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Numerical modeling of upstream propagation of a positive surge wave in an open-channel flow caused by a sudden rise of downstream water level, either by gate operation or by tidal influence, remains an important challenge from many aspects. A perusal of literature suggests that the Serre-Green-Naghdi (SGN) models have not been methodically explored for a positive surge flow modeling. In this study, the SGN equations for variable bed profiles are solved for simulating the positive surge waves. The governing equations are reformulated in the form of a conservation law, which is solved using a hybrid finite volume-finite difference method. The eddy-viscosity type wave breaking model is coupled with the governing equations for simulating a breaking surge. The performance of second- and fourth-order time stepping schemes and second- and fourth-order accurate schemes for determining the numerical flux is assessed. The results indicate that using an overall fourth-order accurate scheme is preferred for an accurate depiction of the positive surge waves. A comparison is also made with laboratory observations from a wide range of experiments conducted under different discharge, Froude number and bed slope conditions, which demonstrates that the proposed model can accurately reproduce the key free surface characteristics corresponding to positive surge waves. The importance of computing an accurate initial gradually varied flow profile before applying the transient downstream condition, such as a gate closure, is highlighted. Further, the significance of considering full non-linearity is demonstrated through numerical tests as the weakly non-linear Boussinesq-type equations are found to perform poorly in predicting the secondary undulations for an undular surge. The non-hydrostatic pressure field occurring during the propagation of an undular surge has rarely been reported from laboratory experiments. In this study, the bed pressure beneath a propagating undular surge is measured and compared with that computed according to the SGN equations. Finally, the results obtained from the proposed SGN model are compared with those obtained from Large Eddy Simulation results available in the literature.

Summary The areas of glacial lakes in the Himalayas continue to increase alarmingly due to global warming with consequent risk of glacial lake outburst flood (GLOF). The outburst is most common for moraine-dammed lakes as a result of a failure of the dam by overtopping and erosion or piping due to seepage. In the present context, GLOF events, especially for the moraine dam failure process needs to be predicted to assess the drastic and detrimental impacts on the downstream river valley. This study focuses on validating an integrated model for simulating the failure of moraine dam by overtopping and erosion using a coupled numerical simulation model. The proposed numerical methodology is validated with the data from experiments in laboratory scale physical models. The results of the model are compared for both the erosional profiles during collapse of the dam and the resulting outflowing flood hydrograph. The primary finding is that the moraine dam height and the volume of the lake upstream of the dam are the most sensitive parameters influencing the GLOF peak. The model is also applied to the field problem of the Tangjiashan lake outburst and dam failure and shows reasonably good agreement with observations. The validated model is also run for the South Lhonak glacial lake in the Sikkim Himalayas, India to obtain the probable flood hydrograph in case of failure of the moraine dam.

A two-dimensional cell-centred finite volume model for quadrilateral grids is presented. The solution methodology of the depth-averaged shallow water equations is based upon a Godunov-type upwind finite volume formulation, whereby the inviscid fluxes of the system of equations are obtained using the HLL Riemann solver. A simple yet precise analytical expression is presented to compute hydrostatic flux through an interface of a quadrilateral cell in order to achieve exact balance between flux gradient and bed slope source terms under still water condition. A multidimensional gradient reconstruction procedure and a continuously differentiable multidimensional slope limiter based on a wide computational stencil are proposed to maintain second-order spatial accuracy. The proposed second-order scheme is shown to be more accurate even when distorted grids are used and is therefore more suitable for practical applications. The presented model is verified and validated by solving a wide variety of test cases having analytical solutions and laboratory measurements.