Solute transport simulation in hyporheic zone based on time-space fractional order model
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Abstract:
hyporheic zone is a saturated sediment layer with the interaction between surface and groundwater in rivers.The riverbed medium is highly inhomogeneous and the flow direction is complex.Solute diffusion is prone to exhibit abnormal diffusion characteristics of trailing and non-Gaussian distribution.It is difficult to describe such diffusion characteristics by traditional convection dispersion equation.Therefore,a space-time fractional derivative term is introduced in the hyporheic zone solute transport model,and the applicability of the fractional derivative method in the hyporheic zone solute transport simulation is discussed from one-dimensional and two-dimensional perspectives,respectively. The influence of fractional order on the physical meaning of solute transport and the sensitivity of fractional order to physical parameters of solute transport were discussed.A two-dimensional fractional-order derivative model was also established to compare the simulation results of different dimensions to the fractional-order derivative method with field tracing experiments. The physical significance of fractional order is analyzed and it is found that timefractional orderαreflects the lagging effect of the solute transport process and makes the breakthrough curve have obvious trailing characteristics.Space fractional-order β characterize the phenomenon of solute hyper-diffusion caused by inhomogeneity of media.The results of parameter sensitivity -analysis show that the fractional-order method is more sensitive to velocity and dispersion coefficient than the traditional convection-dispersion equation.It overcomes the defect that the traditional integer-order method can not accurately describe the strong inhomogeneity in the hyporheic zone.Field tracing test shows that the traditional two-dimensional integer-order convection-diffusion equation has shortcomings in characterizing the solute transport process due to strong inhomogeneity and multi-dimensional flow in the hyporheic zone.The one-dimensional fractional derivative model can more accurately calculate the peak time of solute concentration and describe the tailing phenomenon of the penetration curve when simulating the solute transport in the hyporheic zone.Affected by parameter settings in different directions,the simulation results of the two-dimensional fractional-order model are inferior to the one-dimensional fractional-order model.However,more point-level solute data can be observed on the isometric plane by the two-dimensional fractional-order model and it would be more applicable without the difference of flow and medium parameters caused by medium differences in the depth direction. Although the applicability of one-dimensional and two-dimensional fractional derivative models differs in different scenarios,the introduction of fractional derivative improves the simulation effect of traditional convection-dispersion equations and is suitable for special media with strong inhomogeneity and complex flow conditions,such as hyporheic zone.
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