Under investigation in this paper is the Whitham-Broer-Kaup (WBK) system, which describes the dispersive long wave in shallow water. Through a variable transformation, the WBK system is casted into a general Broer-Kau...Under investigation in this paper is the Whitham-Broer-Kaup (WBK) system, which describes the dispersive long wave in shallow water. Through a variable transformation, the WBK system is casted into a general Broer-Kaup system whose Lax pair can be derived by the Ablowitz-Kaup-Newell-Segur technology. With symbolic computation, based on the aforementioned Lax pair, the N-fold Darboux transformation is constructed with a gauge transformation and the multi-soliton solutions are obtained. Finally, the elastic interactions of the two-soliton solutions (including the head-on and overtaking collisions) for the WBK system are graphically studied. Those multi-soliton collisions can beused to illustrate the bidirectional propagation of the waves in shallow water.展开更多
The French Atlantic coast seismicity is minor to moderate. Nevertheless, in western （north and central） part of France, the active tectonics related to the south Armorican and the Bay of Biscay context results somet...The French Atlantic coast seismicity is minor to moderate. Nevertheless, in western （north and central） part of France, the active tectonics related to the south Armorican and the Bay of Biscay context results sometimes in shallow earthquakes with magnitude above five （e.g., the Oleron seismic crisis, magnitude （local） = 5.2, 1972）. The Charente region is featured by semi-diurnal tides that reach about six meters in height during the high tide period. Inlets are the main features of the Atlantic margin geomorphology nearby the Charente. Minor tsunamis have been observed and reported in the past. Here, we present a tsunami modelling computed with the TELEMAC package that solves the non linear shallow water equations. This work helps to identify the role of the inlets that characterize the Charente＇s geomorphology on water wave＇s propagation. A tidal model is considered while the tsunami simulation is performed. The modelling results show that the Antioche, the Maumusson and the Pertuis inlets protect the Charente coast from destructive waves.展开更多
The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow.The 1D-2D coupling model solves the generalized shallow water equations,the non-equil...The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow.The 1D-2D coupling model solves the generalized shallow water equations,the non-equilibrium sediment transport and bed change equations in a coupled fashion using an explicit finite volume method.It considers interactions among transient flow,strong sediment transport and rapid bed change by including bed change and variable flow density in the flow continuity and momentum equations.An unstructured Quadtree rectangular grid with local refinement is used in the 2D model.The intercell flux is computed by the HLL approximate Riemann solver with shock captured capability for computing the dry-to-wet interface for all models.The effects of pressure and gravity are included in source term in this coupling model which can simplify the computation and eliminate numerical imbalance between source and flux terms.The developed model has been tested against experimental and real-life case of dam-break flow over fix bed and movable bed.The results are compared with analytical solution and measured data with good agreement.The simulation results demonstrate that the coupling model is capable of calculating the flow,erosion and deposition for dam break flows in complicated natural domains.展开更多
By considering the one-dimensional model for describing long, small amplitude waves in shallow water, a generalized fifth-order evolution equation named the Olver water wave （OWW） equation is investigated by virtue ...By considering the one-dimensional model for describing long, small amplitude waves in shallow water, a generalized fifth-order evolution equation named the Olver water wave （OWW） equation is investigated by virtue of some new pseudo-potential systems. By introducing the corresponding pseudo-potential systems, the authors systematically construct some generalized symmetries that consider some new smooth functions {Xiβ}β=1,2…,N^i=1,2…,n depending on a finite number of partial derivatives of the nonlocal variables vβ and a restriction i,α,β∑（ ξi/ vβ）^2＋（ ηα/ vβ）^2≠0,ie.,i,α,β∑（ ξi/ vβ）^2≠0. Furthermore, i,a,B i,a,~ the authors investigate some structures associated with the Olver water wave （AOWW） equations including Lie algebra and Darboux transformation. The results are also extended to AOWW equations such as Lax, Sawada-Kotera, Kaup-Kupershmidt, It6 and Caudrey-Dodd-Cibbon-Sawada-Kotera equations, et al. Finally, the symmetries are ap- plied to investigate the initial value problems and Darboux transformations.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No. 60772023by the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. BUAA-SKLSDE-09KF-04+1 种基金Beijing University of Aeronautics and Astronautics, by the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos. 20060006024 and 200800130006,Chinese Ministry of Education
文摘Under investigation in this paper is the Whitham-Broer-Kaup (WBK) system, which describes the dispersive long wave in shallow water. Through a variable transformation, the WBK system is casted into a general Broer-Kaup system whose Lax pair can be derived by the Ablowitz-Kaup-Newell-Segur technology. With symbolic computation, based on the aforementioned Lax pair, the N-fold Darboux transformation is constructed with a gauge transformation and the multi-soliton solutions are obtained. Finally, the elastic interactions of the two-soliton solutions (including the head-on and overtaking collisions) for the WBK system are graphically studied. Those multi-soliton collisions can beused to illustrate the bidirectional propagation of the waves in shallow water.
