Two-dimensional Water Flow Research Articles

Development and Application of a New Open-Source Integrated Surface–Subsurface Flow Model in Plain Farmland

Accurately characterizing rainfall runoff processes in plain farmland, especially at the plot scale with significant micro-topographic features, has presented challenges. Integrated surface–subsurface flow models with high-precision surface flow modules are appropriate tools, yet open-source versions are rare. To address this gap, we proposed an open-source integrated surface–subsurface flow model called the FullSWOF-Plain model, in which the one-dimensional subsurface module Hydrus-1D was integrated with a modified two-dimensional surface water flow module (FullSWOF-2D) using the sequential head method. Various experimental scenarios were simulated to validate the model’s performance, including two outflow cases (i.e., 1D and 2D) without infiltration, a classical one-dimensional infiltration case, and two typical rainfall events at the experimental field. The results demonstrate the accuracy of this proposed model, with the Nash–Sutcliffe efficiency (NSE) of the simulated discharge exceeding 0.90 in the experimental field case and the root mean squared error (RMSE) values for soil moisture at five depths consistently below 0.03 cm3/cm3. However, we observed a lag in the simulated response time of soil moisture due to the neglect of preferential flow. The micro-topography significantly influenced ponding time and ponding areas. Lower local terrain normally experienced earlier surface ponding. Scattered surface ponding water first occurred in the ditch and followed in the relatively low areas in the main field. The concentration process of surface runoff exhibited hierarchical characteristics, with the drainage ditch contributing the most discharge initially, followed by the connection of scattered puddles in the main field, draining excess surface water to the ditch through rills. This quantitative study sheds light on the impact of micro-topography on surface runoff in plain farmland areas.

Effect of unsaturated soil water transport function linearization for mulched drip irrigation

Water flow in the unsaturated zone is an important component of the water cycle. Linearized methods have been widely adopted to solve unsaturated flow problems described with Richards’ equation, which is nonlinear. To better understand the effect of unsaturated soil water transport function linearization, this article presents an analytical study of a two-dimensional soil water flow system. Analytical solutions, experimental observations and numerical simulations were compared, and the results indicated that the soil water content variation trends were the same, but the values were a little different. The analytical solutions have a certain reference value for researching unsaturated water flow. However, the soil volumetric water content (SWC) results were sensitive to linearized water flow parameter variations in soil water diffusivity (D). The D changes with the SWC. The results showed that unsaturated water flow function linearization affected the analytical solution results essentially. As the nonlinear math problem was not solved, we recommend the numerical solution when more precise values are needed and complex conditions are considered.

REGULARITIES OF HYDROCHEMICAL DYNAMICS IN A TWO-DIMENSIONAL TURBULENT FLOW OF NATURAL WATER

The variability of the composition and properties of natural waters, which creates numerous difficulties in water use, cannot always be explained by the influence of external influencing factors, such as weathering or leaching of rocks, a change in the phases of the water regime, etc. This is especially true for subdiurnal and subhourly quality variability, which can be caused by complex, previously unknown dynamic hydrochemical processes. Such a conclusion follows from the results of the study of turbidity and pH of natural water given in the work, obtained with an increased frequency of measurements. These results indicate the existence of a quasi-cyclic change in the controlled parameters with different periods, from every minute to daily. The study of observational data allows us to make an assumption that in this case the hydrochemical dynamics is due to direct and reverse energy cascades in a two-dimensional turbulent flow of natural water, in which the impurity subsystem is prone to stratification.

Regularities of Hydrochemical Dynamics in a Two-Dimensional Turbulent Flow of Natural Water

Variations in the composition and properties of natural waters, which creates numerous difficulties in water use, cannot always be explained by the influence of external forcing such as weathering or leaching of rocks, changes in the phases of the water regime, and other causes. This is especially true for sub-daily and sub-hourly variations in the water quality, which can be caused by complex, previously unknown dynamic hydrochemical processes. Such a conclusion follows from study of the turbidity and pH of natural water measured with increased frequency, the results of which are presented in this work. These results provide evidence about the existence of quasi-cyclic variations in the controlled parameters with different periods, from minute to daily. Study of the observational data allows us to assume that in this case the hydrochemical dynamics is caused by direct and reverse energy cascades in a two-dimensional turbulent flow of natural water, in which the impurity subsystem may be stratified.

