This article presents a mathematical model of the plane evolution of alluvial meandering streams,through downstream migration and lateral expansion of meander loops.Under the conditions prevailing in natural streams,the channel centerlines follow sine-generated curves,with an assumed steady-state turbulent and subcritical flow,of large width-to-depth ratio（≥ 15,for example） and small Froude number（Fr ）.The plane deformation of the channel is caused by the action on the banks of the convective vertically-averaged meandering flow.The growth（migration and expansion） of meander loops is attributed to the regime-trend.The computational results of the model show that the obtained migration and expansion patterns of the meander loops are in good agreement with those of observations and measurements in similar meandering streams.
The simulation of a one-dimensional river network needs to solve the Saint-Venant equations,in which the variable parameters normally have a significant influence on the model accuracy.A Trial-and-Error approach is a most commonly adopted method of parameter calibration,however,this method is time-consuming and requires experience to select the appropriate values of parameter.Consequently,simulated results obtained via this method usually differ between practitioners.This article combines a hydrodynamic model with an intelligent model originated from the Genetic Algorithm（GA） technique,in order to provide an intelligent simulation method that can optimize the parameters automatically.Compared with current approaches,the method presented in this article is simpler,its dependence on field data is lower,and the model accuracy is higher.When the optimized parameters are taken into the hydrodynamic numerical model,a good agreement is attained between the simulated results and the field data.
The velocity dip phenomenon may occur in a part of or in the whole flow field of open channel flows due to the secondary flow effect. Based on rectangular flume experiments and the laser Doppler velocimetry, the influence of the distance to the sidewall and the aspect ratio on the velocity dip is investigated. Through application of statistical methods to the experimental results, it is proposed that the flow field may be divided into two regions, the relatively strong sidewall region and the relatively weak sidewall region. In the former region, the distance to the sidewall greatly affects the location of maximum velocity, and, in the latter region, both the distance to the sidewall and the aspect ratio influence the location of the maximum velocity.
The hydrodynamics of a single jet and four tandem jets in a cross flow are simulated by using the Computational Fluid Dynamics （CFD） software Fluent. The realizable model is used to close the Reynolds-Averaged equations. The flow characteristics of the jets, including the jet trajectory, the velocity field and the turbulent kinetic energy are obtained with various jet-to-cross flow velocity ratios in the range of 2.38-17.88. It is shown that a single jet penetrates slightly deeper than the first jet in a jet group at the same , although the difference decreases with the decrease of . It is also found that the way in which the velo-city decays along the centerline of the jet is similar for both a single jet and the first jet in a group, and the speed of the decay increases with the decrease of . The downstream jets in a group are found to behave differently due to the sheltering effect of the first jet in the group. Compared with the first jet, the downstream jets penetrate deeper into the cross flow, and the velocity decays more slowly. The circulation zone between the two upstream jets in the front is stronger than those formed between the downstream jets. The Turbulent Kinetic Energy （TKE） sees a distinct double-peak across the cross-sections close to each nozzle, with low values in the jet core and high values in the shear layers. The double-peak gradually vanishes, as the shear layers of the jet merge further away from the nozzle, where the TKE assumes peaks at the jet centerline.
Sand ripples are common bedforms. The formation of sand ripples is related to flow conditions; different flow conditions cause different ripple geometries. The main aim of this study was to assess the relationship between flow intensity and two-dimensional ripple geometry characteristics. The experiments were carried out in a laboratory flume with natural sand whose bulk density Ps was 2 650 kg/m3 and median diameter D50 was 0.41 mm. The Froude number （Fr）, a flow intensity parameter, varied from 0.16 to 0.53, entirely within the subcritical range. Two-dimensional sand ripple geometry was measured and processed via statistical methods. The probability distributions of ripple length and height were obtained with different flow conditions. Through dimensionless analysis, the relationship between the flow intensity parameter （grain size Reynolds number Re. ） and the sand ripple geometry characteristic length （ ∧ ） and height （ △ ） was analyzed, and two formulas were obtained： ∧/D50 = 191.76Re 0.3 and △/D50 = 1.97Re 1.3, which are consistent with previous research results.