文摘The French Atlantic coast seismicity is minor to moderate. Nevertheless, in western （north and central） part of France, the active tectonics related to the south Armorican and the Bay of Biscay context results sometimes in shallow earthquakes with magnitude above five （e.g., the Oleron seismic crisis, magnitude （local） = 5.2, 1972）. The Charente region is featured by semi-diurnal tides that reach about six meters in height during the high tide period. Inlets are the main features of the Atlantic margin geomorphology nearby the Charente. Minor tsunamis have been observed and reported in the past. Here, we present a tsunami modelling computed with the TELEMAC package that solves the non linear shallow water equations. This work helps to identify the role of the inlets that characterize the Charente＇s geomorphology on water wave＇s propagation. A tidal model is considered while the tsunami simulation is performed. The modelling results show that the Antioche, the Maumusson and the Pertuis inlets protect the Charente coast from destructive waves.
基金supported by the National Basic Research Program of China(Grant No.2013CB430403)the Public Science and Technology Research Funds Projects of Ocean(Grant No.201205023)+3 种基金the Program for Liaoning Excellent Talents in University(Grant No.LJQ2013077)the Science and Technology Foundation of Dalian City(Grant No.2013J21DW009)the Special Funds for Postdoctoral Innovative Projects of Liaoning Province(Grant No.2011921018)the Special Funds for Talent Projects of Dalian Ocean University(Grant No.SYYJ2011004)
文摘The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow.The 1D-2D coupling model solves the generalized shallow water equations,the non-equilibrium sediment transport and bed change equations in a coupled fashion using an explicit finite volume method.It considers interactions among transient flow,strong sediment transport and rapid bed change by including bed change and variable flow density in the flow continuity and momentum equations.An unstructured Quadtree rectangular grid with local refinement is used in the 2D model.The intercell flux is computed by the HLL approximate Riemann solver with shock captured capability for computing the dry-to-wet interface for all models.The effects of pressure and gravity are included in source term in this coupling model which can simplify the computation and eliminate numerical imbalance between source and flux terms.The developed model has been tested against experimental and real-life case of dam-break flow over fix bed and movable bed.The results are compared with analytical solution and measured data with good agreement.The simulation results demonstrate that the coupling model is capable of calculating the flow,erosion and deposition for dam break flows in complicated natural domains.
基金supported by the National Natural Science Foundation of China(Nos.11301527,11371361)the Fundamental Research Funds for the Central Universities(No.2013QNA41)the Construction Project of the Key Discipline of Universities in Jiangsu Province During the 12th FiveYear Plans(No.SX2013008)
文摘By considering the one-dimensional model for describing long, small amplitude waves in shallow water, a generalized fifth-order evolution equation named the Olver water wave （OWW） equation is investigated by virtue of some new pseudo-potential systems. By introducing the corresponding pseudo-potential systems, the authors systematically construct some generalized symmetries that consider some new smooth functions {Xiβ}β=1,2…,N^i=1,2…,n depending on a finite number of partial derivatives of the nonlocal variables vβ and a restriction i,α,β∑（ ξi/ vβ）^2＋（ ηα/ vβ）^2≠0,ie.,i,α,β∑（ ξi/ vβ）^2≠0. Furthermore, i,a,B i,a,~ the authors investigate some structures associated with the Olver water wave （AOWW） equations including Lie algebra and Darboux transformation. The results are also extended to AOWW equations such as Lax, Sawada-Kotera, Kaup-Kupershmidt, It6 and Caudrey-Dodd-Cibbon-Sawada-Kotera equations, et al. Finally, the symmetries are ap- plied to investigate the initial value problems and Darboux transformations.