Two-dimensional non-linear hydrodynamics and nanofluidics

A water monolayer squeezed between two solid planes experiences strong out-of-plane confinement effects while expanding freely within the plane. As a consequence, the transport of such two-dimensional water combines hydrodynamic and nanofluidic features, intimately linked with each other. In this paper, we propose and explicitly solve a non-linear hydrodynamic equation describing two-dimensional water flow with viscosity parameters deduced from molecular dynamic simulations. We demonstrate that the very ability of two-dimensional water to flow in short channels is governed by the second (dilatational) viscosity coefficient, leading to flow compression and velocity saturation in the high-pressure limit. The viscosity parameter values depend strongly on whether graphene or hexoganal boron nitride layers are used to confine 2D water that offers an interesting opportunity to obtain various nanofluids out of the same water molecules just by using alternate materials to fabricate the 2D channels.

Analyticity of rotational traveling capillary–gravity waves with critical layers

We establish real analyticity of the free surface of a two-dimensional steady rotational flow of water with critical layers. The flow is acted upon by gravity and surface tension. We show that any Wloc2,∞-regular free surface is analytic provided the vorticity distribution is analytic. In particular, the surface of a water flow with constant vorticity is analytic.

THE MODEL OF FREE SPREADING A FLOW RAPID BEHIND A RECTANGULAR PIPE

The article considers the free spreading of a turbulent stationary two-dimensional open potential water flow into a wide diverting riverbed behind a non-pressure pipe of a rectangular section. A system of nonlinear partial differential equations of motion has been adopted as the mathematical model of the flow in the physical plane. When moving to the plane of the velocity hodograph, the nonlinear system of equations is transformed into a linear system with respect to partial derivatives. Using the obtained system of equations, various problems along the flow of two-dimensional water streams have been solved analytically. The paper determines the flow kinetics parameter t and the angle q characterizing the direction of the local flow velocity vector at the intersection points of an arbitrary equipotential and an arbitrary current line. The X, Y coordinates of these points are found. The peculiarities of changing the angle θ during the transition of the vertical front of the XD are taken into account.
 Article proposes a module for the transition from a two-dimensional water flow model to a one-dimensional one. This module is necessary for using the laws of flow resistance and taking into account the resistance forces.
 The model proposed in this paper is a development of analytical methods for calculating potential flows with previously unknown boundaries and before the flow expands. It allows determining the entire range of geometric and kinematic parameters of the flow with an error not exceeding 10%.
 The adequacy of the model for all flow parameters improves the accuracy of previously existing methods. This allows the designers of road culverts to increase its reliability.

A complex-analytic approach to kinetic energy properties of irrotational flows

Using methods from complex analysis we obtain some qualitative results for the kinetic energy of two-dimensional irrotational water flows (monotonicity of horizontal averages with depth, location of the extrema).

Large-Amplitude Steady Downstream Water Waves

We study wave-current interactions in two-dimensional water flows of constant vorticity over a flat bed. For large-amplitude periodic traveling gravity waves that propagate at the water surface in the same direction as the underlying current (downstream waves), we prove explicit uniform bounds for their amplitude. In particular, our estimates show that the maximum amplitude of the waves becomes vanishingly small as the vorticity increases without limit. We also prove that the downstream waves on a global bifurcating branch are never overhanging, and that their mass flux and Bernoulli constant are uniformly bounded.

Transient Free Convective Flow of CNT Water Nanofluid with Heat Transfer from a Moving Cylinder

Background: In this paper, transient two-dimensional laminar boundary layer viscous incompressible free convective flow of water based nanofluid with carbon nanotubes (CNTs) past a moving vertical cylinder with variable surface temperature is studied numerically in the presence of thermal radiation and heat generation. Methods: The prevailing partial differential equations which model the flow with initial and boundary conditions are solved by implicit finite difference method of Crank Nicolson type, which is unconditionally stable and convergent. Results: Influence of Grashof number (Gr), nanoparticle volume fraction (φ), heat generation parameter (Q), temperature exponent (m), radiation parameter (N) and time (t) on velocity and temperature profiles are sketched graphically and elaborated comprehensively. Conclusion: Analysis of Nusselt number and Skin friction coefficient is also discussed numerically for both single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs).

