The development of water management and land reclamation require qualitatively new theoretical and methodological levels of research, in particular, the search for effective mechanisms for solving the associated mass transfer by interconnected flows of surface, groundwater and infiltration moisture ofthe soil, which causes the need to develop more advanced hydrodynamic models of the dynamics of groundwater and surface water, allowing to describe the processes of mass transfer taking into account hydraulic, hydrogeological, physico-chemical processes in systems – open watercourse and upper layers of soil.
By solving scientific and technical problems of water management and reclamation practice, special attention should be paid to the interrelated processes of water movement and mass transfer of various physical nature, namely along furrows, in the humidification zone - infiltration. The article describes comprehensively study the processes of interconnected surface and groundwater. The solution of these problems can be obtained by creating mathematical models of interconnected surface waterand moisture changes in the soilmoisture zone
Introduction
The development of hydrodynamic models for surface and groundwater movement necessitates accounting for the complex nature of these phenomena, as well as the spatial and temporal scales of hydrological reclamation processes. The hydraulic approximation is essential in modeling both groundwater and surface water movement, requiring consideration of the vertical dimensions of currents relative to horizontal measurements in hydrological and reclamation facilities.
Hydrodynamic models of interconnected surface and groundwater are based on the equations of Richards, Boussinesq, and Saint-Venant. The one-dimensional Richards model is employed to describe vertical infiltration in the unsaturated soil zone, while the Boussinesq and Saint-Venant equations are used for surface water flow modeling. Despite their utility, challenges remain in fully understanding mass transfer in interconnected groundwater and surface water flows using spatial formulations. Consequently, a coupled approach is often adopted, integrating surface and groundwater models to simulate complex hydraulic and geohydrodynamic processes.
Modeling soil moisture dynamics, which involves complex processes like transformation and transpiration of moisture by plant roots, requires special attention to infiltration runoff. Hydraulic methods are particularly useful in this context.
General Provisions
For modeling mass transfer by interacting surface and groundwater currents, considering moisture migration in the humidification zone, the dimensional analysis method is applied. This approach ensures that equations expressing relationships between parameters and variables are dimensionally consistent, with all terms having the same dimensions. The π-theorem is a fundamental aspect of dimensional analysis, stating that a functional dependence between various quantities can be represented as a product of dimensionless parameters.
In the context of mass transfer, the mass transfer coefficient β is defined as a function of characteristic body size r, flow velocity V, flow density ρ, viscosity η, and diffusion coefficient D. Through dimensional analysis, an empirical expression for β is derived, leading to the Sherwood number (Sh), which represents the ratio of convective mass transfer to diffusive mass transport. The Sherwood number is expressed as a function of the Reynolds number (Re) and Schmidt number (Sc), with coefficients determined through experimental data.
Similarly, the heat transfer coefficient 'a' is derived using dimensional analysis, considering parameters such as flow rate V, body size r, viscosity η, density ρ, thermal conductivity λ, and heat capacity C_p. The Nusselt number (Nu), representing the ratio of convective to conductive heat transfer, is expressed as a function of the Reynolds and Prandtl numbers, with coefficients determined experimentally.
The resistance force of solid particles is also modeled using dimensional analysis, considering particle diameter a, flow velocity V, flow density ρ, and dynamic viscosity η. The drag coefficient C_D is determined as a function of the Reynolds number, with empirical correlations available for different flow regimes.
Probabilistic Approach to Particle Size Dynamics
The dynamics of particle sizes in mass transfer processes are described by a nonlinear law, incorporating stochastic elements. The function governing particle size evolution is influenced by convective mass transfer and is modeled using differential equations. Linearization around a mean value leads to a system of equations describing the normal distribution of particle sizes over time.
By solving these equations with appropriate initial conditions, the mean particle size and variance can be determined, providing insights into the dynamics of particle sizes in mass transfer processes.
Conclusion
Effective mechanisms have been developed for the numerical implementation of the shallow water and Richard’s equations, which allow numerical experiments of the obtained hydrodynamic models with a high degree of accuracy, and an effective hydraulic model of convective mass transfer has been developed, which allows describing the processes of surface runoff and infiltration with varying degrees of accuracy and detail
Based on the developed hydraulic model of convective mass transfer the interacting with surface water flows along a furrow with a non-stationary bottom and between the dynamics of moisture in the soil-humidification zone, it can be used to develop devices and algorithms for controlling the state of the soil humidification zone
References
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