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.

Influence of Canopy Seasonal Changes on Turbulence Parameterization within the Roughness Sublayer over an Orchard Canopy

In this observational study, the role of tree phenology on the atmospheric turbulence parameterization over 10-m-tall and relatively sparse deciduous vegetation is quantified. Observations from the Canopy Horizontal Array Turbulence Study (CHATS) field experiment are analyzed to establish the dependence of the turbulent exchange of momentum, heat, and moisture, as well as kinetic energy on canopy phenological evolution through widely used parameterization models based on 1) dimensionless gradients or 2) turbulent kinetic energy (TKE) in the roughness sublayer. Observed vertical turbulent fluxes and gradients of mean wind, temperature, and humidity, as well as velocity variances, are used in combination with empirical dimensionless functions to calculate the turbulent exchange coefficient. The analysis shows that changes in canopy phenology influence the turbulent exchange of all quantities analyzed in this study. The turbulent exchange coefficients of those quantities are twice as large near the canopy top for a leafless canopy than for a full-leaf canopy under unstable and near-neutral conditions. This turbulent exchange coefficient difference is related to the differing penetration depths of the turbulent eddies organized at the canopy top, which increase for a canopy without leaves. The TKE and dissipation analysis under near-neutral atmospheric conditions additionally shows that TKE exchange increases for a leafless canopy because of reduced TKE dissipation efficiency relative to that when the canopy is in full-leaf stage. The study closes with discussion surrounding the implications of these findings for parameterizations used in large-scale models.

Asymptotic Analysis of Equilibrium in Radiation Fog

A vertical distribution formulation of liquid water content (LWC) for steady radiation fog was obtained and examined through the singular perturbation method. The asymptotic LWC distribution is a consequential balance among cooling, droplet gravitational settling, and turbulence in the liquid water budget of radiation fog. The cooling produces liquid water, which is depleted by turbulence near the surface. The influence of turbulence on the liquid water budget decreases with height and is more significant for shallow fogs than for deep fogs. The depth of the region of surface-induced turbulence can be characterized with a fog boundary layer (FBL). The behavior of the FBL bears some resemblance to the surface mixing layer in radiation fog. The characteristic depth of the FBL is thinner for weaker turbulence and stronger cooling, whereas if turbulence intensity increases or cooling rate decreases then the FBL will develop from the ground. The asymptotic formulation also reveals a critical turbulent exchange coefficient for radiation fog that defines the upper bound of turbulence intensity that a steady fog can withstand. The deeper a fog is, the stronger a turbulence intensity it can endure. The persistence condition for a steady fog can be parameterized by either the critical turbulent exchange coefficient or the characteristic depth of the FBL. If the turbulence intensity inside a fog is smaller than the turbulence threshold, the fog persists, whereas if the turbulence intensity exceeds the turbulence threshold or the characteristic depth of the FBL dominates the entire fog bank then the balance will be destroyed, leading to dissipation of the existing fog. The asymptotic formulation has a first-order approximation with respect to turbulence intensity. Verifications with numerical solutions and an observed fog event showed that it is more accurate for weak turbulence than for strong turbulence and that the computed LWC generally agrees with the observed LWC in magnitude.