Two-dimensional (2D) numerical modelling of rainfall induced overland flow, infiltration and soil erosion: comparison with laboratory rainfall-runoff simulations on a two-directional slope soil flume

Abstract This paper presents a two-dimensional (2D) numerical model of soil erosion and sediment transport resulting from rainfall induced overland flow. It is a spatial and temporal dynamic model combining physical and empirical laws and comprises: i) An overland flow module that solves the two-dimensional unsteady water flow equations on an infiltrating surface; ii) A soil infiltration module that uses a combined Horton-SCS scheme; and iii) A soil erosion and sediment transport module that solves the two-dimensional sediment transport equation, distinguishing between rill erosion, interrill erosion and sediment deposition. The performance of the model was evaluated by comparing its results with observed data from laboratory rainfall-runoff experiments on a two-directional 2.00 × 2.00 m2 soil flume set at 1% and 10% slopes in the x- and y-directions, respectively. The x-direction produced remarkably lower runoff and transported sediments than the y-direction. The numerical model significantly underestimated x-direction lower values of runoff and transported sediments. However, in the y-direction the model presented very good performance. Overall, in total terms (x- plus y-direction), the numerically simulated graphs of runoff and sediment transport were in very good agreement with corresponding experimental measurements, demonstrating the laboratory proof-of-concept of the model.

Two-dimensional liquid water flow through snow at the plot scale in continental snowpacks: simulations and field data comparisons

Abstract. Modeling the multidimensional flow of liquid water through snow has been limited in spatial and temporal scales to date. Here, we present simulations using the inverse TOUGH2 (iTOUGH2) model informed by the model SNOWPACK, referred to as SnowTOUGH. We use SnowTOUGH to simulate snow metamorphism, melt/freeze processes, and liquid water movement in two-dimensional snowpacks at the plot scale (20 m) on a sloping ground surface during multi-day observation periods at three field sites in northern Colorado, USA. Model results compare well with sites below the treeline and above the treeline but not at a site near the treeline. Results show the importance of longitudinal intra-snowpack flow paths (i.e., parallel to ground surface in the downslope direction and sometimes referred to as lateral flow), particularly during times when the snow surface (i.e., snow–atmosphere interface) is not actively melting. At our above-treeline site, simulations show that longitudinal flow can occur at rates orders of magnitude greater than vertically downward percolating water flow at a mean ratio of 75:1 as a result of hydraulic barriers that divert flow. Our near-treeline site simulations resulted in slightly less longitudinal flow than vertically percolating water, and the below-treeline site resulted in negligible longitudinal flow of liquid water. These results show the increasing influence of longitudinal intra-snowpack flow paths with elevation, similar to field observations. Results of this study suggest that intra-snowpack longitudinal flow may be an important process for consideration in hydrologic modeling for higher-elevation headwater catchments.

Two-dimensional plan source, vortex and vortex source

Modern hydraulic structures require highly reliable water-supply channels, free-flow pipes and open spillways. Therefore, they must be built with considering dynamic properties of the affecting flow. The theory of one-dimensional open flows cannot answer many questions raised by the hydraulic engineering practice. Hence, this paper considers two-dimensional graphical open flows, with separate particular models following from the general theory, important for designing couplings, curves in more complex constructions (two different channels) required in hydraulic engineering (Hydraulics technical structures) (HTS). And the more such models are obtained, the more opportunities will appear for scientists and designers to synthesize more complex structures required in HTS.This study identifies three elements, and three simplest models of two-dimensional graphic open water flows similar to flat models: a source, a vortex and a vortex source. The number of such individual models will continue to increase and expand the range of possibilities for designing more complex water technical objects (WTO).The models are obtained analytically from solving the system of two-dimensional graphical open potential water flows in the plane of the velocity hodograph. The elementary construction of each model includes an analytical solution for the potential function and the stream function.The paper considers the problem of determining the parameters of a two-dimensional graphical open water flow at any point in the flow: a source, a vortex, a vortex source. The practical significance of the models lies in the possibility to use the results by the designers of hydraulic structures both at the first stage of solving problems and at the subsequent ones, with flow resistance forces taken into account.The study also represents the transition method from the plane of the flow velocity hodograph to the flow diagram by integrating the models in the plane of the velocity hodograph from the condition of the connection between the considered planes.

