Plug-flow/dispersion model of longitudinal dispersion

A modified Fickian plug-flow/dispersion model (P/D model) is developed in this study. In P/D model, the flow process is divided into two belts, plug flow belt and dispersion belt. P/D model is very similar to Fickian model and rather perfect. The prediction by P/D model can be always consistent with experimental data in river, flume, and pond, even though the data are much skew. Therefore, P/D model is better than Fickian model and other dispersion models.

Two timescales for longitudinal dispersion in a laminar open-channel flow

At small dimensionless timescales T（= tD/H^2）, where t is the time, H is the depth of the channel and D is the molecular diffusion coefficient, the mean transverse concentration along the longitudinal direction is not in a Gaussian distribution and the transverse concentration distribution is nonuniform. However, previous studies found different dimensionless timescales in the early stage, which is not verified experimentally due to the demanding experimental requirements. In this letter, a stochastic method is employed to simulate the early stage of the longitudinal transport when the Peclet number is large. It is shown that the timescale for the transverse distribution to approach uniformity is T= 0.5, which is also the timescale for the dimensionless temporal longitudinal dispersion coefficient to reach its asymptotic value, the timescale for the longitudinal distribution to approach a Gaussian distribution is T= 1.0, which is also the timescale for the dimensionless history mean longitudinal dispersion coefficient to reach its asymptotic value.

EXPERIMENTAL INVESTIGATIONS ON LONGITUDINAL DISPERSION CHARACTERISTICS OF TIDAL RIVERS

The longitudinal dispersion characteristics of tidal rivers areexperimentally investigated in a water channel. The longitudinal dispersion features and influentialfactors on pollutant in various stages of a tidal period in natural rivers are studied; the valueranges and variation trends of the longitudinal dispersion coefficient are obtained by means ofconcentration measurement. The results can provide important parameters for establishing the waterquality mathematical models in tidal rivers.

Shear Flow Dispersion Under Wave and Current

The longitudinal dispersion of solute in open channel flow with short period progressive waves is investigated. The waves induce second order drift velocity in the direction of propagation and enhance the mixing process in concurrent direction. The 1-D wave-period-averaged dispersion equation is derived and an expression for the wave-current induced longitudinal dispersion coefficient （WCLDC） is propased based on Fiscber＇ s expression （1979） for dispersion in unidirectional flow. The result shows that the effect of waves on dispersion is mainly due to the cross-sectional variation of the drift velocity. Furthermore, to obtain a more practical expression of the WCLDC, the longitudinal dispersion coefficient due to Seo and Cheong （1998） is modified to incluee the effect of drift velocity. Laboratory experiments have been conducted to verify the propased expression. The experimental results, together with dimensional analysis, show that tbe wave effect can be reflected by the ratio between the wave amplitude and wave period. A comparative study between the cases with and without waves demonstrates that the magnitude of the longitudinal dispersion coefficient is increased nnder the presence of waves.

Longitudinal dispersive coefficient in channels with aquatic vegetation:A review

The determination of longitudinal dispersion coefficient in rivers is necessary for pollution control,environmental risk assessment,and management.In rivers with aquatic vegetation,the flow field is remarkably modified by canopies,which affects velocity profiles and dispersion characteristics dominated by the heterogeneity of the velocity field.The dispersion is deduced from lateral and vertical longitudinal velocity gradients for compound channels with vegetated floodplains and rectangular channels with river-wide vegetation,respectively.Although many efforts have been exerted to clarify the dispersion process in different conditions and predict the diffusion of contaminants in vegetated rivers,no studies have introduced it systematically.This study reviews the dispersion coefficient characteristics,including magnitude,main impacted factors,and relationships with flow and vegetation features,in channels with aquatic canopies considering the variation of impact factors changing with the different vegetation and river morphology scenarios.Several typical methodologies for determining longitudinal dispersion coefficients are also summarized to understand the dispersion processes and concepts.Apart from the pioneer outcomes of previous studies,the review also emphasizes the deficiency of existing studies and suggests possible future directions for improving the theory of dispersion in vegetated channels.

Determination of groundwater solute transport parameters in finite element modelling using tracer injection and withdrawal testing data

The groundwater tracer injection and withdrawal tests are often carried out for the determination of aquifer solute transport parameters.However,the parameter analyses encounter a great difficulty due to the radial flow nature and the variability of the temporal boundary conditions.An adaptive methodology for the determination of groundwater solute transport parameters using tracer injection and withdrawal test data had been developed and illustrated through an actual case.The methodology includes the treatment of the tracer boundary condition at the tracer injection well,the normalization of tracer concentration,the groundwater solute transport finite element modelling and the method of least squares to optimize the parameters.An application of this methodology was carried out in a field test in the South of Hanoi city.The tested aquifer is Pleistocene aquifer,which is a main aquifer and has been providing domestic water supply to the city since the French time.Effective porosity of 0.31,longitudinal dispersivity of 2.2 m,and hydrodynamic dispersion coefficients from D=220 m^(2)/d right outside the pumping well screen to D=15.8 m^(2)/d right outside the tracer injection well screen have been obtained for the aquifer at the test site.The minimal sum of squares of the differences between the observed and model normalized tracer concentration is 0.00119,which is corresponding to the average absolute difference between observed and model normalized concentrations of 0.0355(while 1 is the worst and 0 is the best fit).

Effect of vegetation on flow structure and dispersion in strongly curved channels

The effect of vegetation on the flow structure and the dispersion in a 180 o curved open channel is studied. The Micro ADV is used to measure the flow velocities both in the vegetation cases and the non-vegetation case. It is shown that the velocities in the vegetation area are much smaller than those in the non-vegetation area and a large velocity gradient is generated between the vegetation area and the non-vegetation area. The transverse and longitudinal dispersion coefficients are analyzed based on the experimental data by using the modified N- zone models. It is shown that the effect of the vegetation on the transverse dispersion coefficient is small, involving only changes of a small magnitude, however, since the primary velocities become much more inhomogeneous with the presence of the vegetation, the longitudinal dispersion coefficients are much larger than those in the non-vegetation case.

A random walk simulation of scalar mixing in flows through submerged vegetations

The scalar transport phenomena in vertical two-dimensional flows are studied using the random walk method. The established Lagrangian model is first applied to study the idealized longitudinal dispersion in open channels, before being used to investigate the scalar mixing characteristics of the flows through submerged vegetations. The longitudinal dispersion coefficients of the fully-developed boundary layer flows, with and without vegetations, are calculated based on the positions of the particles. A convenient way of incorporating the effects of vegetations is proposed, where all the flow parameters are regarded to be continually distributed over the depth. The simulation results show high accuracy of the developed random walk method, and indicate that the new method of accounting for the vegetation effects is appropriate for all the test cases considered. The predicted longitudinal dispersion coefficients agree well with the measurements. The merit of the new method is highlighted by its simplicity and efficiency in comparison with the conventional method that assumes the discontinuous distribution of the flow parameters over the depth.