FLEXURAL-GRAVITY WAVES DUE TO TRANSIENT DISTURBANCES IN AN INVISCID FLUID OF FINITE DEPTH  

作　　者：LU Dong-qiang LE Jia-chun DAI Shi-qiang 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China [2]Shanghai Key Laboratory of Mechanics in Energy and Environment Engineering, Shanghai 200072, China

出　　处：《Journal of Hydrodynamics》2008年第2期131-136,共6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.10602032);the Shanghai Rising-Star Program (Grant No. 07QA14022);the Shanghai Leading Academic Discipline Project (Grant No. Y0103)

摘　　要：The dynamic response of an ice-covered fluid to transient disturbances was analytically investigated by means of integral transforms and the generalized method of stationary phase. The initially quiescent fluid of finite depth was assumed to be inviscid, incompressible, and homogenous. The thin ice-cover was modeled as a homogeneous elastic plate. The disturbances were idealized as the fundamental singularities. A linearized initial-boundary-value problem was formulated within the framework of potential flow. The perturbed flow was decomposed into the regular and the singular components. An image system was introduced for the singular part to meet the boundary condition at the fiat bottom. The solutions in integral form for the vertical deflexion at the ice-water interface were obtained by means of a joint Laplace-Fourier transform. The asymptotic representations of the wave motion were explicitly derived for large time with a fixed distance-to-time ratio. The effects of the finite depth of fluid on the resultant wave pattems were discussed in detail. As the depth increases from zero, the critical wave number and the minimal group velocity first increase to their peak values and then decrease to constants.The dynamic response of an ice-covered fluid to transient disturbances was analytically investigated by means of integral transforms and the generalized method of stationary phase. The initially quiescent fluid of finite depth was assumed to be inviscid, incompressible, and homogenous. The thin ice-cover was modeled as a homogeneous elastic plate. The disturbances were idealized as the fundamental singularities. A linearized initial-boundary-value problem was formulated within the framework of potential flow. The perturbed flow was decomposed into the regular and the singular components. An image system was introduced for the singular part to meet the boundary condition at the fiat bottom. The solutions in integral form for the vertical deflexion at the ice-water interface were obtained by means of a joint Laplace-Fourier transform. The asymptotic representations of the wave motion were explicitly derived for large time with a fixed distance-to-time ratio. The effects of the finite depth of fluid on the resultant wave pattems were discussed in detail. As the depth increases from zero, the critical wave number and the minimal group velocity first increase to their peak values and then decrease to constants.

关 键 词：WAVES ICE-COVER transient disturbances ASYMPTOTIC group velocity 

分 类 号：TV131[水利工程—水力学及河流动力学]