Simulation of the process of free spreading of a two-dimensional water flow behind pressure-free holes

Introduction. Construction of hydraulic structures must meet high reliability requirements applicable to water supply channels, free-flow pipes, and open spillways. Any analysis of hydraulic structures must take account of the dynamic properties of flows that the structures accommodate. The theory of one-dimensional free flows, used in practice, has a number of general guidelines, but lack any details. The co-authors take advantage of the theory of two-dimensional free flows, namely, the method of characteristics proposed and developed in the works of I.A. Sherenkov.
 Materials and methods. In her works, B.T. Emtseva suggests that a uniform flow can be coupled with a general flow only with the help of an intermediate “simple wave” flow, but this statement has no proof. We identified and analyzed a general flow in the plane of the hodograph. Thereafter, characteristics of the first family of the flow were determined. A transition to the physical plane of the flow allowed to determine the coordinates of the points of characteristics of the second family. This allowed to find the coordinates of the points of the extreme streamline and to determine its geometry.
 Results. The proposed mathematical model complied with the system of equations, describing the flow, and the boundary conditions when it was applied to the boundary problem of the free spreading of a stormy, potential, two-dimensional in plan, free, stationary water flow and its free inflow into a wide horizontal smooth channel.
 Conclusions. The concept of a general flow (previously unknown) and equations of motion in the plane of the velocity hodograph made it possible to theoretically prove its applicability to the problem of free flow spreading. A simple analytical solution is obtained in the plane of the velocity hodograph. The theoretical significance of this mathematical model consists in the possibility of its step-by-step application to practical problems and its complication from the identification of the main regularities of a simplified model of a potential flow to the practical use of simulation results. The implementation of the methodology in the form of software will make it usable by designers of hydraulic structures. This is the first stage of problem solving, and at further stages resistance will be taken into account.

Research and Application on Mathematical Model of Ship Manoeuvring Motion under Shallow water effect

When ships sail on the inland river in mountainous areas, the limited water depth can frequently lead to shallow water effect. To some extent, safety and maneuverability of shipping will be impacted. Consequently, it’s necessary to consider the shallow water effect when studying the ship ascending rapids in mountainous rivers. By considering the impact of shallow water effect, a three freedoms maneuvering mathematical model based on shallow water effect was established in this paper on the basis of two-dimensional water flow mathematical model. Application of the model was implemented on the regulation of the waterway in Suoluo rapids section of the Lancang River to obtain ship navigating parameters (helm angle, drift angle, heading angle, ship’s speed and speed against the water) for comparative analysis. Results show that the ship can reduce the impact of shallow water effect by adjusting the rudder angle and reducing the ship speed when navigating in shallow and narrow channel. The obtainment of the voyage line diagram by the simulation of ship’s maneuverability test validates that the ship can ascending rapids through self-propulsion after the river regulation.

Soil water/salt balance and water productivity of typical irrigation schedules for cotton under film mulched drip irrigation in northern Xinjiang

Film mulched drip irrigation (FMDI) has clear benefits for saving water and promoting cotton production in Xinjiang, China. Due to the complicated transport processes for soil water and salt under FMDI, it is still challenging to systematically answer the questions such as the soil water and salt balance in the root zone, cotton yield and water productivity (WP) under typical planting modes and irrigation schedules. Previously, we proposed a HYDRUS-2D model with modified root water uptake (RWU) function and simulated the two-dimensional soil water flow and solute transport in cotton fields under FMDI, but we ignored the effects of the cotton yield and WP. From the perspective of smart irrigation, it is necessary to evaluate the effects of irrigation on crop production, WP, and soil environments. Thus, in the present study, our HYDRUS-2D model coupled with a validated crop water production function was applied to evaluate the effects of typical irrigation schedules and the antecedent soil salinity distributions on the soil water/salt balance, and plant water status, and leaching fraction, as well as the cotton yield and WP under FMDI in 36 scenarios. These scenarios included two antecedent soil salinity distributions (AS), six irrigation amounts (IA) and three irrigation intervals (IF). Compared with the lower AS scenarios, the higher AS scenarios obtained lower cotton transpiration and evapotranspiration but higher evaporation, drainage, and soil water storage, and the crop water status and leaching fraction were also increased due to the soil salt stress restricting RWU. The salt balance results indicated the current irrigation scheduling under FMDI leads to desalination processes in different scenarios. Moreover, the cotton yield and the corresponding WP for cotton (WPETa) and irrigation (WPI) were estimated. Under different AS scenarios, binary quadratic regression equations were developed based on IA and IF data to predict the cotton yield, WPETa, and WPI. Appropriate irrigation strategies are recommended based on the results. Our results could provide a scientific basis for optimizing irrigation schedules and improving the understanding of irrigation management under FMDI among local farmers in Xinjiang.

