A Note on the Solution of Water Wave Scattering Problem Involving Small Deformation on a Porous Channel-Bed

The solution of water wave scattering problem involving small deformation on a porous bed in a channel, where the upper surface is bounded above by an infinitely extent rigid horizontal surface, is studied here within the framework of linearized water wave theory. In such a situation, there exists only one mode of waves propagating on the porous surface. A simplified perturbation analysis, involving a small parameter ε （≤1） , which measures the smallness of the deformation, is employed to reduce the governing Boundary Value Problem （BVP） to a simpler BVP for the first-order correction of the potential function. The first-order potential function and, hence, the first-order reflection and transmission coefficients are obtained by the method based on Fourier transform technique as well as Green＇s integral theorem with the introduction of appropriate Green＇s function. Two special examples of bottom deformation： the exponentially damped deformation and the sinusoidal ripple bed, are considered to validate the results. For the particular example of a patch of sinusoidal ripples, the resonant interaction between the bed and the upper surface of the fluid is attained in the neighborhood of a singularity, when the ripples wavenumbers of the bottom deformation become approximately twice the components of the incident field wavenumber along the positive x -direction. Also, the main advantage of the present study is that the results for the values of reflection and transmission coefficients are found to satisfy the energy-balance relation almost accurately.

Two-Dimensional Mathematical Model of Tidal Current and Sediment for Oujiang Estuary and Wenzhou Bay

A 2-D mathematical model of tidal current and sediment has been developed for the Oujiang Estuary and the Wenzhou Bay. This model accomodates complicated features including multiple islands, existence of turbidity, and significant differ-ence in size distribution of bed material. The governing equations for non-uniform suspended load and bed load transport are presented in a boundary-fitted orthogonal curvilinear coordinate system. The numerical solution procedures along with their initial conditions, boundary conditions, and movable boundary technique are presented. Strategies for computation of the critical condition of deposition or erosion, sediment transport capacity, non-uniform bed load discharge, etc. are suggested. The model verification computation shows that, the tidal levels computed from the model are in good agreement with the field data at the 18 tidal gauge stations. The computed velocities and flow directions also agree well with the values measured along the totally 52 synchronously observed verticals distributed over 8 cross sections. The coraputed tidal water throughputs through the Huangda'ao cross section are close to the measured data. And the computed values of bed deformation from Yangfushan to the estuary outfall and in the outer-sea area are in good agreement with the data observed from 1986 to 1992. The changes of tidal volumes through the estuary, velocities in different channels and the bed form due to the influence of the reclamation project on the Wenzhou shoal are predicted by means of this model.

Non-capacity transport of non-uniform bed load sediment in alluvial rivers

Rivers often witness non-uniform bed load sedim ent transport. For a long tim e, non-uniform bed load transport has been assum ed to be at capacity regime determined exclusively by local flow. Yet whether the capacity assumption for non-uniform bed load transport is justified remains poorly understood. Here, the relative time scale of non-uniform bed load transport is evaluated and non-capacity and capacity models are compared for both aggradation and degradation cases with observed data. As characterized by its relative time scale, the adaptation of non-uniform bed load to capacity regime should be fulfilled quickly. However, changes in the flow and sedim ent inputs from upstream or tributaries hinder the adaptation. Also, the adaptation to capacity regime is size dependent, the finer the sediment size the slower the adaptation is, and vice versa. It is shown that the capacity model may entail considerable errors compared to the non-capacity model. For modelling of non-uniform bed load, non-capacity modelling is recommended, in which the temporal and spatial scales required for adaptation are explicitly appreciated.

2-D NUMERICAL SIMULATION OF CRUSH BEDROCK RIVER

In this paper, the erosion-resisting coefficient was introduced to computebed deformation in a crush bedrock river. In the case of crush bedrock, there has been no propercontrol equation to describe bed stability, which leads to difficulty in calculation of the beddeformation with conventional methods. The data from field survey were used to give thee-rosion-resisting capability with an appropriate coefficient. After the determination oflongitudinal distribution expressed by polynomial regression and transversal distribution expressedby normal distribution function, the plane distribution of erosion-resisting coefficient in a crushbedrock river was obtained. With the computational results from a 2-D horizontal flow mathematicalmodel, the erosion-resisting coefficient and controlling condition of local stability were employedto compute the values of bed deformation when riverbed is stable. The above method was applied in acase study, and the computational results of flow and bed deformations are in good a-greement withphysical model test data.

2-D FLOW AND SEDIMENT SIMULATION FOR THE FLOOD REGULATION OF A RESERVOIR WITH WATER INTAKE

In this paper, the flood regulation by operating the downstream sluice gates for a reservoir with a water intake is studied. The two-dimensional depth-averaged flow equations are solved by the boundary fitted finite volume method (FVM) based on MacCormack prediction-correction scheme. The bed deformation caused by both the bed load and incoming suspended sediment is determined in a coupled way. The model is used to simulate the practical flood regulation operation of a reservoir. The results have been compared with the physical experiment.