Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for on...Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for one dimensional zero-pressure gas dynamics system.Here the first equation is the Burgers equation and the second one is the continuity equation.We consider the solution with initial data in the space of bounded Borel measures.First we prove a general existence result in the algebra of generalized functions of Colombeau.Then we study in detail special solutions withδ-measures as initial data.We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves.This gives an understanding of plane-wave interactions in the multidimensional case.We use the vanishing viscosity method in our analysis as this gives the physical solution.展开更多
Based on Hong's theory, previous random models, and a generalized expression suitable for FFT calculation, the interaction between irregular waves and vertical walls is numerically simulated. The results of simu...Based on Hong's theory, previous random models, and a generalized expression suitable for FFT calculation, the interaction between irregular waves and vertical walls is numerically simulated. The results of simulation demonstrate that the wave energy changes with the incidence angle and the distance from the wall. Particularly, the Mach effect and the combined wave spectrum characteristics are analyzed in detail, which are significant in both theory and practice.展开更多
This article is devoted to the study of the propagations of the non- linear water waves on the shear flows. Assuming μ = kh is small and ε/μ~2 ～ 0 (1), and the base flow is uniformly sheared, the modified Boussine...This article is devoted to the study of the propagations of the non- linear water waves on the shear flows. Assuming μ = kh is small and ε/μ~2 ～ 0 (1), and the base flow is uniformly sheared, the modified Boussinesq equation is obtained. We calculate propagations of the single sohtary wave with vorticity Γ = 0, >0 and <0. The influences of the vorticity are manifested. At the end examples of the interactions of two solitary waves, moving in opposite and the same directions, are given. Besides the phase shift, there also occur second wavelets after head-on collision.展开更多
The Euler equations for two dimensional, steady, isentropic, and inviscid flow are considered. All the elementary waves are classified into incoming and outgoing waves under the assumption that there is a singular po...The Euler equations for two dimensional, steady, isentropic, and inviscid flow are considered. All the elementary waves are classified into incoming and outgoing waves under the assumption that there is a singular point in the configuration of the solution.The interactions of at most two incoming waves are dealt with in this paper, and all six kinds of configurations for the solutions are obtained. They are the Mach reflection (one kind), the shock wave S transmits contact discontinuity J (two kinds), the overtaking of two incoming shock waves (two kinds), and the collision of two incoming shock waves (one kind).展开更多
基金supported by the TIFR-CAM Doctoral Fellowship and the NISER Postdoctoral Fellowship(through the project“Basic research in physics and multidisciplinary sciences”with identification#RIN4001)during the preparation of this papersupported by the Raja Ramanna Fellowship.
文摘Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for one dimensional zero-pressure gas dynamics system.Here the first equation is the Burgers equation and the second one is the continuity equation.We consider the solution with initial data in the space of bounded Borel measures.First we prove a general existence result in the algebra of generalized functions of Colombeau.Then we study in detail special solutions withδ-measures as initial data.We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves.This gives an understanding of plane-wave interactions in the multidimensional case.We use the vanishing viscosity method in our analysis as this gives the physical solution.
文摘Based on Hong's theory, previous random models, and a generalized expression suitable for FFT calculation, the interaction between irregular waves and vertical walls is numerically simulated. The results of simulation demonstrate that the wave energy changes with the incidence angle and the distance from the wall. Particularly, the Mach effect and the combined wave spectrum characteristics are analyzed in detail, which are significant in both theory and practice.
基金The project supported by the National Natural Science Foundation of China
文摘This article is devoted to the study of the propagations of the non- linear water waves on the shear flows. Assuming μ = kh is small and ε/μ~2 ～ 0 (1), and the base flow is uniformly sheared, the modified Boussinesq equation is obtained. We calculate propagations of the single sohtary wave with vorticity Γ = 0, >0 and <0. The influences of the vorticity are manifested. At the end examples of the interactions of two solitary waves, moving in opposite and the same directions, are given. Besides the phase shift, there also occur second wavelets after head-on collision.
文摘The Euler equations for two dimensional, steady, isentropic, and inviscid flow are considered. All the elementary waves are classified into incoming and outgoing waves under the assumption that there is a singular point in the configuration of the solution.The interactions of at most two incoming waves are dealt with in this paper, and all six kinds of configurations for the solutions are obtained. They are the Mach reflection (one kind), the shock wave S transmits contact discontinuity J (two kinds), the overtaking of two incoming shock waves (two kinds), and the collision of two incoming shock waves (one kind).