Transport characteristics of non-cohesive sediment with different hydrological durations and sediment transport formulas

River sediment transport is an important global environmental issue, for it leads to waterway sedimentation, ecological degradation, and river geomorphologic evolution, its quantification is of the highest importance for river and watershed management. However, it remains unclear what the applicability of different sediment transport formulas in sediment transport process, and what the characteristics of non-cohesive sediment transport processes with different hydrological durations. This study developed a two-dimensional (2D) surface water Flow Model (FM) coupled with a Sediment Transport (ST) model in the MIKE 21 modelling system. The characteristic difference on simulated non-cohesive sediment transport under different sediment concentrations, hydrological durations, and sediment transport formulas were quantified by calculating the bed load, suspended load, and bed level change. Results indicated that the bed load and suspended load using the Engelund and Fredsøe formula were significantly lower than the Van Rijn formula for individual rainfall simulation scenarios. With the increase in peak flow, both suspended load and bed load first increased and then decreased. In the long-term duration simulations, high sediment concentrations were accompanied by higher bed load and lower suspension load for the Engelund and Fredsøe formula, but by lower bed load and suspension load for the Van Rijn formula. The high sediment concentrations resulted in a higher erosion rate, and low sediment concentrations resulted in a higher deposition rate. The two formulas had a high degree of consistency in seasonality and the bed level changes in spring and summer were mainly sedimentary, while in autumn and winter they were mainly erosive. The Engelund and Fredsøe formula produced high riverbed erosion capacity at low discharge, but the Van Rijn formula had high erosion capacity at high discharge.

МЕТОД АНАЛОГИЙ МЕЖДУ ГИДРАВЛИКОЙ ДВУХМЕРНЫХ В ПЛАНЕ ВОДНЫХ ПОТОКОВ И ГАЗОВОЙ ДИНАМИКОЙ

Real potential two-dimensional flows of practical hydraulics are considered, which can be considered with a certain accuracy as two-dimensional in terms, which confirms the relevance of the work. It is proposed to use the method of analogies when applying gas dynamics equations in hydraulics. An important result was obtained for the development of the analytical theory of two-dimensional potential water flows.

МЕТОД РЕШЕНИЯ ЗАДАЧИ СВОБОДНОГО РАСТЕКАНИЯ БУРНОГО ПОТЕНЦИАЛЬНОГО ПОТОКА ЗА БЕЗНАПОРНОЙ ТРУБОЙ

The paper substantiates the design scheme and General formulation of the method for solving the problem of coupling various flows necessary in the practice of hydraulic engineering construction of GTS.
 In the scheme given in the article, when solving the problem of free spreading of a turbulent two-dimensional water flow with a uniform flow, a simple wave borders, and not a General flow, such as a radial flow. The analysis of the three characteristic zones of the flow. It is proved that a turbulent flow under free spreading transforms into a radial one, and the elements of the radial expansion of the flow are determined. The equations for determining the geometric shape and flow parameters for all three sections of the flow with its free spreading are obtained. The research results in this paper are obtained for the first time and complete the research started in the works of other authors.

Rainfall Runoff and Dissolved Pollutant Transport Processes Over Idealized Urban Catchments

Urban stormwater runoff is often considered as one of the most significant contributors to water pollution. Particulates are commonly regarded as the primary form of pollutant transport in the urban environment, but the contribution from the dissolved pollutants can also be significant. This study aims to investigate the dissolved pollutant transport process over urban catchments, especially the effects of buildings and spatial distribution of pollutants. The concept of “exchange layer” has been adopted and an equation has been proposed to describe the release process of dissolved pollutant from the exchange layer to the runoff water. A horizontal two-dimensional water flow and pollutant transport model has been developed for predicting dissolved pollutant runoff based on the shallow water assumptions and the advection-diffusion equation. A series of laboratory experiments have been conducted to verify the proposed model. It has been demonstrated that both the rainfall runoff and the pollutant runoff can be predicted accurately. Buildings slow down the runoff and pollutant transport processes, especially when buildings are staggered. The non-uniform distribution of pollutants over the catchment greatly influences the pollutant transport process over the catchment. This work provides insight into the effects of buildings and initial pollutant distribution on the dissolved pollutant transport phenomenon, which can help better design the pollution mitigation strategies.