| As the direct boundary between land and ocean,the hydrodynamic properties in the swash zone are complicated,contributing to various coastal issues such as the coastal structure design,sediment transport and geomorphic evolution,and coastal biochemical processes.It is of great scientific significance and engineering application value to study the hydrodynamic properties and mechanism of bore-induced wave movement in the swash zone.As for the theoretical study of the wave motion in the swash zone,the hydrodynamic properties are affected by different external factors,including the seaward boundary condition(which controls the mass and momentum fluxes into the swash zone)and the bottom resistance(which retards the swash movement).However,there are still great deficiencies in the relevant theoretical studies on the influence of the above two external factors on the swash motion,especially the change mechanism of the hydrodynamics under the combined action of the two factors is still unclear.The nonlinear shallow water equations can describe the bore-induced swash event mainly governed by the gravity well.There are two main theoretical models based on the equations: the dam-break model and the shock wave model.This study adopts the method of theoretical analysis to derive an approximate theoretical solution of the frictionless dam break model with the improved seaward boundary conditions,and the influence of different seaward boundary conditions on the smooth swash hydrodynamics is discussed.Then,a dam-break model and a shock wave model are constructed considering the combined action of improved seaward boundary condition and the bottom resistance.Based on the method of characteristics,the spatiotemporal variation features of different hydrodynamic parameters in the uprush and backwash stages are solved semianalytically.The law of the wave motion in the swash zone under the influence of the aforementioned two external conditions is clarified.Finally,based on the theoretical model study,the differences and connections between the dam-break and shock wave models in describing the hydrodynamic process in the swash zone are deeply analyzed.At the same time,physical experiments are carried out to further elucidate the mechanism of the influence of the improved seaward boundary condition and the bottom resistance on the swash hydrodynamics during the uprush and backwash stages,and the applicability of the different theoretical models are also verified.In addition,by introducing nonlinear seaward boundary conditions,the different influences of linear and nonlinear seaward boundary conditions on characteristic variables and corresponding swash hydrodynamics are analyzed.Firstly,considering the influence of improved seaward boundary condition,the method of characteristics is applied here to derive a simple approximate theoretical solution based on the dam-break model which describes the wave movement in the smooth swash zone.Compared with the existing theoretical solution,the present solution can directly obtain the explicit expression of hydrodynamic parameters(i.e.,flow velocity and water depth,etc.),which is simple to calculate and can include the traditional seaward boundary condition scenario.Although the current solution is approximate,it can accurately analyze the swash hydrodynamics at the seaward boundary and can give satisfying results in describing the hydrodynamic properties in the entire swash zone compared with the existing implicit analytical solution.In this study,the temporal and spatial variations of hydrodynamic parameters such as water depth,velocity and free surface elevation under different seaward boundary conditions are presented,and the influence of improved seaward boundary condition on the swash hydrodynamics is clarified.By analyzing the variation of incident mass and momentum fluxes during the uprush stage,the reasons why the improved seaward boundary conditions could enhance the incident mass and momentum fluxes are explained.Secondly,considering the joint action of improved seaward boundary conditions and bottom resistance,the semi-analytic solution of wave motion on the frictional inclined bed described by the dam-break model is obtained based on the method of characteristic.In this study,the variation of characteristic curves and characteristic variables under different bottom friction coefficients and seaward boundary condition parameters are presented.The swash hydrodynamics carried by the characteristic curves could be obtained by relating to the characteristic variables.The influence of different seaward boundary condition parameters on the frictional swash hydrodynamics is discussed.Through the analysis of the flow acceleration,the roles of bottom friction,hydrostatic pressure and gravity in different swash stages under different seaward boundary conditions are specified.Thirdly,by solving the shock relations(Rankine-Hugoniot relations)and the nonlinear shallow water equation,the semi-analytic solution of bore-induced swash process described by the shock wave model under the combined action of the improved seaward boundary condition and the bottom resistance is derived.The features of the forward characteristic variable field under the influence of different external conditions are revealed,and the influence of the bottom friction and the improved seaward boundary condition on the forward characteristic variable is discussed.In this paper,the influence of bottom friction on the hydrodynamic properties of shock wave propagation and it induced swash are investigated,and the most significant area of bottom friction is pointed out(the area where the shock wave collapses after propagating to the initial shoreline and the area where the backflow approaches the offshore boundary).Based on the analysis of hydrodynamics such as total incident flux,maximum run-up height,water depth and flow velocity,the influence of improved seaward boundary conditions on swash hydrodynamics is specified.In addition,the influence of improved seaward boundary condition on the temporal and spatial characteristics of bottom friction force is analyzed.Fourthly,this paper compares and analyzes the influence of the improved seaward boundary condition and the bottom resistance on the two theoretical models describing the wave motion in the swash zone,i.e.,the dam-break model and the shock wave model,and illustrates the differences and relations between the two models.The results show that under the traditional seaward boundary condition,the spatiotemporal variation of swash hydrodynamics described by the two models are quite similar.The improved seaward boundary condition has similar effects on the swash hydrodynamics of the two models,that is,increasing the water depth and the flow velocity during the uprush stage and decreasing the flow velocity during the backwash stage.Quantitatively,the impact of the improved seaward boundary condition on the shock wave model is not as significant as that of the dam-break model,while the impact of the bottom friction is consistent.In addition,this paper also carried out swash experiments based on the dam-break flume under different initial conditions.By comparing the experimental results with the theoretical model,the influence of bottom friction on the swash flow was further studied.It is also determined that the influence of seaward boundary conditions on the swash process is related to the initial upstream tank length.The applicability of the two models is also explored by comparing with the experimental results,and it is shown that the shock wave model with appropriate parameter values can reproduce the water depth change process in the experiment well.Finally,two kinds of nonlinear seaward boundary conditions(lower convex type,upper convex type)are introduced into the dam-break model.By comparing the results of characteristic variables and swash hydrodynamics with those obtained by the linear seaward boundary condition,the influence of different forms of seaward boundary conditions on the swash process is clarified.By influencing the spatiotemporal distribution features of the forward characteristic lines,seaward boundary conditions affect the swash hydrodynamics.The forward characteristic lines obtained by lower convex type boundary condition accumulate in the interim backwash stage so that the water depth decreases and flow velocity increases sharply in this stage.The effect of upper convex type boundary condition is similar to that of linear seaward boundary condition.The forward characteristic lines gather at the late backwash stage,while the velocity increases sharply in this stage. |
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