Random Displacement Method Research Articles

Characterizing suspended particle dispersion in wetland flows: Impact of settling velocity and vegetation factor

Predicting the dispersion process of suspended particles with settling velocity in wetland flows holds significant implications for various ecological and environmental applications. This study analytically investigates the dispersion process of fine settling particles in wetland flows due to an instantaneous release source through the asymptotic expansion method. The effect of high-order terms is incorporated. The impact of vegetation factor and settling velocity on characteristic coefficients (including mass retained in the flow, advection velocity, longitudinal dispersion coefficient, skewness, and kurtosis), vertical mean, and two-dimensional concentration distribution are analyzed. Analytical solution is validated by numerical result through random displacement method. Results demonstrate that the vegetation factor does not influence the vertical mass distribution, and a larger settling velocity results in a higher concentration of mass in the bed wall layer. The longitudinal dispersion coefficient does not exhibit a monotonic relationship with the settling velocity. The position of mass centroid of the vertical mean concentration is biased more to the upstream with the larger settling velocity. At larger times, the vertical mean concentration approximates a normal distribution, with skewness and kurtosis nearing zero. Under the influence of settling velocity, the bed wall layer exhibits a high concentration zone in the two-dimensional concentration distribution. These results can help the understanding of sediment dynamics, nutrient cycling, pollutant transport associated with the wetland flows.

ПРИМЕНЕНИЕ МЕТОДОВ ИСКУССТВЕННОГО ИНТЕЛЛЕКТА ДЛЯ КОМПЬЮТЕРНОГО МОДЕЛИРОВАНИЯ ФРАКТАЛЬНЫХ ПОВЕРХНОСТЕЙ

The paper considers the possibility of using artificial intelligence methods for computer modeling of fractal surfaces. Fractals act as a mathematical model for creating a random surface relief. The random profile is constructed using the random displacement method, which is an algorithm for generating random functions with a spectrum. Surfaces are defined with the help of data arrays, which are checked by the self-similarity condition. Based on the defined arrays, models are built using the Weierstrass function. The algorithm for constructing surfaces has been refined and improved using machine learning neural network generative models. Thus, instead of simply creating a fractal surface using random functions, the generator creates fractal surfaces based on the distribution learned during training. The verification criterion is an algorithm based, in general, on a mathematical Monte Carlo method. The obtained results show the realism of the constructed fractal surfaces using neural networks. The models of the obtained surface reliefs can be used in modeling contact mechanics, mechanics of deformable solid bodies.

Numerical simulation of velocity distribution and pollution retention in flexible submerged vegetated channel

Vegetation is an important factor that affects the hydrodynamics of river channels. Using hydrodynamic and water quality models in vegetated channels can help better understand the problem of river water pollution. In this paper, the lattice Boltzmann method (LBM) is used to simulate the hydrodynamics of flexible vegetated channels, and the projected area characteristics of flexible vegetation are input into the model to obtain better simulation results for the vertical velocity distribution. At the same time, the random displacement method is used to simulate the transport law of pollutants and calculate the pollutant retention rate under different vegetation projected area characteristics. The results show that both vegetation species and average flow velocity have significant effects on pollutant retention efficiency. This method helps to optimize the selection of species, density, and distribution of river vegetation.

Solute dispersion in an open channel turbulent flow: Solution by a generalized model

In this work, the classic problem in environmental hydraulics of solute dispersion in an open channel turbulent flow is analytically investigated by Gill’s generalized dispersion model to account for all the basic characteristics as dispersivity, skewness and kurtosis of the mean concentration evolution. A complete solution is presented for the whole process and three typical time-scales are determined: after a convection-dominated initial stage, a transient stage with essential transverse diffusion effect begins at a dimensionless time-scale of t∼0.1 and gives way to an asymptotic stage of normal distribution of mean concentration from t∼1, slowly approaching to a final stage with relative uniformity in transverse concentration distribution at t∼10. Two-dimensional concentration distribution shows that there is a high concentration zone near the free water surface at a small time due to the small velocity gradient, indicating that it is not enough to characterize the dispersion process by the mean concentration, especially for the transient stage. The obtained analytical solutions of concentration distribution consist well with numerical simulation results by the random displacement method (RDM).

Transient Solute Dispersion in Wetland Flows With Submerged Vegetation: An Analytical Study in Terms of Time‐Dependent Properties

AbstractPredicting the concentration distribution of solute transport in vegetated flows is significant for associated environmental applications in water resources. While a semianalytical study has been made for the steady dispersion with a continuous release (Rubol et al., 2016, https://doi.org/10.1002/2016WR018907), an in‐depth analytical investigation has yet to be performed for the more complicated case of transient dispersion due to an instantaneous release. In regard to the pioneering benchmark observation (Murphy et al., 2007, https://doi.org/10.1029/2006WR005229) of transient solute dispersion in a submerged vegetated flow for an instantaneous source release at the top of the canopy, an extensive analytical effort is paid in this work to derive the time‐dependent basic properties and to investigate the temporal evolution of concentration distribution. Obtained large‐time asymptotic dispersivities agree well with available experimental results (Murphy et al., 2007, https://doi.org/10.1029/2006WR005229), with higher significance ( , ) for correlation between analytical results and experimental data. Analytical solutions covering effects of dispersivity, skewness, and kurtosis of detailed concentration distribution are compared satisfactorily with numerical results obtained by the random displacement method. The findings illuminate the applicability of this analytical approach in environmental risk assessment and water quality management.