL TURBULENT EXCHANGE COEFFICIENT PARAMETRIZATION IN THE FRAMEWORK OF THE LES APPROACH

The vertical turbulent exchange coefficient parametrization based on the LES approach is constructed in this paper. To implement this approach, water flow velocities pulsations full-scale data at some points of shallow-water systems obtained using an acoustic Doppler flow meter (ADCP) during expedition studies were filtered using two-stage Kalman algorithm, and then averaged, after which the LES approach was applied using subgrid turbulence model. The parametrization of the coefficient of vertical turbulent exchange is used in the wave hydrodynamics mathematical model.

Estimation of the Vertical Turbulent Exchange Intensity in the Main Pycnocline Layer in the Prikerchensky Area of the Black Sea Shelf

The paper investigates the seasonal variability of the vertical turbulent exchange coefficient in the upper stratified layer of the Black Sea. The expedition data used in this work containing information on the microstructure of physical fields were obtained in different hydrological seasons covering the northeastern part of the Black Sea in the Prikerchensky area of the shelf slope. The data were collected during cruises of r/v “Professor Vodyanitsky” in 2016–2019 using “Sigma-1” sounding complex. Based on the semi-empirical methods of assessment of vertical turbulent exchange in the deep-water area of the Black Sea, the dependence of the vertical turbulent diffusion coefficient K on the buoyancy frequency N in the studied layer was established from the flow fluctuation characteristics, with the corresponding graphs and their approximating power-law dependences K  A  N  plotting. In addition, the vertical distribution of the K coefficient with depth was analyzed. Comparative analysis of the obtained dependences with the results of the 1.5D model was carried out. The analysis of the measurement data showed that the results obtained in this work do not contradict the original model. The results can also be used to assess the vertical fluxes of heat, salt and other dissolved chemical and biological substances depending on stratification in the studied part of the Black Sea for different seasons.

Model and Experimental Estimates of Vertical Mixing Intensity in the Sea Upper Homogeneous Layer

Purpose. The study is aimed at qualitative and quantitative analysis (based on the updated previously proposed multiscale model) of the experimental data on turbulence intensity and their comparison with theoretical and semi-empirical relationships for the purpose of describing the contributions of various turbulence sources. Methods and Results. A comparative analysis of experimental data and model calculations of turbulence characteristics near the sea surface was performed. The methods of theoretical assessing generation of turbulence in the near-surface sea layer by various physical processes are considered. The results of calculations by the well-known models of turbulent exchange were compared with the experimental data collected by the scientists of the Turbulence Department of MHI, RAS, using the specialized equipment. The analysis results made it possible to determine the possibility of applying the considered models for calculating turbulence intensity under different hydrometeorological conditions. At light winds, none of the models yielded the results which matched the measurement data. At moderate winds, the simulation results showed quite satisfactory agreement with the experiment data; and for strong winds, the multiscale model results were the best. This model was modified to assess the contributions of two other mechanisms of turbulence generation: the Stokes drift and the Langmuir circulations. Conclusions. Objective assessment of the turbulent exchange intensity requires taking into account of three main mechanisms of turbulence generation, namely flow velocity shear, wave motions and wave breaking. Depending on the hydrometeorological situation, each of these mechanisms can dominate in a certain depth range. The calculations performed using the updated model showed that the Stokes drift added 2–17 % to the total dissipation in the upper 30-meter layer, whereas the contribution of the Langmuir circulations calculated through dependence of the vertical velocity of kinetic energy transfer upon the Langmuir number, can reach 15 % for small Langmuir numbers.

Model and Experimental Estimates of Vertical Mixing Intensity in the Sea Upper Homogeneous Layer

Purpose. The study is aimed at qualitative and quantitative analysis (based on the updated previously proposed multiscale model) of the experimental data on turbulence intensity and their comparison with theoretical and semi-empirical relationships for the purpose of describing the contributions of various turbulence sources. Methods and Results. A comparative analysis of experimental data and model calculations of turbulence characteristics near the sea surface was performed. The methods of theoretical assessing generation of turbulence in the near-surface sea layer by various physical processes are considered. The results of calculations by the well-known models of turbulent exchange were compared with the experimental data collected by the scientists of the Turbulence Department of MHI, RAS, using the specialized equipment. The analysis results made it possible to determine the possibility of applying the considered models for calculating turbulence intensity under different hydrometeorological conditions. At light winds, none of the models yielded the results which matched the measurement data. At moderate winds, the simulation results showed quite satisfactory agreement with the experiment data; and for strong winds, the multiscale model results were the best. This model was modified to assess the contributions of two other mechanisms of turbulence generation: the Stokes drift and the Langmuir circulations. Conclusions. Objective assessment of the turbulent exchange intensity requires taking into account of three main mechanisms of turbulence generation, namely flow velocity shear, wave motions and wave breaking. Depending on the hydrometeorological situation, each of these mechanisms can dominate in a certain depth range. The calculations performed using the updated model showed that the Stokes drift added 2–17 % to the total dissipation in the upper 30-meter layer, whereas the contribution of the Langmuir circulations calculated through dependence of the vertical velocity of kinetic energy transfer upon the Langmuir number, can reach 15 % for small Langmuir numbers.

VARIOUS APPROXIMATIONS OF VERTICAL TURBULENT EXCHANGE PARAMETERIZATION FOR THE ANALYSIS OF THE WAVES HYDRODYNAMIC IMPACT ON THE BOTTOM OF THE RESERVOIR

The article discusses the possibilities of using various types of approximations for parametrization of vertical turbulent exchange for calculating and evaluating the hydrophysical characteristics of the wave regime in the accumulative coastal zone of the southwestern corner of the Tsimlyansk reservoir. It is impossible to carry out these studies without using various types and classes of approximations for parametrization of vertical turbulent mixing. Algebraic models for calculating the coefficient of vertical turbulent exchange and semi-empirical turbulence models are compared. Using ADCP data on velocity pulsations for several stations to measure hydrological characteristics, the results of parameterization of the vertical turbulent exchange coefficient were analyzed. The developed numerical algorithms and the software package implementing them are used to study the pressure field, the velocity vector field of the aquatic environment and the prediction of the baric field for this section of the reservoir water area.