Transient flexural-and capillary-gravity waves due to disturbances in two-layer density-stratified fluid  

作　　者：卢东强 孙翠芝 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University [2]Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University

出　　处：《Journal of Hydrodynamics》2013年第3期339-347,共9页水动力学研究与进展B辑（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 11072140);the State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University(Grant No. 0803);the Shanghai Program for Innovative Research Team in Universities

摘　　要：Generation of the transient flexural- and capillary-gravity waves by impulsive disturbances in a two-layer fluid is investi- gated analytically. The upper fluid is covered by a thin elastic plate or by an inertial surface with the capillary effect. The density of each of the two immiscible layers is constant. The fluids are assumed to be inviscid and incompressible and the motion be irrotational. A point force on the surface and simple mass sources in the upper and lower fluid layers are considered. A linear system is establi- shed within the framework of potential theory. The integral solutions for the surface and interracial waves are obtained by means of the Laplace-Fourier transform. A new representation for the dispersion relation of flexural- and capillary-gravity waves in a two- layer fluid is derived. The asymptotic representations of the wave motions are derived for large time with a fixed distance-to-time ratio with the Stokes and Scorer methods of stationary phase. It is shown that there are two different modes, namely the surface and interracial wave modes. The wave systems observed depend on the relation between the observer＇s moving speed and the intrinsic minimal and maximal group velocities.Generation of the transient flexural- and capillary-gravity waves by impulsive disturbances in a two-layer fluid is investi- gated analytically. The upper fluid is covered by a thin elastic plate or by an inertial surface with the capillary effect. The density of each of the two immiscible layers is constant. The fluids are assumed to be inviscid and incompressible and the motion be irrotational. A point force on the surface and simple mass sources in the upper and lower fluid layers are considered. A linear system is establi- shed within the framework of potential theory. The integral solutions for the surface and interracial waves are obtained by means of the Laplace-Fourier transform. A new representation for the dispersion relation of flexural- and capillary-gravity waves in a two- layer fluid is derived. The asymptotic representations of the wave motions are derived for large time with a fixed distance-to-time ratio with the Stokes and Scorer methods of stationary phase. It is shown that there are two different modes, namely the surface and interracial wave modes. The wave systems observed depend on the relation between the observer＇s moving speed and the intrinsic minimal and maximal group velocities.

关 键 词：HYDROELASTICITY CAPILLARITY wave generation density stratification two layers 

分 类 号：O35[理学—流体力学]